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Rethinking buffer operations in a dual-store framework

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Rethinking buffer operations in a dual-store framework
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Lehman, Melissa
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Context
Episodic Memory
Long-term Memory
Memory Models
Short-term Memory
Dissertations, Academic -- Psychology -- Doctoral -- USF   ( lcsh )
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bibliography   ( marcgt )
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Abstract:
ABSTRACT: Atkinson and Shiffrin's (1968) dual-store model of memory includes a structural memory store along with control processes conceptualized as a rehearsal buffer. I present a variant of Atkinson and Shiffrin's buffer model within a global memory framework that accounts for findings previously thought to be difficult for it to explain. This model assumes a limited capacity buffer where information is stored about items, along with information about associations between items and between items and the context in which they are studied. The strength of association between items and context is limited by the number of items simultaneously occupying the buffer. New findings that directly test the buffer assumptions are presented, including serial position effects, and conditional and first recall probabilities in immediate and delayed free recall, in a continuous distractor paradigm, and in experiments using list length manipulations of single item and paired item study lists. Overall, the model's predictions are supported by the data from these experiments, suggesting that control processes, conceptualized as a rehearsal buffer, are a necessary component of memory models.
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Disseration (Ph.D.)--University of South Florida, 2011.
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Includes bibliographical references.
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by Melissa Lehman.
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ABSTRACT: Atkinson and Shiffrin's (1968) dual-store model of memory includes a structural memory store along with control processes conceptualized as a rehearsal buffer. I present a variant of Atkinson and Shiffrin's buffer model within a global memory framework that accounts for findings previously thought to be difficult for it to explain. This model assumes a limited capacity buffer where information is stored about items, along with information about associations between items and between items and the context in which they are studied. The strength of association between items and context is limited by the number of items simultaneously occupying the buffer. New findings that directly test the buffer assumptions are presented, including serial position effects, and conditional and first recall probabilities in immediate and delayed free recall, in a continuous distractor paradigm, and in experiments using list length manipulations of single item and paired item study lists. Overall, the model's predictions are supported by the data from these experiments, suggesting that control processes, conceptualized as a rehearsal buffer, are a necessary component of memory models.
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Rethinking Buffer Operations in a Dual-Store Framework by Melissa Lehman A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Psychology College of Arts and Sciences University of South Florida Major Professor: Kenneth Malmberg, Ph.D. Jonathan Rottenberg, Ph.D. Mark Goldman, Ph.D. Cathy McEvoy, Ph.D. Joseph Vandello, Ph.D. Date of Approval: March 29, 2011 Keywords: episodic memory, context, dir ected forgetting, memory models, serial position effects Copyright 2011, Melissa Lehman

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Acknowledgements First and foremost, I would like to tha nk my advisor, Ken Malmberg, for his guidance and expertise, for teaching me how to do good research, and for drilling into my awareness the idea that data always comes fi rst! I have learned more than I could possibly explain in my time as a graduate student in your lab. Thanks also for your flexibility, for giving me the freedom to deve lop new lines of research while continuing to guide me toward my goal. I am extremely grateful for the opportuni ty to have such an experience as a graduate student. Thanks to Jon Rottenberg, Cathy Mc Evoy, Mark Goldman, Joe Vandello, and Doug Nelson for taking the time to serve on my committee, and for putting much thought into improving my work. Your guidance has been invaluable to me in this process. I would also like to thank Dewe y Rundus for chairing my defense. Thanks also to Judy Bryant for all of the work you have put in to making our department a pleasant and productive environment for graduate stude nts, and for your general guidance about research, program requirements, and the academic career. Thanks to all of my friends and colleagues in the psychology department who have provided me with thoughtful conversation and many encouraging words. Thanks to my family, none of whom understand why I would want to go to school for so long, but who supported me with pride th e entire time anyway. Finally, I want to thank my husband, Erik Lundberg, for being ca ring, helpful, and supportive of all of my ventures, both in and outside of academia. Thanks for helping me with mathematical formulas whenever I need to use them, for keeping me sane when I am overwhelmed, for tolerating my quirks, and for alwa ys putting the toilet seat down.

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i Table of Contents List of Tables iii List of Figures iv Abstract v Chapter 1 Introduction 1 1.1 Serial Position Effects 5 1.2 Criticisms of Buffer Models 7 1.3 Directed Forgetting 11 1.3.1 Differential Rehearsal 12 1.3.2 Inhibition 14 1.3.3 Context Differentiation 15 1.4 Mathematical Model of Dir ected Forgetting 17 1.4.1 Improved Design 18 1.4.2 Mathematical Model 19 1.4.3 Experimental Findings 23 1.5 REM Model 31 1.5.1 Representation 31 1.5.2 Encoding 32 1.5.3 Recognition 32 1.5.4 Free Recall 33 1.6 Lehman-Malmberg Model 34 1.6.1 Representation 34 1.6.2 Encoding 35 1.6.3 Retrieval 36 1.6.4 Free Recall 37 1.6.5 Recognition-Exclusion 38 1.6.6 Directed Forgetting 38 1.6.7 Model Evaluation 39 1.7 Testing Predictions of Lehman-Malmberg Model 41 1.7.1 Categorized Lists 41 1.7.2 Empirical Support 44 Chapter 2 Evaluating the Lehman-Malmberg Model 47 2.1 Craik & Watkins (1973) 48 2.2 Continuous Distractor Task 52 2.3 Experiment 1 55 2.3.1 Methods 55 2.3.1.1 Participants and Materials 55

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ii 2.3.1.2 Procedure 55 2.3.2 Results 57 2.3.3 Discussion 58 2.4 Single Versus Paired It em Study Lists 62 2.5 Experiment 2 66 2.5.1 Methods 66 2.5.1.1 Participants and Materials 66 2.5.1.2 Procedure 66 2.5.2 Results and Discussion 67 2.6 List Length Manipulations 69 2.7 Experiment 3 74 2.7.1 Methods 74 2.7.1.1 Participants, Materials, and Procedure 74 2.7.2 Results 75 2.7.3 Discussion 77 Chapter 3 General Discussion 79 3.1 Buffer as an Encoding Process 79 3.2 Buffer as a Retrieval Process 80 3.3 Comparing the Lehman-Malmberg Model to Other Models 83 3.3.1 TCM 83 3.3.2 Activation Models 84 3.4 Utilizing the Buffer in Chunking Operations 85 3.5 Extending the Model 86 3.5.1 Individual Differences 87 3.5.2 Neuroscience Models 89 3.6 Conclusion 90 References 91

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iii List of Tables Table 1.Parameter Values and Descriptions for Lehman-Malmberg Model 49

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iv List of Figures Figure 1. The SAM model of directed forgetting. 22 Figure 2. Data and SAM model predictions for probability of correct recall and intrusion errors for free recall in directed forgetting. 24 Figure 3. REM model predictions and serial position data in a directed forgetting free recall task. 27 Figure 4. REM model predictions for firs t recall probability data for free recall in directed forgetting. 28 Figure 5. REM model predictions for exclusion recognition in directed forgetting. 29 Figure 6. REM model predictions for se rial position data for exclusion recognition in directed forgetting. 30 Figure 7. Data and REM model predictions for probability of correct recall and intrusion errors for free recall in directed forgetting. 31 Figure 8. REM Model predictions and data from a directed forgetting task with categorized lists. 45 Figure 9: Data from Craik and Watkins (1973) and model predictions from the Lehman-Malmberg Model. 50 Figure 10: Continuous distractor da ta and model predictions. 54 Figure 11: Single versus pairs data and model predictions. 65 Figure 12: Single item list length data and model predictions for first recall probabilities and serial position effects. 72 Figure 13: Paired item list length data and model predictions for first recall probabilities and serial position effects. 73 Figure 14: Conditional response probability data and model pr ediction for single and paired item study lists of length 6 and 24. 74 Figure 15: Reaction time data for single and paired item study lists of each length 77 Figure 16: Model predictions for conditional response probabilities using fifferent buffer sizes in continuous distractor free recall. 81 Figure 17: Model without retrie val from the buffer. 82

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v Abstract Atkinson and Shiffrin's (1968) dual-store model of memory includes a structural memory store along with control processes concep tualized as a rehearsal buffer. I present a variant of Atkinson and Shiffrins buffer m odel within a global memory framework that accounts for findings previously thought to be difficult for it to explain. This model assumes a limited capacity buffer where information is stored about items, along with information about associations between ite ms and between items and the context in which they are studied. The strength of asso ciation between items and context is limited by the number of items simultaneously occupying the buffer. New findings that directly test the buffer assumptions are presente d, including serial position effects, and conditional and first recall probabilities in immediate and delayed free recall, in a continuous distractor paradigm, and in expe riments using list lengt h manipulations of single item and paired item study lists. Overall, the models predictions are supported by the data from these experiments, suggesting th at control processes, conceptualized as a rehearsal buffer, are a necessary component of memory models.

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1 Chapter 1 Introduction Any introductory cognitive psychology te xtbook will likely include a distinction between short-term memory and long-term memory. Short-term memory is often described as a mechanism that can hold a limited amount of information for a short time, from which that information will escape if st rategies are not used to maintain it, and longterm memory as a more permanent memo ry store which can hold vast amounts of information (Goldstein, 2008). Th eories that distinguish two t ypes of memory stores date back to William James. In Principles of Psychology (1890), James describes primary memory the temporary knowledge of an initial en counter with a stimulus which must be attended to in order to main tain it in consciousness, and secondary memory the knowledge of a stimulus one has experienced before which has since been dropped from consciousness. James further specified that primary memory is an accurate representation of events th at occurred, whereas seconda ry memory is subject to distortion. During what is often called the Cognitiv e Revolution in psychology, Broadbent (1958) devised an information pr ocessing model of attention and memory, which includes an immediate memory system and a more permanent long-term module where learned information is stored. Thus, dual-store theories of memory, those positing separate and distinct short-term and long-term memory stores, en joy a long history in psychology research.

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2 Waugh and Norman (1965) expanded on the primary/secondary memory distinction in an initial attempt to devel op a formal model of these processes. The Atkinson and Shiffin (1968) dual-store m odel of memory, building on this same framework, is perhaps the most commonly cite d formal model of memory, often referred to as the modal model. According to th e Atkinson and Shiffin (A-S) model, memory consists of not only structural components, including short-term and long-term stores, but also of control processes that allow an individual to focus atte ntional resources on to-beremembered stimuli in order to increase the likelihood of encoding those stimuli (or, increase the amount of informa tion that is encoded about thos e stimuli). These processes are under the control of an i ndividual, and they influence the way that memories are stored. Of particular intere st, their model includes a rehearsal buffer, a flexible control process which an individual may use in order to encode information relevant to a given task. The buffer was designed to account for the rehear sal of items during the study of a list of items. According to the A-S model, the rehearsal buffer is a limited capacity system that allows for the temporary storage of information; it is limited in terms of the number of items it can simultaneously accommodate, and when the capacity is reached, an item must be dropped. The model assumed that the number of trials for which an item resides in the rehearsal buffe r is positively corre lated with its encoding in long-term memory. Though dual-store models have received much empirical su pport (Atkinson & Shiffrin, 1971), controversy surrounds the nature of these memory processes. Theorists in the dual-store camp point to evidence from examinations of serial position effects, in addition to findings of differential deficits in short-term and long-term memory in

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3 neuropsychological case studies in support of dual store mo dels (Atkinson & Shiffin, 1968; Cowan, 1995; Davelaar, Goshen-Gottste in, Ashkenazi, Haarmann, & Usher, 2005; Glanzer & Cunitz, 1966; Waugh & Norman, 1965 ). On the other hand, others have criticized dual-store models and developed single-store mode ls that are able to account for findings said to be troublesome for dua l-store models (Bjork & Whitten, 1974; Craik & Watkins, 1973; Crowder, 1989; 1993; Howard & Kahana, 1999; Nairne, 1996). The purpose of the current project is to explore the importance of buffer processes typically associated with dualstore models. It should be noted that the buffer operates independently of any structural components of the model and should not be confused with the short-term store. Atkinson and Shiffr in (1968) explicitly stated that the buffer is a process under the control of a subject, used in an attempt to maximize performance. Thus, we focus not on the issue of whether sh ort-term memory is a structural component of the memory system, but whether control processes that allow an individual to manipulate to-be remembered information in a way that is optimal for a given task are necessary for models to account for a variety of memory phenomena. In addition to exploring the function of the buffer as a memory process, we also wish to revisit another area from classic me mory research by exploring the process of chunking combining small units of informati on into larger meaningful units of information in order to increase the numb er of items that can simultaneously be maintained by the memory system (Miller, 1956 ), into the framework of this model. Ideas related to chunking also date back to James (1890), who suggested that one can attend to an indefinite number of things and that the number of things that can be attended to depends on the nature of those th ings. Miller proposed that information can

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4 be better remembered if it is of a type th at can be chunked together. Theories that grouping information together into meaningful units will allow for remembering more information have a long history of empirical su pport, and may be consistent with intuitive notions about memory (Gobet, Lane, Croker, Cheng, Jones, Oliver, and Pine, 2001); thus there is little controversy su rrounding the issue of whether chunking serves as a memory process. However, chunking does not play a large role in mo st formal memory models. Aside from Murdocks (1995) description of the role of chunking in serial order effects, chunking processes are rarely described in formal models of episodic memory (others have developed computational models of chunking in learning new information, though these are quite different from models of episodic memory; see Gobet et al., 2001, for a description of such models). Thus, our goal is to explore the interaction of chunking and buffer operations in the framework of a formal memory model. In sum, the broad intent of this project is to outline a formal computational model of memory that accounts for a variety of patterns of data in different experimental paradigms with very few free parameters. This model will include assumptions based in the A-S buffer model framework and integr ate ideas about chunki ng in the encoding process. The model will generate testable predictions, which can inform us about the nature of human memory in a clear cut manne r (Widaman, 2008). In this manuscript, I will address various criticisms of dual store models, beginning with a discussion of such criticisms, followed by a descri ption of the Lehman-Malmber g model, a model initially developed in order to account for directed forgetting effects (Lehman & Malmberg, 2009; 2011; Malmberg, Lehman, & Sahakyan, 2006). I will next discuss the ways in which this model can account for data that have troubled buffer models in the past. Finally, I will

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5 present the results of some e xperiments conducted in order to test the models predictions in a novel experimental paradigm. Specifica lly, I will examine whether retrieval from a buffer is a necessary component of the model, or whether the model can account for the data without such a process. Ultimately, I wi sh to show that a model based in the A-S framework which includes a buffer process is both able to handle data that has been claimed to trouble such models in the past and new data that will be hard for a singlestore model that does not include such control processes to account for. 1.1 Serial Position Effects The A-S model is well known for its account of serial position curves, specifically primacy and recency effects. Primacy refers to the greater probability of recall for items that come from the beginning of a list, and re cency to the greater probability of recall for items that come from the end of a list (Deese & Kaufman, 1957). According to dualstore models, primacy occurs because items fr om early serial positions occupy a spot in the rehearsal buffer for a longer period of time, whereas recency occurs due to the retrieval of items that occupy th e rehearsal buffer at time of test, which is assumed to be highly accurate (Atkinson & Shiffrin, 1968). Using an overt rehearsal procedure, Rundus (1971) showed that items at the beginning of the list receive more rehearsals throughout the list than items that occur later in the list, consistent with the hypothesis th at items at the beginning of the list spend more time in the rehearsal buffer. Additional support for dual-store models came from studies showing that certain factors differentially influen ce primacy and recency. For example, increases in presentation time of st udied items increases recall for items toward

