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Alternative formulations of joint model systems of departure time choice and mode choice for non-work trips

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Alternative formulations of joint model systems of departure time choice and mode choice for non-work trips
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Tringides, Constantinos A
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econometric models
simultaneous equation system
travel behavior
travel demand models
causal relationship
Dissertations, Academic -- Civil Engineering -- Masters -- USF   ( lcsh )
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government publication (state, provincial, terriorial, dependent)   ( marcgt )
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ABSTRACT: Modeling travel demand by time of day is gaining increasing attention in travel demand forecasting practice. This is because time of day choice has important implications for mode choice and for quantifying potential modal and time of day shifts in response to traffic congestion and peak period travel demand management strategies. In this context, understanding the causal relationship between time of day (departure time) choice and mode choice behavior would be useful in the development of time of day based travel demand modeling systems both within the four-step modeling paradigm and within newer tour-based and activity-based microsimulation paradigms. This thesis investigates the relationship between departure time choice and mode choice for non-work trips as work trips tend to be constrained with respect to time of day choice. Two alternative causal structures are considered in this thesis: one structure in which departure time choice is determined first and mode choice is subsequently influenced by departure time choice and a second structure in which mode choice is determined first and affects departure time choice. These two causal structures are analyzed in a recursive bivariate probit modeling framework that allows random error covariance. The estimation is performed separately for worker and non-worker samples drawn from the 1999 Southeast Florida Regional Household Travel Survey. For workers, model estimation results show that the causal structure in which departure time choice precedes mode choice performs significantly better. For non-workers, the reverse causal relationship in which mode choice precedes departure time choice is found to be a more suitable joint modeling structure. These two findings can be reasonably explained from a travel behavior perspective and have important implications for advanced travel demand model development and application.
Thesis:
Thesis (M.S.C.E.)--University of South Florida, 2004.
Bibliography:
Includes bibliographical references.
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by Constantinos A. Tringides.
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ABSTRACT: Modeling travel demand by time of day is gaining increasing attention in travel demand forecasting practice. This is because time of day choice has important implications for mode choice and for quantifying potential modal and time of day shifts in response to traffic congestion and peak period travel demand management strategies. In this context, understanding the causal relationship between time of day (departure time) choice and mode choice behavior would be useful in the development of time of day based travel demand modeling systems both within the four-step modeling paradigm and within newer tour-based and activity-based microsimulation paradigms. This thesis investigates the relationship between departure time choice and mode choice for non-work trips as work trips tend to be constrained with respect to time of day choice. Two alternative causal structures are considered in this thesis: one structure in which departure time choice is determined first and mode choice is subsequently influenced by departure time choice and a second structure in which mode choice is determined first and affects departure time choice. These two causal structures are analyzed in a recursive bivariate probit modeling framework that allows random error covariance. The estimation is performed separately for worker and non-worker samples drawn from the 1999 Southeast Florida Regional Household Travel Survey. For workers, model estimation results show that the causal structure in which departure time choice precedes mode choice performs significantly better. For non-workers, the reverse causal relationship in which mode choice precedes departure time choice is found to be a more suitable joint modeling structure. These two findings can be reasonably explained from a travel behavior perspective and have important implications for advanced travel demand model development and application.
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Alternative Formulations of Joint Model Systems of Departure Time Choice and Mode Choice for Non-Work Trips by Constantinos A. Tringides A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Civil Engineering Department of Civil and Environmental Engineering College of Engineering University of South Florida Major Professor: Ram M. Pendyala, Ph.D. Jian J. Lu, Ph.D., P.E. Edward Mierzejewski, Ph. D., P.E. Date of Approval: March 26, 2004 Keywords: travel behavior, travel dema nd models, causal relationship, simultaneous equation system, econometric models Copyright 2004 Constantinos A. Tringides

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ACKNOWLEDGMENTS The author would like to thank Dr. Ram Pendyala for his continuous guidance and contribution to the accomplishment of this thesis The author also thanks Dr. Jian J. Lu and Dr. Edward Mierzejewski for serving on the committee for this thesis and for their valuable suggestions. Funding provided by the Florida Department of Transportation is gratefully acknowledged. The author also thanks Shi-Chiang Li of the Florida Department of Transportation District 4 office in Fort La uderdale for providing the data used in this study. Finally, the author would like to acknowledge Xin Ye for his contribution to the accomplishment of this thesis.