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6 the beginning of the lis t without affecting the recency porti on of the list. On the other hand, the addition of a distractor task at the end of a study list, which presumably prevents rehearsal of items in the buffer, eliminates recency without affecting the primacy portion of the list (Glanzer & Cun itz, 1966). Murdock (1962) showed that whereas primacy effects are reduced with increasing list length, recency effects were unaffected by list length, suggesting that items in the recency portion of the list exist in a different state than other items on the list, cons istent with the idea that they are present in a buffer at time of test. Further work has shown other dissociations between primacy and recency effects. For example, whereas recency is seen in immediate free recall, a negative recency effect, worse recall for the items at th e end of the list compared to the middle of the list, is present in final free recall of items from lists that were previously tested under immediate conditions; however, items at the beginning of the list are not differentially recalled in the final test (Craik, 1970). This s uggests that the end of list item s are present in a privileged state during immediate testing, when they still reside in the buffer, but these items have not been well encoded in long-term memor y, so they suffer on a later recall test. Similarly, proactive interference occurs wh en memory for new items is negatively affected by preceding items. While items thr oughout a list are increasingly subject to proactive interference, items from the very end of a list are not affected (Craik & Birtwistle, 1971). Dual store models are able to account for these distinctions between primacy and recency effects with the use of buffer processes during encoding. It is important to note that encoding in long-term memory was not explicitly described by Atkinson and

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7 Shiffrin, aside from the inclusion of an assumption that information about items and about the context in which the item is studi ed is represented. Later developments in modeling these encoding processes were made in the framework of SAM, most important for the current purposes, the assumption that associations among items that simultaneously share the buffer are en coded (Raaijmakers & Shiffrin, 1981). 1.2 Criticisms of Buffer Models Despite a myriad of empirical support fo r the A-S model, dual-store models have been criticized due to some experimental findings which some have suggested are inconsistent with such models. First, such models are based on assumptions that items that spend more time in the rehearsal buffer will be better encoded in long-term memory: An item's likelihood of being retained incr eases in direct proportion to its total presentation time within a list. (Waugh, 1970, p. 587; see also Atkinson & Shiffrin, 1968). Thus, such models predict that items that are studied for longer periods of time should be better remembered, regardless of whether the longer study time is due to increases in presentation time or increases in the number of presentations of the items. While increases in study time have been shown to be related to greater recall (Glanzer & Cunitz, 1966; Mur dock, 1962), this is not always the case. For example, Craik and Watkins (1973) repor ted that recall did not incr ease linearly with study time when maintenance rehearsal was used, specifically neither the length of an item's stay in short-term storage nor the number of overt rehearsals it received was related to subsequent recall (Craik & Watkins, 1973, abstract).

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8 Additional criticisms of buffer models have been made in res ponse to findings of recency effects in a continuous distractor task, where a short distractor task is presented after each item on a list (Bjork & Whitten, 1974) Despite the distractor task presented after each item, including the la st item, the last items on th e list are better recalled than earlier items, a finding referred to as long-term recency (Bjork & Whitten, 1974; Howard & Kahana, 1999). Critics of buffer models s uggest that, as the distractor task should eliminate the most recent items from the buffer, a long-term recency effect in a continuous distractor task is hard for a buffer model to explain (Bjork & Whitten, 1974; Crowder, 1989; 1993; Howard & Kahana, 1999). Another challenge to buffer models came from findings of contiguity effects in continuous distractor tasks (Howard & Kaha na, 1999). Contiguity effects refer to findings that during recall, items from n earby serial positions tend to be output successively. Kahana (1996) examined these conditional response probabilities (CRPs) and found that in a standard fr ee recall paradigm, transitions were most likely to be made to items that were presented in the closest te mporal proximity to a recalled item, and that transitions were more likely to be made in the forward direction than the backward direction. These patterns are referred to as lag-recency effects. Howard and Kahana (1999) suggested that CRP functions in a continuous distractor task can be useful in distinguishing different models They proposed that according to a buffer model, a continuous distractor task should disrupt buffer operations preventing the encoding of associative information between items; thus nearby transitions shoul d not be more likely to occur than distant transitions. They found contiguity effects in a continuous distractor paradigm similar to those seen in standard free recall.

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9 Howard and Kahana (1999) showed that while a two-store model was unable to account for these data, a single store model wa s able to account for both lag-recency and long-term recency effects. Later, Howard and Kahana (2002) developed the Temporal Context Model (TCM), which assumes that c ontext fluctuates over time, but that this fluctuation is driven by retrieval of prior co ntextual states. TCM was able to account for long-term recency effects in a single-store model which does not include a rehearsal buffer, because it assumes that the context during test is most similar to the most recently learned item, and this context is used to probe memory. Further, the model accounts for lag-recency effects because it assumes that the context retrieved from a recalled item during test is used to probe memory, thus item s in a similar temporal context (i.e. studied in a nearby serial position) will be most likely to be recalled next (see the discussion for a more detailed description of TCM). More recent developments in buffer m odels have been important for addressing some of the problems that have troubled such models in the past. Malmberg and Shiffrin (2005) assumed that the encoding of item information and the encoding of context information followed different time courses. Whereas item information is encoded as long as the item occupies the buffer, a fixed am ount of context, or one shot of context, is stored in perhaps as littl e as 1-2 seconds. Thus, incr eases in study time may increase the encoding of inter-item associative inform ation. Malmberg and Shiffrin implemented the one-shot hypothesis in the REM model. These assumptions may be useful in understanding the results of studies using manipulations of study time in incidental learning tasks.

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10 The Lehman-Malmberg model of direct ed forgetting fleshed out a set of assumptions concerning the encoding of a ssociations in the REM framework. This model included a limited capacity buffer, where information is stored about items, association between items that simultaneousl y reside in the buffer, and associations between items and the context in which it ems are studied. Importantly, this model assumed that the strength of association be tween items and context, and among different items is limited by the number of items occupying the rehearsal buffer. Lehman and Malmberg (2009) experimented with various versions of the mode l and concluded that buffer operations were necessary in order to account for serial position effects in directed forgetting. These more recent developments in buffer models may be useful in accounting for the aforementioned phenomena that have tr oubled the original Atkinson and Shiffrin model. For example, the one-shot model assu mption allows buffer models to account for Craik and Watkins' (1973) findings that ma intenance rehearsal does not increase recall (though it should be noted that th is claim itself is problematic, as recall did increase with lag in their study, albeit not si gnificantly). Lehman and Malmbergs (2009) assumptions regarding buffer operations in the model may allow the model to account for contiguity effects in continuous distractor tasks. Before describing th e ways in which the LehmanMalmberg model can account for these findings I will first review the development of the Lehman-Malmberg model and describe the da ta that it has been able to account for using a similar set of parameter values.

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11 1.3 Directed Forgetting Our interest in buffer models grew out of a goal to develop a model of intentional forgetting. Intentional forgetting is often studied in the lab using the list method of directed forgetting In this task, two lists are stud ied and subjects are instructed to remember both lists (the remember condition) or they are instructed after studying the first list to forget the first list (the forget condition). Contrary to the instructions, both lists are tested. Typically in free recall, memory is worse in the forget condition compared to the remember condition for words from the to-be-forgotten list and better for words from the to-be-rememb ered list (Basden, Basde n, & Gargano, 1993; Bjork, 1972, 1978; Bjork & Geiselman, 1978; Bjork, LaBerge, & Legra nd, 1968; Bjork & Woodward, 1973; Block, 1971; Geiselman & Bagheri, 1985; Geiselman, Bjork, & Fishman 1983; MacLeod, 1998; MacLeod, Dodd, Sheard, Wils on, & Bibi, 2003; Malmberg, Lehman, & Sahakyan, 2006; Sahakyan, 2004; Sahakyan & Delaney, 2003; Sahakyan & Kelley, 2002; Sheard & MacLeod, 2005). These e ffects are referred to as the costs and benefits of directed forgetting, respectively. While the cost s and benefits of di rected forgetting are fairly typical findings in free recall, they ar e not always observed. Sahakyan and Delaney (2003) have suggested that th e costs may be obtained independently from the benefits, and Sahakyan and Goodmon (2010) observed costs, but not benefits, ac ross five directed forgetting experiments. Additionally, costs and benefits have been shown in recognition testing by some researchers (Lehman & Malm berg, 2009), whereas others have reported partial effects (Benjamin, 2006; Loft, Humphreys, & Whitney, 2008; Sahakyan & Delaney, 2005; Sahakyan, Waldum, Benjamin, & Bi ckett, 2009) and others have reported

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12 no effects (Basden, Basden, & Gargano, 1993; Block, 1971; Elmes, Adams, & Roediger, 1970; Geiselman, Bjork, & Fishman, 1983). While there are many not necessarily mutually exclusive hypotheses about specific intentional forgetting findings, until recently, a comprehensive explanation was lacking. The following section will describe various hypotheses for directed forgetting and review work that has been done to de velop a comprehensive account of intentional and unintentional forgetting in both recall and recognition. 1.3.1 Differential Rehearsal Rehearsal plays a well-documented role in many memory models as a mechanism that maintains an item in an accessible st ate, thereby also increasing the amount of information that is encoded about that item (Atkinson & Shiffrin, 1968; Rundus, 1971). Rehearsal has also been proposed to play an important role in intentional forgetting. According to the differential-rehearsal hypothesis (Bjork, LaBerg, & Legrand, 1968; Sheard & MacLeod, 2005) instruc tions to forget alter the al location of limited resources during study, and hence the extent to whic h some items are encoded. Accordingly, subjects stop rehearsing words from the to-be-forgotten list 1 (i.e., L1) after the forget instruction is given and devote all further rehearsals to the following list 2 (i.e., L2).1 In contrast, subjects in the remember c ondition covertly rehearse items from L1 while they 1The models that we discuss focus on the list method because it is for this procedure that the interactions between recall and recognition have been observed. For the item method of directed forgetting items are presented with a subsequent cue to remember or forget each item. Recogniti on and free recall for to-beremembered words is better than for to-be-forgotten words (Roediger & Crowder, 1972; MacLeod, 1975; Woodward & Bjork, 1971). Thus, the differential reh earsal hypothesis assumes that upon the presentation of the remember instruction subjects engage in an ela borative rehearsal process that is not invoked after the instruction to forget (MacLeod, 1975; Woodward, Bjork, and Jongeward, 1973).

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13 study L2. This reduces the average number of rehearsals allocated to L2 items and increases the average number of rehearsals allocated to L1 items. Because the items on L1 receive more rehearsals after an in struction to remember compared to L1 items in the forget condition, they are encoded better, a nd they are more likely to be remembered. This explains the costs of direct ed forgetting. Because items from L2 compete with L1 items for limited rehearsals in the rememb er condition, they are remembered worse compared to L2 items in the forget condition, and this produces the benef its of directed forgetting. Indeed, the instruction to forget affects the form of free recall serial position curves (MacLeod, 1998; MacLeod, Dodd, Sh eard, Wilson, & Bibi, 2003; Sheard & MacLeod, 2005). For L2, there is a pronounced primacy effect in the forget condition, and an almost absent primacy effect in the remember condition. Thus, most of the L2 benefits are associated with enhanced memory for items in the early serial positions. For L1, the instruction to forget has a smaller effect on the form of the serial position curves, although performance is greater in the remember versus the forget condition, of course. The differential rehearsal hypothesis is unlik ely to provide a complete explanation of list-method directed forgetting for severa l of reasons. First, the instruction to remember should enhance memory for L1 items presented at th e end of the list on the assumption that they are the L1 items given extra rehearsals during L2 in the remember condition. However, this has not been observed at times (Sheard & MacLeod, 2005), and thus, directed forgetting can be observed even when the recency portion of L1 is unaffected by the instruction to forget. Next, the differential rehearsal hypothesis predicts that directed forgetting should not be observed when rehe arsal is discouraged, but it is (Bjork et al., 196 8; Block, 1971 Geiselman, et al., 1983; Sahakyan & Delany,

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14 2005). Moreover, every theory of memory pr edicts that altering the extent of item encoding, via enhanced rehearsal or other means, should improve both free recall and recognition (cf. Malmberg, 2008). The fact th at directed forgetti ng has been observed rarely for recognition memory is problematic for these models. Acknowledging this, Sheard and MacLeod noted that serial positi on effects might be smaller for recognition, and thus it might be difficult to observe di rected forgetting because prior experimental designs were not suitable fo r observing reliable effects. 1.3.2 Inhibition The role of inhibition in episodic memo ry is under active investigation, most notably as it relates to unintentional fo rgetting in the domain of retrieval-induced forgetting (Anderson & Bjork, 1994; Norman, Newman, & Detre, 2007). However, the possibility that inhibition is used to intenti onally forget has also been investigated; some have proposed that inhibition of to-be-forgotten items produces the costs and a concomitant reduction in interference produces the benefits of directed forgetting (Elmes, Adams, and Roediger, 1970; Weiner, 1968; We iner & Reed, 1969). For instance, subjects might mentally group the to-be-forgotten and to-be-remembered mate rial separately, and then inhibit the to-be-forgotten set during retrieval (Geiselman, Bjork, & Fishman, 1983). Because they are inhibited, these items create less proactive interfer ence, leading to the benefits. However, the inhibition hypothesis also has difficulty explaining the null effects of intentional forgetting on recognition. To account for them, sometimes the inhibition hypothesis assumes that recognition testing r eleases the to-be-forgotten items from

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15 inhibition (Geiselman & Bagheri, 1985; Basden et al., 1993; MacLeod et al., 2003). This suggestion is circular, and usua lly there is no evidence that th e to-be-forgotten items were ever inhibited to start (Basden, Basd en, & Wright, 2003; Bjork & Bjork, 1996; Geiselman et al., 1983). Inhi bition accounts are further chal lenged to explain why some recognition experiments exhibit no costs, a nd yet the benefits remain (Benjamin, 2006; Sahakyan & Delaney, 2005). That is, under what conditions should a release from inhibition be observed, and under what conditions should a release from inhibition not be observed and why? Last, the inhibition hypot hesis should explain how subjects place the traces into two separate sets, and inhibit on e set and activate the other. In this sense, inhibition accounts describe the data well, but they do not of fer much insight into the operations of memory. 1.3.3 Contextual Differentiation Changes in context play a primary role in forgetting according to many theories (Dennis & Humphreys, 2001; Estes, 1955; G illund & Shiffrin, 1984; Humphreys, Bain, & Pike, 1989; Howard & Kahana, 2002; Ja ng & Huber, 2008; Mensink & Raaijmakers, 1989; Murdock, 1997; Murnane, Phelps, & Malm berg, 1999). As the difference between the context features encoded during study and context cues available at test increases, forgetting increases. Acco rding to Sahakyan and Kelle ys (2002) variant of the set differentiation hypothesis of directed forgetting (Bjo rk et al., 1968; Bjork, 1970), study involves the storage of information representi ng the studied items (i.e., item information) and the context in which the items occur (i.e., context information). L1 and L2 are associated with an overlapping set of contex tual elements (e.g., Es tes, 1955; Mensink &

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16 Raaijmakers, 1989). The instruction to forget causes an accelerate d change in context between lists, and there is less interference between L1 and L2. When recalling from L2, less interference from the L1 traces produces the benefits of the instruction to forget. The costs are the result of the relative inaccessibility of an effective L1 context cue due to the relatively rapid change in cont ext that occurred between the lis t presentations. This is the contextual differentiation hypothesis. The logic behind the contextual-different iation hypothesis is derived from the literature on context-dependent memory (e.g., Anderson, 1983; Godden & Baddeley, 1975; Goodwin, Powell, Bremmer, Hoine & Stern, 1969; Eich, Weingartner, Stillmin & Gillin, 1975; Macht, Spear, & Levis, 1977, Murnane et al., 1999; Smith, 1979). Sahakyan and Kelley (2002) compared standa rd directed forgetting conditions to a between-list context-change condition. In the context-change c ondition, some subjects were given the remember instruction, followe d by an instruction to imagine that they were invisible, in order to create a mental context change. Subjects in the remember-pluscontext-change condition performed almost iden tically to subjects in the standard forget condition showing both costs a nd benefits of the context ch ange. A strong prediction of the contextual differentiation hypothesis is that the costs and benefits of directed forgetting are dependent on the ability of the subject to mentally reinstate appropriate context cues at test. Indeed, context effects are eliminated or reduced when appropriate context cues are available for both intenti onal and unintentional fo rgetting procedures. For instance, Smith (1979) showed that the mental reinstatement of the environmental context eliminates the costs of context dependent memory. In the intentional forgetting literature, Sahakyan and Kelley (2002) used standard remember and forget conditions,

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17 but after studying the second list, half of subjects participated in a context reinstatement procedure. Afterward, subjects in the forget and remember-p lus-context-change groups showed reduced costs and benefits compared to the groups that did not receive the reinstatement. Presumably, the remaining costs and benefits are due to the use of some contextual elements found at test. In any case, these findings revealed that context reinstatement has similar effects on intentional and unint entional forgetting. 1.4 A Mathematical Model of Directed Forgetting Malmberg, Lehman, & Sahakyan (2006) set ou t to develop a formal model of the contextual differentiation hypothesis for directed forgetting, but noted various inconsistencies between existi ng data sets and the contextu al differentiation hypothesis. One problem for the contextual differentiation hypothesis concerned th e lack of a recency effect observed in many free recall directed forgetting experiments. All things being equal, any model of free recall that assumes that temporal context plays an important role during retrieval predicts that L2 should be better remembered than L1 in the remember condition because L1 was learned prior to L2 (Ebbinghaus, 1885). In contrast, sometimes L1 is actually remembered better than L2 in the remember condition (Geiselman, Bjork, & Fishman, 1983; Sahakyan & Kelley, 2002; Sahakyan, 2004). This reversed recency effect, better memory at longer retention intervals, suggested to us that the traditional designs used in list-method directed forgetting confound several variab les with list order, such as the location of distractor tasks a nd the presence of proactive interference, and thus give L1 an advantage over L2.

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18 Because the list method usually makes use of only two lists, L1 and L2, the effect of L1 versus L2 is confounded with presence of an in terfering prior lis t. In addition, subjects usually do not perform a distractor task after L2. Lack of a subsequent distractor task benefits L1 because the last items on L1 maybe rehearsed during L2 (Peterson & Peterson, 1959; Rundus, 1971). Lastly, subj ects are typically asked recall both L1 and L2at test simultaneously, which makes it some what plausible that output interference explains directed forgetting. 1.4.1 Improved Design To control for these variables, Malmberg et al. (2006) used a three-list design (cf. Sahakyan, 2004), where only the second and third lis ts were tested. Thus, the first list was referred to as L0, and for consistency in making comparisons to previous experiments, the second was referred to as L1, and the third as L2. Thus, both L1 and L2 were preceded by a prior list. Additionally, a distractor tas k, traditionally used a means for controlling rehearsals (Peterson & Pete rson, 1959), was performed after each list. Finally, subjects recalled one list at time in order to control for output interference; those subjects asked to recall L1 can do so when not also attempting to recall L2 items (e.g., Sahakyan & Kelley, 2002). Given these cha nges, Malmberg et al. predicted better memory for L2 compared to L1, in addition to the costs and bene fits of directed forgetting. A second prediction concerned intrusion erro rs. While intrusion rates are usually very low and hard to investigate, the assu mptions of this model did generate a few predictions. Because context at test is more similar to the context of L2 than to the context of L1, the number of intrusions from L2 while trying to recall L1 should be greater

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19 than the number of intrusions from L1 when trying to recall L2. Additionally, Malmberg et al. predicted that the context differentiati on that occurs as the result of the forget instruction will make intrusions le ss likely in the forget condition. 1.4.2 Mathematical Model Malmberg et al. (2006) developed a mode l for the context differentiation that occurs with directed forgetting in a free r ecall paradigm, based with in the framework of the Search of Associative Memory theory (SAM; Raaijmakers & Shiffrin, 1981). According to the SAM model, remembering in volves a process of sampling and recovery of stored memory traces (images). Sampling probabilities are dete rmined by the strength of association between contexts and images in memory. This association strength is represented by the parameter, a, and is referred to as context strength The parameter, b, is the strength of association between two ite ms that were recently rehearsed together when one item is used to cue the image of the other item ( inter-item strength ). The parameter, c is referred to as self strength and it is the associa tive strength between an items image and the same item used as a cue. Lastly, the parameter, d, is the strength of association between two items th at were not recently rehearse d together, and it is referred to as residual strength This is often considered to be a source of noise. The context strength parameter, a, is the key parameter for implementing the context change model in SAM (Shiffrin, Ratc liff, & Clark, 1990; Malmberg & Shiffrin, 2005). For this model, the parameters b, c and d do not influence the model, and thus will be left out of this discussion.

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20 According to SAM, the probability of sampling image, I given Q as a retrieval cue is: m JQJS QIS QIP1),( ),( |, where m images are stored, and S(J,Q) is the strength of association between the retrieval cue and image, J = 1m We assumed that each probe of memory is with a context cue only. While SAM assumes that both item and cont ext cues can be used to probe memory, we made the simplifying assumption that b is the same for all images, and hence item cues do not differentially affect directed forgetting. Thus, the model attempted to account for directed forgetting using the list method without appeal to a rehearsal account. Since the list method involves studying more than one list, we assumed that the context changes between them (cf. Mens ink & Raaijmakers, 1989). Call the lists Lx and Ly. Given that one is trying to recall items from Lx, there will be an item-to-context association for each Lx image and the context that is used as the retrieval cue ( aLx) and an item-to-context association for each Ly image and context used to probe memory (aLy). On these assumptions, the probabi lity of sampling image I from Lx is: m J Ly m J Lx Lx Lxaa a QIP1 1|, ( 1 ) and the probability of mistak enly sampling image I from Ly is: m J Ly m J Lx Ly Lyaa a QIP1 1|. ( 2 )

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21 SAM assumes that the process of sampling is noisy and error prone, so we need a recovery process in order to actually retrie ve items from memory. Once an image has been sampled from memory a re covery of the contents of that image is attempted, which is successful with the following probability: )exp(1)),(exp(1),(Ln n na QIS QIR ( 3 ) where n = x or y Thus, the product of Equations 1 and 3 give the probability of successfully recalling a given it em from the target list. In contrast, the product of Equations 2 and 3 give the probability of r ecalling a given item from a non-target list (i.e., an intrusion error). The SAM model for the context change asso ciated with directed forgetting had three necessary assumptions: 1. aLx aLy. Context is assumed to change from list to list, and a different context cue is used when attempting to recall Lx versus Ly items. For the sake of simplicity we assumed that context does not change within a given list (cf. Mensink & Raaijmakers, 1989). Thus, the strength of the context-to-i mage association differs between images on Lx and Ly depending on whether one attempts to recall Lx or Ly. When we want to recall from Lx we use the Lx context cue. When successfully recalling items from Lx, aLx > aLy, and when successfully recalling items from Ly, aLx < aLy. This assumption allows the model to predict that it is possible to reca ll items from a specific list, and that when attempting to recall from a specific list, items fr om that list are more likely to be sampled than items from another list. Figure 1 illustrates the relationship between the ratio of aLx to aLy and recall performance. When one attempts to recall Lx, the probability of recalling an Lx item

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22 Figure 1. The SAM model of directed forgetting. aLx / aLy 0 5101520 P(recall) 0.0 Lx item Ly item Attempting to Recall Ly Attempting to Recall Lx Correct Recall Intrusions Note: aLy was set to .05 and aLx was varied from .001 to 1.0 increases and the probability of recalling an Ly item decreases as aLx / aLy increases. When one attempts to recall Ly, the probability of recalling an Ly item increases and the probability of recalling an Lx item decreases as aLx / aLy decreases. 2. The more recent the list, the greater the strength of the context-to-image association is. The context at test will be more similar to the context of the most recent lists than to the context of earlier lists. Thus, more recen t lists should be better recalled than less recent lists. This is implemented by assuming that aLx < aLy when attempts are made to recall Lx and Ly, respectively. The assumption al so leads to the prediction that intrusions from L2 will be more likely when recalling from L1 than intrusions from L1 when recalling L2.

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23 3. The forget instruction increases the difference between contexts for different lists by decreasing the context strength for the to-be-forgotten list. Specifically, if Lx was studied before Ly, the instructions to forget Lx will decrease aLx. We assumed that the instructions to forget Lx, however, have no effect on the strength of the association between the test context used and the Ly images in memory. According to the sampling equation mentioned above, when one is trying to recall from Lx, instructions to forget Lx decrease aLx, thus causing a decrease in the probability of recalling an Lx item. This creates the costs of directed forgetting. On the other hand, wh en one is trying to recall from Ly, instructions to forget have decreased aLx, but not affected aLy, thus the probability of recalling an Ly item increases creating the bene fits of directed forgetting. Additionally, this context differentiation allows the model to predict decreased intrusions in the forget conditions, where the contexts associated with each list have less overlap than in the remember condition. Consider Figure 1. Assume th at one is trying to recall Ly. Instructions to forget Lx, that is, decreasing aLx / aLy, causes an increase in the probability of recalling an Ly item. This is the benefit of directed forgetting. Now assume that one is trying to recall Lx. Instruction to forget Lx causes a decrease in the probability of recalling an Lx item. This is the cost of directed forgetting. 1.4.3 Experimental Findings Malmberg et al. (2006) conducted an experi ment using the three-list design in order to test the SAM model s predictions in directed forgetting, and found that the models predictions were supported. The da ta and model fits are shown in Figure 2.

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24 First, recency was present in both the re member and forget conditions, such that L2 was better remembered than L1 in both conditions. Further, the costs and benefits of directed were also present. Finally, while intrusion rates were low and differences were for the most part unreliable, the trends in intr usion rates supported the models predictions: subjects were more likely to have intrusions from L2 while being tested on L1 than they were to have intrusions from L1 while being tested on L2, and the probability of either type of intrusion was lower for subjects in the forget condition than in the remember condition. Figure 2. Data and SAM model predictions for proba bility of correct recall and intrusion errors for free recall in directed forgetting. List 12 P(Recall) 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Remember Forget List 12 P(Recall) 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Remember Model Forget Model Note. The intrusions in these graphs refer to intrusions that came from either List 1 or List 2. When recalling from List 1, any List 2 item that was output is referred to as an intrusion and vice versa.

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25 Overall, the SAM model provi ded good fits to the correct recall and intrusion data from a directed forgetting experiment using an improved design to eliminate experimental confounds. The findings suppor t a contextual diffe rentiation model of directed forgetting. Lehman and Malmberg ( 2009) extended the work of Malmberg et al. (2006) by examining serial position effects a nd first recall probabilities in directed forgetting, and by investigating the effects of directed forgetting on recognition memory. They utilized the three-list design in order to accurately test the c ontextual-differentiation theory and to generate data which coul d be accounted for in a formal model of contextual-differentiation. In addition to a ddressing issues of recency, their design also addressed another challenge for the contextu al-differentiation mode l: the often observed null effect for recognition memory. Most mode ls assume that context plays an important role in episodic recognition. The assumption is supported by findings that show contextdependent recognition performance (Dennis & Humphreys, 2001; Light & Carter-Sobell, 1970; Murnane et al., 1999). Thus, the context-differentiation model predicted that there should be an effect of the instruction to forget on recognition memory if recognition depends on the use of mental ly reinstated context. The nature of the recognition tests used to assess directed forg etting is a critical issue. The list method requires multiple st udy lists. Under these conditions, recognition experiments can use either an inclusion test or an exclusion test (Jacoby, 1991; Winograd, 1968). In an inclusion test, one should endor se any item studied during the experiment. Hence, context cues that differentiate th e study lists are not re quired. In contrast, exclusion recognition requires the subject endorse only words from a specified list. In this case, the subject must use a context cue that differentiates the st udy lists in order to

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26 accurately perform the task. Note that list-m ethod free recall also requires a context cue for a particular list. Thus, the exclusion task is more similar to what is required for free recall than the inclusion task, and if the contextual-differe ntiation hypothesis is accurate, then we should see robust effects of directed forgetting on exclusi on task performance. Interestingly, most of the recognition experi ments in the directed forgetting literature used an inclusion procedure rather than an exclusion procedure. Lehman and Malmberg (2009) predicted th at the effects in an exclusion task should be similar to those observed for free re call, where intrusion rates are reduced by the forget instruction (Malmber g et al., 2006). Thus, there shou ld be costs and benefits on hit rates and the recency advantage for L2. There should also be more L2 false alarms when a subject is attempting to recognize from L1 than there will be L1 false alarms when a subject is attempting to recognize from L2, and false alarm rates should be lower in the forget condition. Lehman and Malmberg (2009) completed serial position analyses on the data collected by Malmberg et al. (2006), including analyses of first recall probabilities. As shown in Figures 3 and 4, these analyses reveal ed that most of the effect of the forget instruction in free recall is driven by what happens during the initial memory probe. When recalling from L1, participants in the remember condition are more likely to begin recall by first outputting the first item on the li st; the opposite is true when recalling from L2. Lehman and Malmberg also examined di rected forgetting in a recognition task. Standard effects of directed forgetting were found in an exclusion task: costs and benefits, reflected in decreased hit rates on L1 and increased hit rates on L2 for

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27 Figure 3 REM model predictions and serial po sition data in a directed forgetting free recall task. Data Model Bin 12345678 P(Recall) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Remember Forget Bin 12345678 P(Recall) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Bin 12345678 P(Recall) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Bin 12345678 P(Recall) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Note. For the sake of clarity, the 16 ite m list was compiled into 8 bins spanning two serial positions. For instance, bin n contains the data fr om serial positions 2n-1 and 2n. participants in the forget condition. Thes e are shown in Figure 5. Additionally, false alarm rates mirrored intrusion rates seen in free recall: false alarms from L2 when attempting to recognize items from L1 were greater than false alarms from L1 when attempting to recognize items from L2, and false alarm rates were greater in the remember condition than in the forget condition. As show n in Figure 6, serial position effects in the recognition task did not show the same patter ns as in free recall; the directed forgetting effect was not driven by differences only in the beginning of the list. list 2 list 3

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28 Figure 4 REM model predictions for first re call probability data for free recall in directed forgetting.. Data Model Bin 123456 P(First Output) 0.0 0.1 0.2 0.3 0.4 0.5 Bin 123456 P(First Output) 0.0 0.1 0.2 0.3 0.4 0.5 Note. For the sake of clarity, the 16 item list was compiled into bins. For first item output, bin 1 represents the first item on the list (s ince this is where differences are seen) and all other serial positions are grouped by three. While Malmberg et al. (2006) developed a model of the retrieval mechanisms supporting the contextual differe ntiation model for free recall, which was able to account for the costs and benefits of directed fo rgetting in the contextual differentiation framework, this simple model was not suitable for examining serial position analyses and other fine-grained aspects of the intentional forgetting, or for simultaneously fitting recognition findings. Lehman and Malmberg (2009) developed a context differentiation Bin 123456 P(First Output) 0.0 0.1 0.2 0.3 0.4 0.5 Bin 123456 P(First Output) 0.0 0.1 0.2 0.3 0.4 0.5 list 2 list 3

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29 Figure 5 REM model predictions for exclusi on recognition in directed forgetting. Data Model List 23 P(Old) 0.2 0.4 0.6 0.8 1.0 Remember Forget Foils Targets List 23 P(Old) 0.2 0.4 0.6 0.8 1.0 Foils Targets model of intentional and unintentional forg etting in the Retrieving Effectively from Memory (REM) framework (Shiffrin & Stey vers, 1997). While SAM and REM are both descendents of the A-S model, the SAM mode l is a mathematical model with provides average recall predictions. The REM model, on the other hand, is a probabilistic computation model which allows us to generate predictions for serial position effects in addition to overall recall proba bilities. Additionally, as it was designed to account for recognition findings, which have troubled other models (Shi ffrin et al., 1990), the REM model is more suitable for making predicti ons regarding recogniti on tasks in directed forgetting. The Lehman-Malmberg REM model was able to account for

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30 not only the costs and benefits of directed forgetting in free recall, but also serial position and sequential dependency data, in addition to directed forgetting effects in recognition. Figure 6 REM model predictions for serial po sition data for exclusion recognition in directed forgetting. Data Model Bin 12345678 Hit Rate 0.4 0.6 0.8 1.0 Remember Forget Bin 12345678 Hit Rate 0.4 0.6 0.8 1.0 Bin 12345678 Hit Rate 0.4 0.6 0.8 1.0 Bin 12345678 Hit Rate 0.4 0.6 0.8 1.0 list 2 list 3

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31 Figure 7. Data and REM model predictions for proba bility of correct recall and intrusion errors for free recall in directed forgetting. List P(Recall) 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Remember Forget Correct recall Intrusions 12 List P(Recall) 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Correct recall Intrusions 12 Note. The intrusions in this graph refer to in trusions that came from either List 1 or List 2. When recalling from List 1, any List 2 item that was output is referred to as an intrusion and vice versa. 1.5 REM Model 1.5.1 Representation According to REM, general knowledge of items is stored in lexical/semantic memory traces and information about past ev ents is stored in ep isodic memory traces. Lexical/semantic traces are acquired over a li fetime. They contain information about how words are spelled and pronounced and what they mean. In addition, they contain information about the contexts or situations in which they have been encountered. As such, they are accurate, complete, and generalizab le to the contexts in which they usually occur.

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32 These traces are represented by a vector of features. The w features comprising the vectors are generated according to a geometric distribution with the base rate parameter, g : ,...,1,)1(][1jggjVPj. When a word is studied, the w item features of its lexical semantic trace are copied to form a new episodic trace that represents this occurrence. 1.5.2 Encoding Episodic encoding is an incomplete and error-prone process; a feature may be copied correctly, it may be copied incorrectly, or it ma y fail to be copied. Each lexical/semantic feature associated with an item is copied to an episodic trace with the probability, tuc*11 where *u is probability of st oring a feature given t attempts to do so and c is probability of copying that feature correc tly. An item will be stored bu t copied incorrectly from a lexical/semantic trace with a probability 1-c If a feature is stored but copied incorrectly, a feature is drawn randomly from the geometric distri bution identified by the g parameter. If a feature is not en coded, it takes the value zero. 1.5.3 Recognition A global-matching process is used for recognition memory in REM (Malmberg, 2008; Malmberg, Zeelenberg, & Shiffrin, 2004; Shiffrin & Steyvers, 1997). Whereas

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33 sampling of items in free recall is determin ed by the match between a single item and a given memory cue, recognition judgments are made based on the overall degree of match between all items on the list and the given cu e. A decision about whether an item is judged as old is made based on the likeli hood ratios calculated for all items in the comparison set. The odds, or the probability that a test item is old divided by the probability that the test item is new, are calculated according to the following equation: n j jn11, where j is a likelihood ratio com puted for each trace, ijm jqn i ni gg i ggcc c j 11 )1( 1 )1()1( 1 and where njq is the number of mismat ching features in the jth trace and nijm is the number of features in the jth trace that match the features in the retrieval cue. Matching features increase and mismatching feat ures decrease the likelihood ra tio; cases where no features are stored do not contribute to the likelihood ratio either way. If the odds exceed 1.0, the item is judged as old, otherw ise it is judged as new. 1.5.4 Recall Recall is conceived of a series of sa mpling and recovering operations in REM (Malmberg & Shiffrin, 2005; Raaijmakers & Sh iffrin, 1981; Shiffrin & Steyvers, 1997). Sampling is governed by a Luce choice rule which assumes that the probability of sampling a given trace, j is positive function of the match of trace j to the retrieval cue and negative function of the match of other N -1 traces to retrieval cue,

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34 N k k jQjP1)|( Once a trace is sampled, recovery of its c ontents is attempted (Malmberg & Shiffrin, 2005). 1.6 Lehman-Malmberg Model 1.6.1 Representation According to the Lehman-Malmberg model, the contextual differentiation in directed forgetting is implemented by integrat ing context into the model. Memory traces are represented by two concatenated vectors; one vector represents th e item, and consists of w item features, and the other represents the context in which the item has been encountered, and consists of w context features. When items are studied, context informati on is stored in episodic traces in the same way as item information. For the sake of simplicity in conducting model simulations, we assumed that context features change between lists with a probability of but not within lists (Criss & Shiffrin, 2004; Malmberg & Shiffrin, 2005), although it is likely that context changes slightly within lists (later versions of this model include context that changes gradually within lists; see below). Thus, for each list a single context vector was generated to represent the current context, and all items within that list were associated with the same context information, which is stored according to the rules for item storage outlined above. When a context feature value is changed it is randomly sampled from the geometric distribution. We further assumed that context features change after the final study list, in the same manner as they change between lists.

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35 1.6.2 Encoding The Lehman-Malmberg model assumes that the content of a stored trace is determined by the operations of a limited cap acity buffer (Raaijmakers & Shiffrin, 1981; also Atkinson & Shiffrin, 1968; Malmberg & Shiffrin, 2005). As a descendent of the Atkinson and Shiffrin theory (1968), the intera ction of control processes and structural aspects of memory are used to model serial position data. Control processes operate on items located in a limited capacity rehearsa l buffer during encoding. The capacity of the buffer is not known, but we assumed for the curren t purposes that it is two items (see also Atkinson & Shiffrin, 1968; Lehman & Malm berg, 2009). While study items are attended to, they reside in the buffer, and information is encoded about them in one or more episodic traces. Thus, upon the presentation of th e first list item, it en ters the buffer, and an episodic trace is stored. Assuming that no items repeat, each lexical/semantic feature associated with the first list item and each c ontext feature is copied to an episodic trace according to the equation above, where iuis probability of storing an item feature, and cuis probability of stori ng a context feature. Upon the presentation of the second list item, it enters th e rehearsal buffer, and a new episodic trace is stored. The trace consis ts of item information associated with the second list item and context information st ored according to th e equation above. We further assumed that a result of the capacity limitation is that encoding is split between the storage of item, context, and associative information (Lehman & Malmberg, 2009). In this example, the two buffered items compete for encoding resources. Some of the resources are spent encoding th e second list item, and we assume that the resources spent

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36 encoding it are similar to those spent encodi ng the first list item when it was initially presented. The remainder of the encoding reso urces is divvied up be tween the storage of associative information and context. This is accomplished in the model by reducing the xu parameter for context features such that cu<* 1 cu, where the latter term is the probability of encoding a context feature for the first list item, and the former is the probability of encoding a context feature for a ll other list items. In addition, some of the buffer capacity is spent encoding associative information representing the fact that the first and second items were corehearsed. This is represented by a ppending to the trace representing the second list item a relatively weak encoding of the first items lexical/semantic features. Again, th is is implemented by reducing the xu value for associative information, au. With the presentation of the thir d list item, the oldest item in the buffer is knocked out with probability and the encoding cycle begins anew. 1.6.3 Retrieval Lehman and Malmberg (2009) extended the REM model to account for directed forgetting in both recall and rec ognition. The first step of the retrieval process is similar across all test conditions (recall, recognitio n-inclusion, and recognition-exclusion). A relevant subset of memory is created that consists of the items with the strongest association to the context used as the initial retrieval cue (cf. Shiffrin & Steyvers, 1997; REM.5). In order to create the relevant subs et, the current context cue is matched against the context stored in the episodic images. Likelihood ratios are calculated according to the above equation, and those with higher likeli hood ratios are most likely to become part of the subset.

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37 1.6.4 Free Recall The free recall task begins with the cr eation of the cue with which to probe memory. The initial cue consists of only c ontext features; it is a combination of the current test context and reinst ated list context. The proportion of reinstated list context features is represented by the parameter. The remaining cont ext features in the cue are from the test context. Free recall operates in REM cycles of sampling and recovery (Malmberg & Shiffrin, 2005). The initial context cue is matche d against all traces in the activated subset in an attempt to sample an item from the give n list, and an item is sampled. Lehman and Malmberg (2009) assumed for simplicity th at all sampled traces are recovered successfully (however modificat ions to the recovery proce ss were later made, Lehman & Malmberg, 2011). Thus, when an item is sampled and recovered, and it comes from an incorrect list, the subject unde rtakes a monitoring process to determine whether it is an intrusion. We assumed that items from the corr ect list are rarely wit hheld, and hence if an item is sampled and it is from the correct list, it is output with a probability of 1.0. The probability, of making an intrusion error given th at an item from the incorrect list is sampled and recovered is a positive function of the overlap in c ontext between lists (represented by this parameter). Thus, is greater in the rememb er condition than in the forget condition. If an item is output, the next cue used to probe memory will consist of both context and the recovered item information. Ag ain, the context portion of the cue consists of both current context features and context features associat ed with the given list. The item portion of the cue consists of the item vector from the last item recalled. Thus, it is

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38 most likely that co-rehearsed items, which share the current items information, will be sampled next. If no item is output, then the orig inal context cue is used for the next probe of memory. The sample-and -recovery process repeats times (Davelaar et al., 2005). 1.6.5 Recognition Exclusion For the exclusion task, a subject positiv ely endorses only items that came from a given study list. A global matchi ng process is first used to cr eate the relevant subset of items, using the same context cue that was used to create this subset in free recall. After this set of traces is created, a retrieval cue consisting of only the item information that represents the test word is used to probe memory, and the odds are calculated. This is followed by a monitoring task, as in free recall : after an item is identified as old, an output decision is made in the same manner as was used for free recall. That is, it is dependent on the overlap in context between the two lists, and this is captured by the parameter at test. This is essentially a recall-to-reject process (Dosher, 1984; Humphreys, 1976; Malmberg, 2008). For the sake of simp licity, however, we did not implement the sampling and recovery processes for the exclus ion task, since all of the water is carried by the overlap between the contexts: A large overl ap in context means that it is harder to distinguish between the two lists and the fals e alarm rate will be increased. A description of these processes is f ound elsewhere (Malmberg, 2008). 1.6.6 Directed Forgetting The context differentiation model assumes that directed forgetting instructions lead to increased context change between lists and better encoding for L2 in the forget

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39 condition (Lehman & Malmberg, 2009; Sahakyan & Delaney, 2003). As such, the directed forgetting instructions have effects on both encoding and retrieval operations in the model. The context differentiation occurs by an increased rate of context change between lists after the forget inst ruction, represente d by an increased parameter. Additionally, the encoding of cont ext associated with the first item on a list is increased for the first item on L2, represented by an increased u*c1, under the assumption that all other items have been dropped from the buffer. Finally, the forget instruction decreases the probability of reinstating context features used in the cue to probe memory for L1. 1.6.7 Model Evaluation The major modeling challenge was to simultaneously account for unintentional and intentional forgetting in a comprehensiv e and detailed manner. This was difficult because despite the costs and benefits for free recall and recognition, differences remain. For instance, intrusion rates are low for free recall but false-alarm rates are relatively high for exclusion recognition, and the tasks produce different serial position curves. Another challenge was to model the first recall probability functions in a manner that made list discrimination possible and produced costs and benefits. The first r ecall probabilities are critically important because most of the direct ed forgetting effect in free recall appears to be driven by them. Our approach was to account for both task s with a single cont extually driven mechanism. Hence, we refer to this as a g lobal model because we are explaining these findings and the relationship between intenti onal and unintentional forgetting with just a few assumptions. The only differences between the models of free recall and recognition

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40 are the assumptions concerni ng retrieval, and they account ed for a wide variety of episodic memory phenomena (Criss & Shi ffrin, 2004; Malmberg, 2008; Malmberg, Holden, & Shffrin, 2004; Malmberg & Mu rnane, 2002; Malmberg & Shiffrin, 2005; Malmberg & Xu, 2007; Malmberg et al., 2004; Shiffrin & Steyvers, 1997, 1998). Modeling was accomplished with the use of 16 parameters, 12 of which were fixed in all experimental conditions. Without exception, thes e scaling parameters are the same or almost same as those used to fit other REM models to data (Criss & Shiffrin, 2004; Malmberg, 2008; Malmberg, Holden, & Shffrin, 2004; Malmberg & Murnane, 2002; Malmberg & Shiffrin, 2005; Malmberg & Xu, 2007; Malmberg et al., 2004; Shiffrin & Steyvers, 1997, 1998). The model predictions for free recall are shown in Figure 7, and model predictions for serial position effects and first recall probabilities, along with exclusion recognition are shown in Figures 3, 4, 5, and 6. Lehman and Malmberg fit over 250 data points, with only four parameters allowed to vary between the remember and forget conditions in accordance with the assumptions of the model: u*c1, 1, and With these parameters, a set of 1000 Monte Carlo simulations for free recall and recognition. The same set of parameter values were used to generate predictions for all experiments. The model produced the correct patterns of costs, benefits and intrusions for free recall, and the observed inter action between serial position and the forget instruction, where the costs and benefits are greatest at earlier serial positions. The model also produced the correct patterns of costs and benefits in the hit rates for exclusion recognition and the correct false alarm rates in the remember and forget conditions.

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41 Further, the model predicts re latively flat serial position curves in recognition, where the effect of the forget instruction is not driv en by items at particular serial positions. 1.7 Testing Predictions of the Lehman-Malmberg Model Lehman and Malmberg (2011) tested pr edictions of the Lehman-Malmberg model in relation to the effects of specific retrie val cues on memory performance in directed forgetting. Based on the way that memory is probed with context cues in the model, Lehman and Malmberg proposed that other more effective memory cues, such as category cues, may eliminate directed forge tting effects. After generating the model predictions related to directed forgetting in categorized lists, the models predictions were empirically tested. 1.7.1 Categorized Lists According to REM, once a trace is sampled, recovery of its contents is attempted (Malmberg & Shiffrin, 2005). Lehman and Malmberg (2009) assumed for simplicity that all sampled items are recovered. However, in order to develop a model of recall from categorized lists, it was necessary to more clearly specify the recovery process. Since the contents are only a noisy incomplete representa tion of a study event, the contents of some traces are more likely to be recovered than others. The recovery probability is a positive function of the numbe r of features in the sampled trace that match the retrieval cue, x

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42 bxe 1 1, where b is scaling parameter (Lehman & Malmberg, 2011). The traditional assumption made by these models of categorized lists is that recovery is more likely to be successful for traces stored on categorized lists (Raaijmakers, 1979; also see Raaijmakers & Sh iffrin, 1981, for a discussion of retrieval from categorized lists). In this case, the cat egorized list advantage falls right out of the model; it is due to the additional matches ob tained from the use of readily available category features in the retrieval cue. The predictions of the model are consiste nt with directed fo rgetting data when study lists consist of randomly related items (Lehman & Malmberg, 2009). An assumption is implemented to take into account the nature of categorized lists. Prior models of retrieval from categorized lis ts have assumed that category-to-item associations are stored (Raaijmakers & Shi ffrin, 1981). Here we assume that for items that belong to a categorized list, w additional category features are appended to the item vector. These features are shared by all me mbers of a category, thus within a list where all items are members of the same category, th ese features will overlap for all items. These features are encoded in the same way as item features, and the likelihood of storing these features is represented by the catu parameter. Retrieval depends not only on the nature of the list, but also on the cues used to probe memory. If a list is categorized, and a temporal cue is used to probe memory, we assume that the same initial test cue will be used, consisting of current context features and some reinstated context features. If a category cue is used to probe memory,

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43 however, a different initial cue is used, wh ich consists of not only the same context features, but also of the additional category features appended to the cue. Additionally, when an item is recalled, the next cue used to probe memory will consist of context features, item features, and categ ory features that are retrieve d from the last recalled item, giving a recall advantage to items from categor ized lists. Thus, a recovery advantage will lead to higher recall rates fo r any categorized list over unc ategorized lists. Additionally, due to the use of category features in the initi al cue, lists probed with a category cue will incur additional recall advantages over list s probed with a temporal cue alone (the additional advantage will be driven primarily by more successful in itial recall attempts; see Lehman & Malmberg, 2009). With these additional assumptions, the model makes various predictions about what should occur in a directed forgetting ta sk when lists are categorized and different cues are used to probe memory. The model predicts costs of directed forgetting in control conditions, where randomly c onstructed lists are used. When L1 is categorized, and a temporal cue is used to probe memory (the L1-temp condition), the model again predicts costs of dir ected forgetting. When L1 is categorized and a category cue is used to probe memory (the L1-cat condition), an effective category cue is available at test, and the model predicts that the costs of di rected forgetting should be disrupted2. In comparing L1 performance to L2 performance in each of these conditions, recency of L2 is predicted in the control condition (in that performance on L2, the most 2 One might expect that the category cue should lead to improved performance in both the remember and forget conditions, rather than in only the forget cond ition. However, the costs of directed forgetting are the result of an ineffective context cue used to initially probe memory. As context alone is often used as a cue only on the first recall attempt (later attempts also use item information), the costs are captured primarily by first recall probabilities (Lehman & Malmberg, 2009) In the remember condition, the initial temporal cue is effective, thus performance is limited mostly by encoding strength.

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44 recent list, is greater than performance on L1, the less recent list; see Lehman and Malmberg, 2009). A recovery advantage for categorized lists should lead to better recall for L1 in all of the categorized lis t conditions when compared to L1 in the control condition. 1.7.2 Empirical Support We tested these predictions with an expe riment in which the lists consisted of either unrelated words or categorical exemplars. Our assumption was that the structured list (consisting of categorical exemplars) w ould provide additional category cues with which to probe memory. In addition, we varied the instructions given to the subjects at test. In two conditions, the control condition, in which L1 consisted of randomly related items and in the L1-temp condition, one of the conditions in which L1 items were exemplars drawn from a common category (e.g., clothing), subject s were provided a temporal cue at test: Recall as many words from L1 as you can. In the L1-cat condition, L1 was categorized and subjects were provided a category cue at test: Recall as many items from the clothing list as you can. The pr ediction was that the cat egory cue would reduce or eliminate the costs of directed forgetting. These data and model predictions are shown in Figure 8. We found that categorized lists produced the costs associated with intentional forgetting, but only when memory was cued with temporal context. When category cues were used to probe memory the costs of intentional forgetting were eliminated. Additionally, L2 was recalled better than L1 in the control conditions, and L1 was recalled better in the categorized conditions than in the control condition. The model correctly

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45 Figure 8. REM Model predictions and data from a directed forgetting task with categorized lists. List 2 Model P(Recall) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 BControlL1-tempL1-cat List 1 Model P(Recall) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Remember Forget ControlL1-tempL1-catA List 2 Data P(Recall) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 DControlL1-tempL1-cat List 1 Data P(Recall) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 CControlL1-tempL1-cat Note. The top row shows the model predictions for List 1 (Panel A) and List 2 (Panel B) in each cue condition: a control conditi on (Control), and two conditions where L1 is categorized and either a temporal cue is gi ven (L1-temp) or a category cue is given (L1cat) at test. The bottom row shows the data from the experiment. Panel C shows List 1 performance (costs) and Panel D shows List 2 performance (benefits). P(Recall) = Probability of recall. Error ba rs represent standard error.

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46 predicted the observed patterns of data, and thus proved to be a viable explanation for how intentional forgetting is accomplished and the conditions under which it will and will not occur. Thus, in addition to accounting for all of the data presented by Lehman and Malmberg (2009), the Lehman-Malmberg model made a priori predictions about what will occur when categorized lists are used in directed forgetting tasks and specific cues were used. The model was able to account fo r data generated from a directed forgetting task using categorized and uncategorized lists without any additional parameters.

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47 Chapter 2 Evaluating the Lehman Malmberg Model I will now extend the Lehman-Malmberg model to provide a more comprehensive account of memory processes, and to account fo r some of the findings that have troubled buffer models in the past. In order to develop the Lehman-Malmberg model used to account for directed forgetting effects, we ma de a few simplifying assumptions. First, we assumed that context does not change within a list. This assumption was made purely for the purposes of creating a simp ler model; however it is not consistent with the general view that context fluctuat es over time (Dennis & Humphreys, 2001; Howard & Kahana, 2002; Mensink & Raaijmakers, 1989). The cu rrent version of the model assumes that context drifts slowly over time not only between lists, but also within a list, and the rate at which context changes may be increased by th e task. For example, context drifts more quickly between lists, and tasks such as dire cted forgetting will increase context change to a greater degree. Next, we assumed for si mplicity that the capacity of the buffer was two items. As the buffer is viewed as a c ontrol process that may be used differently depending on the task, a buffer size of two ma y sometimes be appropriate; however, it is likely that a larger buffer is sometimes needed (Atkinson & Shiffrin, 1968). Thus, the current model includes an increased buffer size of three items and allows the capacity to change according to the demands of the task.3 Finally, while the Lehman-Malmberg 3 One might argue that even a buffer size of three is unrealistic, given Millers (1956) seven-plus or-minustwo theory, another staple of introductory textbooks. Millers data, however, shows that one can remember lists of five to nine items. Other work suggests that when using longer lists, the number of items that can

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48 model included a buffer component that influenced encoding, the buffer did not play a role in retrieval, as the directed forgetting tasks for which this model was derived involved only delayed free recall. In orde r to account for immediate free recall, buffer operations in retrieval were added to the model. The model assumes that in immediate free recall, the contents of the buffer are retrieved in such a way that differs from retrieval of items in long-term storage. Thus, recall is usually initiated by sampling only fr om the buffer, using only the most recent context as a cue. After sampling from the bu ffer occurs, retrieval continues as it does in delayed free recall, with contex t cues that consist of a comb ination of the current context and reinstated beginning of list context. The effect of delay is represented in the model by the storage of additional traces after the study list, which are generated in the same manner as list items. On the assumption that the distractor task eliminates items from the rehearsal buffer, there is no dumping of the buffer as there is in immediate testing. Parameter values are listed in Table 1. 2.1 Craik & Watkins (1973) Important to tests of buffer mode ls is the distinction between maintenance rehearsal and elaborative rehearsal (Craik & Lockhart 1972). Whereas elaborative rehearsal serves to enrich a memory trace, increasing the likelihood of retention, the goal of maintenance rehearsal is to maintain the trace in tempor ary representation. Craik and Watkins (1973) conducting an experiment that required participants to use maintenance rehearsal in an incidental lear ning task. Participants were required to study lists of be simultaneously accommodated is closer to three or four (Cowan, 2001; Crowder, 1989; Wickelgren, 1964), and this is what is represented by the buffer in our model.

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49 Table 1.Parameter Values and Descriptions for Lehman-Malmberg Model Parameter Value Description g .4 Environmental base ra te (standard value) w 8 Number of item and context features c .8 Probability of correct ly storing a feature u*i .5 Probability of storing an item feature u*c .3 Probability of stor ing a context feature u*a .1 Probability of copying a co-rehearsed item's feature u*c1 .5 Probability of storing a contex t feature for first item on a list t 3 Number of storage attempts 10 Number of sampling attempts w .2 Probability of change for c ontext features within lists b .5 Probability of context change between lists, or after a list 1 .4 Probability of reinstating contex t features from beginning of list m .4 Probability of reinstating cont ext features from recovered item b 5 Scaling parameter for recovery Note Parameter values that differ in dela y and continuous distractor conditions. For delay, 1 = .2, and 10 additional items are stored af ter the list. For continuous distractor, 1 = .3. Parameter values that differ in paired-list condition. For pairs, u*a = .5, u*c1 = .6, w between pairs = .3 For the Craik and Watkins (1973) simulations, a single u* value of .1 was used for both item and context information, and 2 of the w item features representing the shared first letter remained the same for a ll critical items on the list. words, which included multiple critical words wh ich were identified by their first letter. At the beginning of each list, the critical letter was indicated, and participants were instructed to report only the mo st recent word that began with that letter. This required participants to maintain each critical word until another word with that letter was presented. The number of words which an item was required to be maintained in memory will be referred to as lag Craik and Watkins varied the lag, presumably varying the amount of maintenance rehearsal that wa s required for each item. Additionally, the words were presented at a rate of one ever y half second, one every second, or one every two seconds. At the end of the experiment, me mory was tested for all of the critical

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50 Figure 9 : Data from Craik and Watkins (1973) a nd model predictions from the LehmanMalmberg Model Study Time 0.00.51.01.52.02.5 P(Recall) 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Reported Replaced Lag 024681012 P(Recall) 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Note: regression lines based on Craik and Watk ins (1973) data are shown as solid lines; model predictions are repr esented by dotted lines. words in the experiment, including both thos e that were reported and those that were replaced and not reported. The data from this experiment is shown in Figure 9. Craik and Watkins (1973) repor ted that increases in st udy time were related to increases in recall for both repor ted and replaced words, but th at lag did not affect recall. Craik and Watkins suggested that these findings were problematic for the A-S model because it predicted that items that spen t more time in the buffer should be better remembered. These claims, however, are problematic themselves, as they are somewhat inaccurate. First, as shown by the solid regres sion lines in Figure 9, recall increases with increasing lag. Next Atkinson and Shiffrin (1968) explicitly stated that information may

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51 only be weakly encoded when incidental enc oding is used. Thus, the Craik and Watkins (1973) data is consistent with th e predictions of the A-S model. We extended the model to account for the data from Craik and Watkins (1973) by assuming that when subjects are using maintena nce rehearsal in an in cidental task, less encoding will occur than when using elaborative rehearsal. Because only one word needed to be rehearsed at a time, we assume th at the buffer size is one, and that additional item information may be encoded with increase d time in the buffer. Thus, we varied the t value, which represents the number of units of storage time for each item, for item and context features, such that increases in study time increased the storage of item features to a greater degree than context features (Malmberg & Shiffrin, 2005). Higher values of t were used for context features in the repor ted condition than in the replaced condition, assuming that reporting the word at the end of the list increases context storage. Thus, the t value for item and context features was ca lculated as follows: For item features, t = lag + 1. For context features, t = studytime a, where a is greater for reported (a = 2) items than for replaced items ( a = 10). The model assumes that no information is stored for non-critical items, as these items are never present in the buffer. Additionally, the model assumes that during retrieval, subjects are aware of some of the first letter in formation that was used during the study lists, and they use this information as part of the cue used to probe memory. As shown in Figure 9, where the dotted line represents the model's predictions, the model provides a good fit to the data, X2 (15) = 4.06, p >.05. Thus, the model is able to account for data once thought to be troublesome to buffer models of memory simply by manipula ting the way that the buffer is used during

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52 maintenance rehearsal. Increases in the t value with increased time spent in the buffer occur differently for item information and context information (Malmberg & Shiffrin, 2005), leading to the prediction that increases in lag have small effects on recall when maintenance rehearsal, but reporting items causes additional storage of context information, which has greater effects on recall. 2.2 Continuous Distractor Task We now wish to further examine the bu ffer process and address long-term recency and lag-recency effects in the model. Our goa l is to address two questions related to the buffer. First, is the buffer used as a cont rol process during encodi ng, such that encoding resources can be differentially allocated dependi ng on the requirements of the task, or can we account for the data from continuous distra ctor experiments without such a process? Second, do items in recent memory exist in a short-term buffer a privileged state such that they are differentially accessible co mpared to items learned less recently? To address the first question, we genera ted model predictions for the continuous distractor paradigm, in which a short distract or task is presented after each item on the list, including the last item. We conducted an experiment comparing serial position effects (SPs), first recall probabilities (FRPs) and CRPs in standard free recall tasks to those in continuous distractor ta sks. Findings that have said to be challenging to buffer models include long-term recency effects and contiguity effects in the continuous distractor task. Despite the distractor task presented after each item on a list, which, according to Howard and Kahana (1999) should prevent the encoding of associations, contiguity effects are still seen. Additionall y, the presence of the distractor task should

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53 eliminate the final item on the list from the bu ffer, eliminating the recency effect (Bjork & Whitten, 1974; Howard & Kahana, 1999). The continuous distractor task is repr esented in the model by reducing the buffer capacity to two items under the assumption that it will be harder to maintain more items in the buffer while completing the distractor task between items. Additionally, for both immediate and delayed free recall in a continuou s distractor task, the model assumes that there are no items remaining in the buffer at th e end of the last dist ractor task, thus the first memory probe uses the combined context cue used in the delayed condition (described previously), with a reduced lik elihood of reinstating features from the beginning of the list, due to the increased c ontext change that has occurred throughout the list as a result of th e continuous distractor task. Model predictions for continuous distractor lists versus contro l lists in both immediate and de layed free recall are displayed by the dotted lines in Figure 10. In order to test the model's predictions, an experiment was conducted examining the continuous distract or task in both immediate and delayed free recall. This experiment examined both st andard and continuous di stractor free recall in both immediate and delayed free recall conditi ons. Rather than a math task, commonly used in such experiments, the distractor task interspersed between items for the continuous distractor conditions required part icipants to provide rhymes for irrelevant words. We hoped that the verbal nature of th is task would make it harder for participants to rehearse the list items during the distractor period.4 Additionally, a delay condition was included in order to exam ine the effect of a long dist ractor period on the recency effects. While a delay of 10 seconds (a time commonly used in the continuous distractor 4 We thank Doug Nelson for this suggestion.

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54 Figure 10 : Continuous distractor da ta and model predictions Serial Position EffectsSerial Position 0 5 10 15 20 P(Recall) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Control Control model Control delay Delay model Serial Position EffectsSerial Position 0 5 10 15 20 P(Recall) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 CD CD model CD delay CD delay model First Recall ProbabilitiesSerial Position 0 5 10 15 20 P(Recall) 0.0 0.1 0.2 0.3 0.4 0.5 Control Control model Control delay Delay model First Recall ProbabilitiesSerial Position 0 5 10 15 20 P(Recall) 0.0 0.1 0.2 0.3 0.4 0.5 CD CD model CD delay CD delay model CRPlag -5-4-3-2-1012345 CRP 0.00 0.05 0.10 0.15 0.20 0.25 Control Control model Control delay Delay model CRPlag -5-4-3-2-1012345 CRP 0.00 0.05 0.10 0.15 0.20 0.25 CD CD model CD delay CD delay model

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55 task) may not be sufficient to eliminate item s from the buffer (Glanzer & Cunitz, 1966), a longer delay may be more effective. Thus, we chose a 5-minute delay in order to assess this possibility. 2.3 Experiment 1 2.3.1 Method 2.3.1.1 Participants and Materials Participants were 86 undergraduate psychology students at the Univer sity of South Florida who participated in exchange for course credit. For each participant, eight wo rd lists were created, each consisting of 20 randomly related concrete nouns (between 20 and 50 occurrence per million; Francis & Kucera, 1982). Additionally, four lists of rhyme words were created. Each rhyme list consisted of 20 monosyllabic words with a rhyme-set size of at least 12 (Nelson, McEvoy, & Schreiber, 1998). The experiment was presented on a computer in an individual subject booth, and the rhyme lists were printed in paper booklets. 2.3.1.2 Procedure. The four conditions were manipulated within subjects in blocks, where two lists were presented in each condition. The order of the conditions was counterbalanced. At the beginning of the expe riment, participants were told that they would be studying multiple lists of words, and the instructions for each list would appear before the list. For all conditions, words appear ed on the screen one at a time for 1s. For all conditions, 60s were allowed for recall. After each test, they were given their percentage score for the list and told to tr y to improve their score for the next list. In the immediate control condition, words appeared on the screen one at a time with a .5s ISI. Immediately after the list was presented, a free recall test was given for

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56 that list, in which participants were instruct ed to enter all of the words they remembered from that list onto the screen. In the delayed control condition, words appeared on the screen one at a time with a .5s ISI. After the list was presented, they completed a 5 minute distractor task. During the task, they watched a 4.5-minute How Its Made video, with a 30s quiz afterward (to assure that they were attending to the video). After the distra ctor task, they completed the same free recall task as described in the immediate control condition. In the immediate continuous distractor condition, participants were to alternate between memorizing a word on the screen and writing rhymes for a different word in the printed booklet. Before beginning the continuous distractor condition, participants read explicit instructions detailing the proce dure, followed by a quiz to be sure they understood the procedure. To enc ourage participation, they were told that they needed to reach a certain number of rhymi ng words in order to complete the experiment. They then saw a demonstration, and completed a tw o word practice list, after which the experimenter checked to be sure that they were attempting to memorize the only words on the screen and write rhymes for only the wo rds in the booklet duri ng the practice trial. Once they correctly completed the task, they began the study list. Words appeared on the screen one at a time, with a 10s delay after each word. During this delay, the ***** symbol appeared on the screen alerting partic ipants that they shoul d now turn to their rhyme booklets and begin creating rhymes for the next word in the booklet. After 10s, a tone alerted them to look back at the screen for the next word. Th is repeated throughout the list, so that after each studied word, they had to provide rhyming words for a word in

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57 the booklet (including after the last item on th e list). Participants then completed the same free recall task as described in the immediate control condition. In the delayed continuous distractor condition, the procedure was the same as in the immediate continuous distractor condition, except that they completed the same 5minute distractor task after study as in the delayed control condition, followed by the same free recall task described above. 2.3.2 Results In the control conditions, recall was significantly greater in the immediate condition than in the delayed condition, t (1,85) = 11.445, SD = .12, p < .001. Serial position analyses revealed a serial position x condition interaction, F (28,2380) = 5.06, MSE = .194 p < .001. As shown in Figure 10, both prim acy and recency are present in the immediate testing condition. In the delayed c ondition, the recency effect was eliminated. All differences were significant at alpha = .05. A significant serial position x condition interaction is also present in first recall probabilities, F (28,2380) = 8.15, MSE = .046 p < .001.. Figure 10 shows that in the immediate c ondition, participants were most likely to initiate recall with the last item on the list, whereas in the delayed condition, they were more likely to begin recall at the beginning of the list. For conditional recall probabilities, there was not a significant lag by condition interaction, F (37,3145) = 1.59, MSE = .024, p = .11, as shown in Figure 10. Because of the marginal p value, planned comparisons were conducted, revealing no significant differences between the two conditions at any lag. In the continuous distractor conditions, recall was significantly greater in the immediate condition than in the delayed condition, t (1,85) = 4.604, SD = .12, p < .001.

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58 Serial position analyses reve aled no significant serial posi tion x condition interaction, F (28,2380) = 1.45, MSE = .145 p = .10. While the interactio n was not significant, planned comparisons revealed differences in re cency (the last item on the list.), but no other differences were significant, as shown in Figure 10. A significa nt serial position x condition interaction is also present in first recall probabilities, F (28,2380) = 1.68, MSE = .046 p = .03. Again, planned comparisons revealed differences in first recall probability for the last item on the list, but for no other serial positions. For conditional recall probabilities, there was not a sign ificant lag by cond ition interaction, F (37,3145) = 1.76, MSE = .025, p = .07, as shown in Figure 10. Because of the marginal p value, planned comparisons were conducted, revealing no significant differences between the two conditions at any lag. 2.3.4 Discussion The model was able to capture all of the effects in a continuous distractor task, including the lag recency effect and the l ong-term recency effect (in fact, the model predicts greater long-term recency than is actually present in the data). The key assumption that allows the model to account for these data is that the buffer size is reduced during the continuous dist ractor task, but that associa tions between items are still possible. The model can simultaneously account for two sets of findings which have been said to be problematic for the buffer model, with a few minor changes to prior versions of the model aimed at developing a mo re realistic account of memory processes. Proponents of single-store models have suggested that long-term recency effects in a continuous distractor paradigm are troubli ng for dual-store models, as such models

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59 assume that recency effects are due to the pr esence of items in a short-term buffer at the time of test (Crowder, 1989; Howard & Kahana, 1999). Crowder (1989) explicitly states, The traditional association of the recency effect in free recall with some transient memory has now been discredited by the work of Bjork and Whitten (1974) (p. 274). We have shown here that these findi ngs are not troubling for a model that assumes that the buffer is stil l utilized in the continuous di stractor task. Koppenaal and Glanzer (1990) showed that changing the di stractor task after the last item on a list eliminates long-term recency effects. They hypothesized that after re peated exposure to a distractor task, subjects hab ituate and become able to simultaneously rehearse items in the buffer and complete the distractor task. Thus, they suggested that recency is due to retrieval from a temporary rehe arsal buffer even in the long-term recency paradigm. Our findings are consistent with such a proposal. First, long-term recency effects were eliminated when a sufficiently long distractor task (5 minutes) was used. Additionally, in a questionnaire given to particip ants after they completed the continuous distractor task in pilot work, over half of partic ipants reported using the time when they were working on the interspersed math problems to rehearse ite ms from the list. This was our motivation for using a rhyme task in the experiment report ed in this manuscript; even with the use of the rhyme task, designed to discourage rehear sal, many subjects stil l reported trying to maintain the to-be-remembered words while completing each rhyme task, so that they could make associations with other words on the list. For example, when asked about strategies used, one subject reported, I tr ied to keep the memorize word in my head while I came up with rhymes for the rhyme wo rd so that I could c onnect it to the next memorize word when it came up. Thus, while the rhyme task was more effective than a

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60 math task at preventing rehearsals, subjects were still able to make use of the buffer during this task. Regardless, we do not wish to argue that long-term recency effects are due to some transient memory phenomenon that w ould be eliminated with a sufficiently distracting task; rather, we argue that l ong-term recency effects do not preclude the existence of some transient memory phenomenon. As suggested by Cowan (1995), even though two memory phenomena may be made to mimic each other, differences in the mechanisms that elicit these phenomena ma y exist. Although recency effects in immediate free recall and continuous-distractor free recall may be similar in appearance, this does not necessarily indicate that they are due to the same mechanism. We argue that recency in immediate free recall is due to retrieval from a rehearsal buffer and longterm recency in continuous-distractor free recall is a long-term memory phenomenon. While both lead to increased memory for the final items on the list, they arise from different processes. Similarities in re cency effects for immediate free recall and continuous distractor free recall may be taken as evidence against a dual-store model only if they display the same prope rties (Cowan, 1995). However, there are various sources of evidence suggesting that recency effects in these two tasks do not display the same properties. First, immediate recency and long-term recency are differentially affected by the presentation of an irrelevant auditory stimulus at the end of an auditorily presented list (Glenberg, 1984). Whereas recency effects are reduced for immediate recall when the same irrelevant stimulus is presented for each trial, recency effects are only reduced in continuous distractor recall when a different stimulus is presen ted after each trial. Next,

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61 the effects of output order on recency eff ects differ for immediate and continuous distractor tasks. In immediate tasks, a r ecency advantage is obtained when subjects are required to initiate recall with items from the end of the list rather than the beginning of the list (Dalezman, 1976). In continuous dist ractor tasks, however, no recency advantage is present when subjects are required to initiate recall with the end of the list versus the beginning of the list (Whitte n, 1978), suggesting that recency effects in immediate recall are subject to output interference, but this is not the case for recency effects in continuous distractor recall. These findi ngs are consistent with the viewpoint that immediate recency effects are due to the presence of the last few items in a short-term buffer at time of test, whereas long-term recency effects arise from a different process. Finally, other work has shown that word length differentially affect s immediate recall and continuous distractor recall (Cowan, Wood, & Borne, 1994), and as does semantic relatedness between words on a list (Davelaar, Haarman, Gosh en-Gottstein, & Usher, 2006). Thus, much empirical evidence suggests that immediate recency and long-term recency are produced via different processes. In fact, Bjork and Whitten (1974) stated that long-term recency effect s and immediate recency effects reflect entirely different memory processes (p. 183). Additionall y, the Lehman-Malmberg model produces both immediate recency effects and long-term recency effects through two different mechanisms that correspond to those used to de scribe differential recency effects in these two procedures; immediate recen cy effects are related to retrieval from the buffer and long-term recency effects are due to contextual similarity between the last items on a list and the retrieval cue. It is apparent in Fi gure 10 that while a recency effect was present in the continuous distractor ta sk with immediate testing, the magnitude of this effect was

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62 notably smaller than in the control c ondition (see also Howard & Kahana, 1999), suggesting that different explanations for these two effects are warranted. As a further test of the model, we exam ined its prediction that encoding resources can be differentially allocated depending on the requirements of the task (Atkinson & Shiffrin, 1968). We used single-item study lists and paired-i tem study lists in order to encourage different rehearsal strategies. If me mory utilizes control pr ocess in the form of a rehearsal buffer, then items may be both encoded and recalled di fferently depending on the nature of the list. 2.4 Single Versus Paired Item Study Lists The critical difference between studying a list of single items and a list of paired items in the model is the way the buffer operate s. For single items, the buffer capacity is three items. For paired items, the buffer cap acity is two items, a nd two items within a pair always share the buffer. Earlier vers ions of the Lehman-Malmberg model did not include chunking operations, but it is now necessary to explore how chunking functions in the model. Many features of classic c hunking theories already exist in the model, though the nomenclature may differ. Johnson (1970) describes chunks as items or information sets which are stored within the same memory code (p. 172), where a memory code is a mental representation of information that was learned, analogous to a trace in our model. As with memory traces in the REM model, codes are representations of information which are distinct from the information itself (lexical/semantic traces in REM can include errors or missing in formation). Johnson also describes recoding the process of learning a code for a chunk, and decoding the process of translating the code

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63 into the information it represents, which r oughly correspond to the encoding and retrieval processes in REM. We implement some new assumptions from original theories about chunking into this model. The two main assumptions, adapted from Johnson (1970) and the way they are implemented are discussed below. Assumption 1: Associations are made between items in the same chunk. If items are from different chunks, the associ ations between them are minimal. Implementation: During encoding, both members of a pair are stored in a single trace. Due to the staggered presentation, encoding occurs as follows: for the first item in a pair, item information and item-context associative information is stored. When the second item in a pair enters the buffer, item information and associative information from the first item in the pair is stored. Thus, the context is more strongly associated with the first item in a pair than the second item in the pair, and the first item in the pair is associated with the second item, but for simplicity, we assume in the current mode l that the second item in a pair is not associated with context. Accordingly, u*a for pairs > u*a for single items, and u*c for the first item in a pair > u*c for the second item in a pair (which is currently set to zero). Assumption 2: Chunks are recalled in an all-or none manner. In order to recall any information from within a chunk, it is necessary to recover the code from memory. If the code is recovered, th en at least implicit recovery of all

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64 information represented by the code occurs. Recall from chunks begins with the first item; the other items are maintained in short-term memory while the first item is being retrieved. Implementation: During retrieval, the current contex t is initially used as a cue. When an item that is the first member of a pair is successfully retrieved, the next item to be sampled is the second item from that pair; the recovery process occurs as it does in the single-item model. The model uses most of the same parameter values for pairs as for single items, aside from those listed above, which vary with for paired items (parameter values are listed in Table 1). The model predictions are shown as dotted lines in Figure 11. The model makes two notable predictions. First, as shown in the top graph, FRPs differ for single and paired items. For single items, th e item on the list that is most likely to be output first is the most recently studied item. However, for paired items, the item that is most likely to be output first is the penultimate item, or the first item from the last pair. This prediction is derived from Assumption 1 described above. Next the model predicts that for paired items, are much more likel y to make a +1 lag transition (representing transitioning within a pair) than in single item s. In order to test the predictions of this model, we conducted an experiment usi ng single and paired item study lists.

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65 Figure 11 : Single versus pairs data and model predictions First Recall ProbabilitiesSP 051015202530 P(Recall) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Singles Singles model Pairs Pairs model SPSP 051015202530 P(Recall) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Singles Singles model Pairs Pairs model CRPlag -5-4-3-2-1012345 CRP 0.0 0.1 0.2 0.3 0.4 0.5 Singles Singles model Pairs Pairs model

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66 2.5 Experiment 2 2.5.1 Method 2.5.1.1 Participants and Materials Participants were 39 undergraduate psychology students at the Univer sity of South Florida who participated in exchange for course credit. For each participant, eight wo rd lists were created, each consisting of 30 randomly related concrete nouns (between 20 and 50 occurrence per million; Francis and Kucera, 1982). The entire experiment was presented on a computer in an individual subject booth. 2.5.1.2 Procedure. At the beginning of the experiment participants were told that they would be studying multiple lists of words. All participants studied four lists of single words in one block and four lists of paired words in another block. The blocks were counterbalanced, with the instructions at the beginning of the block. Instructions for the single lists informed participants that they would be shown the words one at a time, and they should try to create a sentence in or der to memorize each word. Instructions for the paired lists informed participants that th ey would be seeing pairs of words, and they should try to create a sentence in order to memorize both words.5 For the single word lists, the words appear ed on the screen one at a time. For half of the lists, the words remained on the screen for 1s with an ISI of 375ms. For the other half of the lists, the words remained on the sc reen for 875ms with an ISI of 500ms. This was done so that half of the lists would have an equal study time to that of the words in the paired lists, and the other half would have an equal total study list time to that of the 5 These instructions were chosen in order to try to stan dardize strategies used by participants. To be sure that the results from this study were not an artifact of the instructions, another experiment was conducted utilizing the same procedures, but with no instructions given to participants regarding how to memorize the words. No differences were present in the results of the two experiments.

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67 words in the paired lists. As there were no differences in the results between these different study times, these data were collap sed across study times and were not further analyzed. For the paired word lists, the words appeared on the screen in a staggered fashion in order to maintain a temporal order to the words. The first word in a pair appeared on the screen and remained. After 250ms, the second word of the pair appeared on the screen adjacent to the first word. After 1.75s the first word disappeared from the screen, so that the second word from the pair rema ined alone on the screen. After 250ms, the second word also disappeared from the scre en. After an ISI of 500ms, the process continued for the next pair. This staggere d presentation was used so that the words would appear in pairs but maintain a temporal order like that of th e single word lists. Immediately after each list was presented, a free recall test was given for that list, in which participants were instructed to enter all of the words they remembered from that list onto the screen. They we re given 60 seconds to do this. After the test, they were given their percentage score for the list and to ld to try to improve their score for the next list. They then completed a 30s math task before begi nning the next list. 2.5.2 Results and Discussion There was not a significant difference in the proportion of words recalled from single or paired word lists, F (1,38) = 2.49, MSE = .037, p = .123. There was a significant effect of serial position, F (29,1102) = 25.02, p < .001, but there was no significant serial position by condition (single or paired list) interaction, F (29,1102) = 1.33, p = .117.

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68 Figure 11 shows a significant primacy and recen cy effect for both single and paired list conditions. For first recall probabilities, there was a significant effect of serial position, F (29,1102) = 37.16, MSE = .007, p < .001, and a significant serial position by condition interaction, F (29,1102) = 19.01, p < .001. As shown in Figure 11, participants in the single list condition were most likely to ini tiate recall with the last item on the list; whereas participants in the pair ed list condition were most likel y to initiate recall with the second to last item on the list (the first item in the last pair). For conditional recall probabilities, there was a significant effect of lag, F (59,2242) = 37.92, MSE = .001, p < .001, and a significant lag by condition interaction, F (59,2242) = 8.67, p < .001. Figure 11 shows more +1 tr ansitions in the paired list condition (within-pair transitions) than in the single list condition. Thus, as predicted by the model, recall pa tterns differ for single item and paired item study lists, as revealed by SPs, FRPs, and CRPs. The model accurately fits the data for both single item and paired item study list s. As predicted by the model, for single items, the first item output is most likely to be the last item on the list, and for pairs, the first item output is most lik ely to be the penultimate item on the list (the second item from the last pair). The model predicts a zigzag effect in the SP curves (Davelaar et al., 2006). For paired items, we see an up and down pattern throughout the list, where the first item in a pair is more likely to be recalled than the second item in a pair. However, due to the small number of participants used in this experiment, there appears to be too much noise in the data to detect these zigzag patterns. Like the model, the data shows a greater likelihood of making a +1 transition fo r pairs than for single items. Thus, the

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69 model is capturing all of the features that dist inguish recall patterns in single item lists from those of paired item lists. At this poi nt, the model has been shown to account for a variety of directed forgetting data, including data gene rated to confirm a priori predictions of the model, in addition to data from paradigms that have been said to be troublesome for buffer models, including tasks manipulating maintenance rehearsal, and the continuous distractor ta sk. Finally, the model has b een extended to account for findings in a novel paradigm, with the im plementation of assumptions regarding chunking process in memory. In order to increase our confidence in th e Lehman-Malmberg model, it is useful to test a priori predictions of the model in relation to the buffer component, and to further explore the contributions of the buffer to th e retrieval process. Specifically, we would like to address the second question proposed above, to determine whether items present in the buffer exist in a privileg ed state such that they will be more easily retrievable than items not present in the buffer during time of test, and will not be influenced by other items on the list. 2.6 List Length Manipulations Experiment 2 indicates that recall patterns seen in imme diate free recall are due to retrieval of items from a privileged buffer stat e. If recency is due to retrieval from the rehearsal buffer, similar recency effects should be apparent regardless of list length for all lists that exceed the size of the buffer (Mur dock, 1962). Patterns of recency, as evident in SP and FRP effects, should be similar fo r single item lists of all lengths > n and similar for paired item lists of all lengths > n, where n refers to the size of the buffer.

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70 Additionally, while the magnitude of CRP eff ects may change with list length, we would expect to see consistency, such that more +1 lag transitions occur for paired items than single items, regardless of list length. The critical test of the model relates to first recall probabilities. In the previously described experiment, we observed differential first recall probabilities for single versus paired item lists. For single item lists, the last item on the list is the most likely item to be recalled first, whereas for paired item lists, th e second to last item on the list (or first item of the last pair) is most likely to be recalled first. If thes e patterns are due to retrieval from a rehearsal buffer, then additional item s studied should not influence the items that are currently present in the buffer at time of test, and the same first recall patterns should be seen regardless of list length. If, how ever, the memory system does not include a rehearsal buffer, then first recall probabiliti es should be influenced by list length because the most recently studied items would suffer di fferent amounts of interference in lists of different lengths. The model is constrained by data from all of the previous work discussed in this manuscript. Thus, we present predictions re lated to list length manipulations using the same set of parameters used in the previ ously described models. It is necessary, however, to specify the parameters of the model th at will be affected by list length. First, it is assumed that more attempts at sampling and recovery of items will be made for longer list lengths than shorter list lengths, thus the stopping rule is a function of list length, where the n umber of sampling and recovery attempts = Next, we assume that as list length increases (and context changes), it will be harder to reinstate context features from the beginning of the list, and as it becomes harder to

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71 reinstate these features, the probability of sampling from the buffer becomes more likely. Thus, the probability of reinstating beginning of list context features is also a function of list length: = and the probability of initially samp ling from the buffer is equal to 1 The model predictions are shown in the right panels of Figures 4, 5, and 6 for FRPs, SPs, and CRPs, respectively. As with Experiment 2, the model predicts differential patterns of FRPs and CRPs for single versus paired items. Importantly, it predicts that patter ns of FRPs should not change with list length (for al l list lengths greater than fou r). Additionally it makes clear predictions about zigzag eff ects in the SP curves. For paired items, we see a zigzag pattern in both SP and FRP curves. While the penultimate item is most likely to be recalled first, items from earlier in the list are sometimes recalled first; however the first item in a pair is always more likely to be recalled first than the second item in a pair. These effects are consistent for all list lengths (greater than four). A second test of the model involves reaction times in free recall. As suggested by Davelaar et al. (2005), if re trieval in immediat e free recall begins by sampling items from the buffer, then response time to output th e first item during recall should not be influenced by other items on the list that are not present in the buffer. Thus, a model that includes retrieval from the buffer predicts that time delay to output the first item during recall should not be affected by list le ngth, whereas a model that does not include retrieval from the buffer would predict that a memory search should include all items rather than just items that exist in a privileged state, thus response times should be longer

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72 Figure 12: Single item list length data and model predictions for first recall probabilities and serial position effects Singles DataSerial Position 0 51015202530 P(First Recall) 0.0 0.2 0.4 0.6 0.8 1.0 Singles ModelSerial Position 0 51015202530 P(First Recall) 0.0 0.2 0.4 0.6 0.8 1.0 Singles DataSerial Position 0 51015202530 P(Recall) 0.0 0.2 0.4 0.6 0.8 1.0 Singles ModelSerial Position 0 51015202530 P(Recall) 0.0 0.2 0.4 0.6 0.8 1.0 to output the first item from a long list co mpared to a short list. While the LehmanMalmberg model is not a model of reaction tim e, these predictions are consistent with those of other models of reaction time (Davel aar et al., 2005); such assumptions that have yet to be built into th e current model in order to account for reaction time data. However, this prediction is based on the assumption that reaction times are a function of the probability of sampling a given item compared to the probability of sampling all items in a retrieval set; when there are fewer items in the retrieval set, as is the case with sampling from a buffer, the probability of sampling a given item will be greater than when there are more items in a retrieval set. Thus, if the first attempt at retrieval is restricted to the

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73 Figure 13: Paired item list length data and model predictions for first recall probabilities and serial position effects PairsSerial Position 0 51015202530 P(First Recall) 0.0 0.2 0.4 0.6 0.8 1.0 Pairs ModelSerial Position 0 51015202530 P(FirstRecall) 0.0 0.2 0.4 0.6 0.8 1.0 PairsSerial Position 0 51015202530 P(Recall) 0.0 0.2 0.4 0.6 0.8 1.0 Pairs ModelSerial Position 0 51015202530 P(Recall) 0.0 0.2 0.4 0.6 0.8 1.0 items in a buffer, then the probability of sampling a given item in the buffer would not be affected by list length, thus r eaction time should be consistent across list lengths. If, however, retrieval does not occur from a buffe r, then the likelihood of sampling a given item would be decreased, predicting a greater reaction time for items from longer lists. To address the issue of the necessity of a buffer in the retrieval process, we conducted a second experiment utilizing singl e-item and paired-item study lists, where list length was manipulated (cf. Ward, Tan & Grenfell-Essam, 2010), and examined SPs, FRPs, and CRPs, in addition to reaction time to output the first item recalled for each list. The examination of these effects allows us to test the models predictions regarding retrieval from a privileged buffer state.

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74 Figure 14: Conditional response probability data and model prediction for single and paired item study lists of length 6 and 24 List Length 6lag -5-4-3-2-1012345 CRP 0.0 0.2 0.4 0.6 Singles Pairs Singles Model Pairs Model List Length 24lag -5-4-3-2-1012345 CRP 0.0 0.2 0.4 0.6 Singles Pairs Singles Model Pairs Model 2.7 Experiment 3 2.7.1 Method 2.7.1.1 Participants, Materials, and Procedure Participants were 176 undergraduate psychology students at the Univer sity of South Florida who participated in exchange for course credit (as all variable s were manipulated within subject, it was necessary to collect data from many participants in order to eliminate noise and see clear serial position effects). Fo r each participant, two word lists of each list length (2, 4, 6, 8, 10, 12, 16, 20, 24, and 30 items) were created for each study condition (single-item lists and paired-item lists), each consisting of randomly related concrete nouns (between 20 and 50 occurrence per million; Francis and Kucera, 1982). Thus, for each participant, a total of 40 word lists were created, half for the singleitem study list condition and half for the paired-item study condition. Item presentation occurred in the same manner described in Experiment 2 for single and paired lists, with sim ilar study times. In order to reduce the effects of fatigue, the experiment was run in two sessions, a week apart, so

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75 that participants completed only 20 study-test cycles in each session. In one session, participants completed all study-test cycles for paired-item lists, and in the other they completed all study-test cycles for single-item lists (with the order of single and paired conditions counterbalanced). In each study-test cycle, the li sts were randomly presented, such that the length of each new list was not pr edictable, and participants were not told in advance the length of each list. 2.7.2 Results As the focus of this experiment is the qualitative effects of buffer operations and their result on serial position curves as lis t length increases, we primarily focus on qualitative patterns visible in the data rather than quantitative statis tical comparisons (the examination of a serial position by list leng th interaction is not possible, as each list length has a different number of serial position points). As shown on the left panels of Figure 12, there is a shift from primacy towa rd recency as list length increases for both first recall probabilities and seri al position effects; for longer lists, participants are more likely to begin recall with the last item on the list, and more likely to recall items from the end of the list than the beginning of the list. The left panels of Figur e 13 reveal that, as in Experiment 2, the serial position curve and fi rst recall probabilities look quite different for paired item study lists. Whereas participan ts are likely to begi n recall with the last item on the list for long lists of single items, participants are most likely to begin recall with the penultimate item on the list for paired items t (158) = 7.64, SE = .04, p < .001. As seen in the top left panel of Figure 13, this pattern is consistent for all list lengths greater than four. Additionally, for all list lengths we see a zigzag pattern in first recall

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76 probabilities; items that are the first member of a pair are more likely to be first recalled than items that are the second member of a pair (for which the probability of first recall is almost zero). This was confirmed by a Chisquare test comparing the likelihood of first recalling the first member of a pair versus the second member of a pair for a list of 24 items, excluding the first and last pairs on the list, (1) = 16.71 > 3.84. Further, the zigzag pattern is consistent throughout recall, and this does not occur for single items, (1) = 3.00 < 3.84. The bottom panel of Figure 13 shows that throughou t the list, when a first item from a pair is reca lled, the second item from that pair is recalled with almost equal probability, and again this is not the case for single items. Figure 14 shows conditional response probabi lities for two list lengths, one short (6 items) and one long (24 items). For both the short list and the long list, we see the typical patterns in the CRPs a greater likelihood to transition to a nearby serial position, and an asymmetry in that recall is more likely to move in the forward direction. For both list lengths, there is a great er likelihood of movi ng forward one item within a pair than moving forward one item for single items (all p < .05). Finally, we examined reaction time to out put the first item recalled. This was measured from the time the test began until th e participant pushed Enter to submit the word. Participants whose mean response times were greater than three standard deviations from the mean were removed from these analyses. As shown in Figure 15, reaction time to output the first item recalle d was consistent across all list lengths. Reaction times did not differ between single an d paired item lists, and there was no effect of list length on reaction time or no intera ction of condition and list length, all p > .05.

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77 Figure 15: Reaction time data fo r single and paired item st udy lists of each length Reaction Time to Initiate RecallList Length 2468101216202430 Reaction Time (s) 0 1 2 3 4 5 Singles Pairs 2.7.3 Discussion These data give support to the theory that in immediate free reca ll, initial retrieval occurs from a privileged buffer state. Given the zigzag pattern in first recall probabilities in pairs, it is apparent that recall does not always begin w ith the most recent items on the list; however the greater likelihood of first recalling the last item on the list for single items and the penultimate item on the list for paired items is consistent for all list lengths (greater than four) suggests that once the li st length exceeds the buffer size, recent items will be maintained in a privileged state. Finally, reaction time to output the first item during recall did not increase w ith list length, suggesting that the items that are output first are not suffering interferen ce from other items on the list. In general, the model does a good job of fitting the data. It predicts the correct patterns of SPs and FRPs across list lengths. The model also produces good qualitative fits for the CRPs, where lag +1 transitions are more likely for pairs then for single items. Quantitatively, the model is overpredicting such transitions, especially for pairs. This is

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78 mainly due to the simplifying assumptions that we made related to chunking processes context is only stored for the first item in a pair, and if the first item in a pair is retrieved, the next item sampled will always be the se cond item from a pair. Introducing some variation in both of these com ponents, such that context is weakly stored for the second item in a pair, and other items are allowed to be sampled after the first item in a pair is retrieved would likely lead to more accurate qua ntitative fits. However, at this time, we are more interested whether the model is able to produce the qualitati ve patterns of data in these conditions, which it does quite well. It should be noted that while recall patterns were similar for all list lengths greater than four, these patterns differe d for short lists, i.e. lists le ss than four items long. This finding is consistent with prior work showing that for short lists, subjects typically begin recall with items at the beginning of the list rath er than the end of the list as they do with long lists (Ward et al., 2010). As our intention is to examine predictions regarding the privileged state of items present in the buffer, we are more interested in model predictions at longer list lengths The model fits the data le ss well for lists of lengths two and four, because it includes no assumptions about different retrieval processes used for short lists. Additional assumptions would be necessary in or der to fit the data for short lists. For example, one might assume that when the capacity of the buffer has not yet been reached, participants rely solely on reinstating the beginning of list context as a cue rather than relying somewhat on current context.

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79 Chapter 3 General Discussion The challenge for this model was to account for all of the data from the previously discussed paradigms, including intenti onal forgetting, free recall and recognition, immediate and delayed free recall, the conti nuous distractor task, and Craik & Watkins (1973) data, in addition to the data from th e experiments in the single/pairs paradigm with differing list lengths, using the same se t of parameter values. In this sense, the model is able to handle a large number of da ta points with very few free parameters. In order to determine whether our model pr ovides the best possi ble fit to the data from the various experiments described in th is manuscript, we compared the predictions of the version of the model described in this manuscript to those generated from similar versions of the model which differed only in the use of the buffer. 3.1 Buffer as an Encoding Process The first question we were interested in addressing was whether the buffer provides a good model of encoding processes. We showed that our model was able to fit the data from a continuous distractor task, which has been said to be troublesome for dual-store models. Our model accounts for this data by assuming that the buffer size is reduced from two to three items as a result of the continuous distr actor task, however we assume that two items can be simultaneously ma intained despite this task. In order to

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80 show that the use of the buffer is necessary in order to obtain the model fits presented above, we compared the model to one in wh ich the buffer was not used at all (i.e. a single-store model). The results of model si mulations using this model are presented in Figure 16. While the model is ab le to provide qualitatively a ccurate fits of the data for FRPs and SPs, it fails in predicting the forwar d asymmetry seen in the CRPs, as it relies on context retrieved from a recalled item as the retrieval cue, which has an equal likelihood of sampling a previous item or a subsequent item. Thus, this model is at least equally able to account for long-term recency effects and contiguity effects as si ngle-store models, without the use of any additional model parameters. While this alone does not suggest that single-store models are wrong, it does tell us that dual-store models can do the job, in addition to accounting for a variety of other data. Additionally, our model is able to fit new data that will be challenging for single-store models that dont incorpor ate control processes to explain. 3.2 Buffer as a Retrieval Process The second question we addressed concerns the use of the buffer as a retrieval process. In order to assess th e necessity of such a process, we compared our model to a version in which associations are made betw een items in the buffer, but these items do not exist in a privileged state during retrieval, such that ite ms are matched to the current context cue, but any item from the list may be initially sampled (rather than any of the items presently in the buffer at this time). These model simulations are shown in Figure 17. In sum, both models provide good qualitative fits to the data in that they both predict the penultimate item peaks in FRPs for paired lists, in addition to the zigzag patterns

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81 Figure 16 : Model predictions for conditional response probabilities using different buffer sizes in continuou s distractor free recall lag -5-4-3-2-1012345 CRP 0.00 0.05 0.10 0.15 0.20 0.25 CD Data CD Model: Buffer = 2 CD Model: Buffer = 1 throughout the list in SPs and FRPs for pair ed lists. While both models provide good qualitative accounts of the data, the goodness of fit test reveals that neither provides a good quantitative fit when measured by the chi square test. We used a chi square criterion value of 124.3, which corresponds to 100 degrees of freedom because most tables don't include chi square values for more than 100 de grees of freedom; however our true degrees of freedom (528) far exceed this due to the number of parameter values we are fitting. Thus, this test may not be appropriate for determining acceptable fits in a model that includes so many data points. It can, however, show us which model provides a better fit to the data. In this case, the model that includes retrieval from the buffer, however provides a better quantitative fit to the data than the model that does not include

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82 Figure 17 : Model without retrieval from the buffer Singles ModelSerial Position 0 51015202530 P(First Recall) 0.0 0.2 0.4 0.6 0.8 1.0 Pairs ModelSerial Position 0 51015202530 P(FirstRecall) 0.0 0.2 0.4 0.6 0.8 1.0 Singles ModelSerial Position 0 51015202530 P(Recall) 0.0 0.2 0.4 0.6 0.8 1.0 Pairs ModelSerial Position 0 51015202530 P(Recall) 0.0 0.2 0.4 0.6 0.8 1.0 retrieval from the buffer, X2 (528) = 2989 and 4248, respectively. While it may be possible to improve the fit of the non-buffer re trieval model, this would require additional parameters, increasing the complexity of this model. Additionally, further evidence for retrieval from the buffer come s from the reaction time results in the list-length study. For both single and paired-item study lists, reaction times are consis tent across list lengths, suggesting that the items that ar e first output are present in a state that is not subject to interference from other items on the list. A further model test will involve examining the models predictions for reacti on time rather than recall pr ocesses. Such a model is beyond the scope of the current manuscript, but will be the subject of future work.

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83 3.3 Comparing the Lehman-Malmberg Model to Other Models 3.3.1 TCM According to TCM (Howard & Kahana, 2002), context drifts gradually over time. While in the Lehman-Malmberg model contex t drifts in a random manner (Mensinck & Raaijmakers, 1989), context drifts nonrandomly in TCM. When items are being studied, contextual drift is driven by the retrieval of preexperimental contextu al states associated with those items. During r ecall, both the preexperimental and studied contexts are retrieved with a recall item, which drives th e evolution of context during test (whereas the Lehman-Malmberg model utilizes retrieved study context and item information). Thus, TCM includes the use of a single memory store, a nd does not in clude control processes utilized by the subject either during encoding or retr ieval. Howard and Kahana have argued that SP, FRP, and CRP functions are not the result of a rehearsal buffer; rather they are the result of the use of th e current state of context to probe memory, combined with the contextual drift process that occurs during enc oding and retrieval. While they do not deny that control processes may play a function in memory, they argue that recency and contiguity effects are the resu lt of a basic memory process (i.e. out of an individuals control), and not the result of buffer operati ons. We argue, on the other hand, that buffer operations are necessary in orde r to account for the wi de variety of data that can be handled by the Lehman-Malmberg model. Howard and Kahana also suggest that while contextual encoding processes in their model may mimic the functions of the buffer, items do not exist in the buffer in an all-or-none fashion. The data from the experiments reported in this manuscript indicate however, that items at the end of a list

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84 are present in a privileged buffer state a nd do not suffer interference from items not present in the buffer. 3.3.2 Activation Models Davelaar and colleagues (Davelaar et al., 2005; 2006) have developed a dual-store neurocomputational model of memory that includes both short-term and long-term memory components with a foundation in neur opsychological processes. This model proposes a short-term buffer and a long-te rm memory store both as structural components, linked to specific neuroanatomical processes of excita tion and inhibition in the brain. Whereas the Lehman-Malmberg model and TCM are models in which retrieval of an item occurs based on the matc h between a retrieval cue and the item, the activation model specified by Da velaar et al. conceives of retrieval as a result of item activation, where items currently in the buffer are all activat ed, and items in long-term memory may or may not be activated at a give n time. Activation in long-term memory is based on episodic context matching, but, in co ntrast to the Lehman-Malmberg model, retrieval from the short-term buffer is based on current activation levels, and items in the buffer are deactivated via inhibition from other items that have entered the buffer, rather than simply displaced by the new items. Thus, rather than a flexible control system that can be differentially used depending on the way information is rehearsed, the buffer in their model is simply a set of the most recent traces which have activation levels above a threshold; such activation levels are a functi on of the structural memory system and are not under the control of an individual. While our data do not provoke us to make a strong argument against activation models, we believe our model provides more cons istency with past work. For example, it

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85 is possible to maintain a small number of items in a rehearsal buffer while processing unrelated sentences (Baddeley & Hitch, 1974). Such findings are consistent with the idea that the rehearsal buffer is a flexible contro l process that can be adapted to a task, and challenging to models that conc eive of buffer as a structural short-term memory store. While Davelaar et al. (2005) dont include control processe s in their model, they do address the ways in which such processes may c ontribute to the model. However, at this time, their model has not been used to acc ount for rehearsal pro cesses during encoding and serial order information that results from the use of the buffer as a control process during encoding. 3.4 Utilizing the Buffer in Chunking Operations A defining characteristic of the Lehman -Malmberg model is the way in which the buffer may be used to allocate encoding re sources in different ways, depending on the nature of the task, a feature borrowed from the A-S model (Atkinson & Shiffrin, 1968). For example, if a larger buffer size is bei ng used, and a single item is present in the buffer, this allows for more contextual encoding for that item than if a small buffer size is used. As more items enter the buffer, en coding resources are di stributed so that associations between items are also stored. Some tasks may allow an individual to use a larger buffer size, or they may influence the way items are dropped from the buffer. Other tasks will affect whether or not retrieval from the buffer is possible. The flexibility of the rehearsal buffer a llows it to account for chunking operations in memory. For example, when studying pairs of items, subjects may use the buffer to associate a large amount of contextual inform ation with the first item in a pair and a

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86 minimal amount of contextual information with the second item in a pair. Further, strong item to item associations may be made be tween items within a chunk so that this information can be use to produce entire chunks of information during recall. It is not clear how a model without such control processes would be able to account for the effects of chunking on recall. While other memory models such as TCM (Howard & Kahana, 2002) and Davelaar et al.s (2005) activ ation model do not argue agains t control processes, these models do not include any such processes, wh ich we argue are critic al in accounting for the data described in this manuscript. Thes e control processes are necessary in order to produce the patterns of retrieval shown in the SP, FRP, and CRP curves reported in the current experiments. The uti lization of the buffer as a cont rol process also allows the model to account for data that has been said to be troublesome for buffer models in the past. 3.5 Extending the Model One potential limitation of this work is that we typically use lists of words as study materials, thus it is not clear how this model may generalize outside of verbal stimuli. This model has been extended to account for memory of both words and pseudowords (pronounceable nonwords; Lehman & Malmberg, unpublished data), and similar models have also been used to fit da ta from experiments usi ng faces, pictures, or other visual stimuli, such as Chinese ch aracters (Annis & Malmberg, unpublished data; Xu & Malmberg, 2007). Thus, we have confiden ce that our models generalize to various types of stimuli, including both verbal and vi sual stimuli, and semantic and nonsemantic

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87 stimuli. There are many advantages of us ing wordlists; they can be highly controlled, easy to present, and easy to test for in various types of memory tasks. It may be useful to examine our model in the contex t of a more naturalistic para digm; however this is beyond the scope of the present projec t. Regardless, the stimuli used in experimental memory tasks are seen as an analogue to many of those encountered in everyday life, and we assume that our findings will generalize. For example, something that someone might try to remember in everyday life might be a grocer y list or which items to pack for a trip, and we assume that one would make use of similar mechanisms to accomplish such tasks. The goal in developing this model is to create a complete account of various memory processes. The model is able to account for performance on various types of memory tasks, including free recall and recognition, in ad dition to performance that results from many different encoding strate gies, ranging from incidental learning to intentional learning to intentional forgetting. Thus, we now have a more comprehensive account of encoding and retrieval processes, addressing some of the issues that have challenged dual-store models of memory for the past 40 years. 3.5.1 Individual Differences This model is used to generate average pr edictions, for data that is collapsed over many subjects. One of the short-term goals for this model is to begin to account for individual differences in cognitive processes. Typically in cognitive research, we look for group differences in the effects of our independent variables, but rarely use correlational analyses to inform us about why some individuals experience certain cognitive patterns and others do not (Widam an, 2008; see also McDowd & Hoffman, 2008). This model may be extended to account for patterns of cognition seen in special

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88 populations and can allow us to evaluate theories about what leads to these patterns. Further, the model can be used to generate te stable predictions relate d to such patterns. For example, one area of research to which th is model may be applied is in the study of cognitive deficits in depression. There is a large body of research related to cognitive deficits in depression, much of which suggests that depressed individuals show impairments in various cognitive processes, including concen tration, attention, and memo ry (American Psychiatric Association [ DSM-IV-TR ], 2000; Burt, Zembar & Neiderehe, 1995; Christopher & MacDonald, 2005; Cohen, Weingartner, Sm allberg, Pickard & Murphy, 1982; Kalska, Punamaki, Pelli, & Saarinen, 1999), or that they have negative information processing biases (Blaney, 1986; Bradley & Mathews, 1983; Matt, Vasquez, & Campbell, 1992). Recent interest has developed in inten tional forgetting processes in depression, driven by the suggestion that in tentional forgetting is related to inhibitory processes, and that inhibitory processes are impaired in individuals with de pression (Johnson, 2007; Joormann, Yoon & Zetche, 2007; Power, Dalgleish, Claudio, Tata, & Kentish, 2000). If this is true, then depressed individuals would be expected to show deficits on intentional forgetting tasks, particularly when nega tive materials, toward which depressed individuals may be negatively bi ased to attend are involved. Lehman and Malmberg (2009) proposed the context differentiation model for intentional forgetting; the model provides a formal account of the process commonly referred to as inhibition which causes the eff ects of intentional forgetting. Lehman and Malmberg (2011) proposed that impairments seen on directed forgetting tasks in depressed populations may be the result of a fa ilure to use context di fferentiation in order

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89 to compartmentalize information that is not re levant to the task at hand, a problem that may also manifest in the symptoms of de pression, such as ruminating on depressive thoughts when these thoughts are not presently useful. The Lehman-Malmberg model can be utili zed to make formal predictions about what will occur in various tasks for individuals who are not able to use context differentiation in order to complete the comp artmentalization process. These predictions can then be tested in order to evaluate the vi ability of this theory. For example, we can generate predictions based on simulations usi ng trials where contextual differentiation is used and compare these to those for trials wh ere contextual differen tiation is not possible, and trials where contextual differentiation is forced (for exampl e, through the use of changes in environmental context). We can then evaluate these predictions by generating data from depressed participants and compar ing these data to our models prediction (a task that is currently underway). 3.5.2 Neuroscience Models One future direction for this model is to take on these issues from a neural perspective (Cowan, 1995; Widaman, 2008). Di ssociations in neuropsychology are often cited as evidence of separate short-term and long-term memory stores (Davelaar et al., 2005). However, Crowder (1989) suggests that one type of amnesia may be due to a specific type of coding deficit in which the relations of items to their temporal contexts are not properly coded. A model that is ab le to account for biological measures in addition to behavioral measures would be useful in evaluating the dual-store issue. Additionally, it would allow us to make a greate r variety of predictions with the model. For example, depressed individuals show re duced activity in the prefrontal cortex

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90 (Henriques & Davidson, 1991), an area that is associated with various cognitive processes (Posner, 1992). Developing a comprehensive model of both brain and behavioral processes would allow us to furthe r explore the applicati ons of this model in special populations. One advantage of the Da velaar et al. (2005) model is that it incorporates features of the neural proce sses of excitation and i nhibition in order to generate activation levels in memory. Future work will attempt to accomplish similar goals in the framework of the Lehman-Malmb erg model. Perhaps the assumptions of these models can be combined in a way that provides a model with the advantages of the Lehman-Malmberg model and the Davelaar et al. model in order to account for a much larger variety of data than can curr ently be handled by either model alone. 3.6 Conclusion In sum, the Lehman-Malmberg model succ essfully accounts for a variety of data in multiple episodic memory paradigms. It has been shown to make accurate predictions related to both intentional and unintentional forgetting, maintenance rehearsal, continuous distractor tasks, and chunking opera tions. The key characteristics that allow the model to fit this wide array of data are the operations of the bu ffer as a process during both encoding and retrieval. At present, our findings suggest that control processes, which we conceptualize as a rehearsal bu ffer in the Atkinson and Shiffrin (1968) tradition, are a necessary com ponent of episodic memory.

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