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i TABLE OF CONTENTS LIST OF TABLES iii LIST OF FIGURES v ABSTRACT vi CHAPTER 1 INTRODUCTION 1 1.1 Background 1 1.2 Time-of day Travel Demand Modeling 2 1.3 Objective and Scope of the Study 3 1.4 Outline of Thesis 3 CHAPTER 2 LITERATURE REVIEW 5 2.1 Need for Time-of-day Modeling Procedures 5 2.2 Time-of-day Modeling in Four-step Modeling Paradigm 8 2.2.1 Standard Approaches 8 2.2.2 Innovative Approaches 10 2.2.3 Emerging Approaches 12 2.3 Previous Studies on Departure Time Choice 13 CHAPTER 3 MODELING METHODOLOGY 15 3.1 The Recursive Simultaneous Bivariate Probit Model 15 3.2 Model Structure and Formulation 15 3.3 Formulation of Likelihood Functions 19 CHAPTER 4 DATA SET AND SAMPLE DESCRIPTION 21 4.1 The Southeast Florida Household Regional Travel Survey 21 4.2 Household Characteristics of the Survey Sample 22 4.3 Departure Time, Mode Choice, and Travel Patterns of the Sample 24 4.3.1 All Trips 24 4.3.2 Work Trips 27 4.3.3 Non-work Trips 29 4.4 Preparation of Datasets for Modeling 32 4.5 Workers and Non-workers Sample Characteristics 33 CHAPTER 5 RESULTS 40 5.1 Model Estimation Results 40 5.1.1 Estimation Results for Workers Non-work Trips 43

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ii 5.1.2 Estimation Results for Non-workers Non-work Trips 49 5.2 Performance Comparisons 54 5.3 Model Application 58 5.3.1 Comparison of Predictions between Causal Structures 59 5.3.2 Prediction Results 61 CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS 64 6.1 Conclusions and Future Research 64 6.2 Implications on Four-step Modeling Paradigm 66 REFERENCES 69

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iii LIST OF TABLES Table 4.1. Household Characteristics of Southeast Florida Household Travel Survey 23 Table 4.2. Mode Share of All Trips 25 Table 4.3. Mode Share of Work Trips 29 Table 4.4. Mode Share of Non-Work Trips 30 Table 4.5. Person Characteristics of Southeast Florida Household Travel Survey 35 Table 4.6. Crosstabulation of Departure Time Choice by Mode Choice: Worker Sample 39 Table 4.7. Crosstabulation of Departure Ti me Choice by Mode Choice: Non-worker Sample 39 Table 5.1. Description of Variables Used in Workers Non-work Trip Models 41 Table 5.2. Description of Variables Used in Non-workers Non-work Trip Models 42 Table 5.3. Workers Non-work Trip Model (Departure Time Choice Mode Choice) 47 Table 5.4. Workers Non-work Trip Model (Mode Choice Departure Time Choice) 48 Table 5.5. Non-workers Non-work Trip Model (Departure Time Choice Mode Choice) 52 Table 5.6. Non-workers Non-work Trip Model (Mode Choice Departure Time Choice) 53 Table 5.7. Likelihood Ratio Comparison for Worker Models 57 Table 5.8. Likelihood Ratio Comparison for Non-worker Models 57 Table 5.9. Crosstabulation of Departure Time Choice Mode Choice: Worker Sample Predicted Values 62

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iv Table 5.10. Crosstabulation of Mode Choice Departure Time Choice: Worker Sample Predicted Values 62 Table 5.11. Crosstabulation of Departure Time Choice Mode Choice: Non-worker Sample Predicted Values 63 Table 5.12. Crosstabulation of Mode Choice Departure Time Choice: Non-worker Sample Predicted Values 63

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v LIST OF FIGURES Figure 4.1. Time-of-Day Distribution of All Trips 25 Figure 4.2. Distribution of All Trips by Purpose 26 Figure 4.3. Time-of-Day Distribution of All Trips by Mode 26 Figure 4.4. Time-of-Day Distribution of All Trips by Mode: SOV vs Non-SOV 27 Figure 4.5. Time-of-Day Distribution of Work Trips 28 Figure 4.6. Time-of-Day Distribution of Non-Work Trips 30 Figure 4.7. Time-of-Day Distribution of Non-Work Trips by Mode 31 Figure 4.8. Time-of-Day Distribution of Non-Work Trips by Mode: 31 SOV vs Non-SOV Figure 4.9. Time-of-Day Distribution of Non-Work Trips: 35 Workers vs Non-workers Figure 4.10. Time-of-Day Distribution of Workers Non-Work Trips by Mode 36 Figure 4.11. Time-of-Day Distribution of Workers Non-Work Trips by Mode: 36 SOV vs Non-SOV Figure 4.12. Time-of-Day Distribution of N on-workers Non-Work Trips by Mode 37 Figure 4.13. Time-of-Day Distribution of Workers Non-Work Trips by Mode: 37 SOV vs Non-SOV Figure 6.1. Time-of-Day Modeling Procedure for Non-work Trips 68

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vi ALTERNATIVE FORMULATIONS OF JOINT MODEL SYSTEMS OF DEPARTURE TIME CHOICE AND MODE CHOICE FOR NON-WORK TRIPS Constantinos A. Tringides ABSTRACT Modeling travel demand by time of day is gaining increasing attention in travel demand forecasting practice. This is because time of day choice has important implications for mode choice and for quantifying potential m odal and time of day shifts in response to traffic congestion and peak period travel demand management strategies. In this context, understanding the causal relationshi p between time of day (departure time) choice and mode choice behavior would be useful in the deve lopment of time of day based travel demand modeling systems both within the four-step modeling paradigm and within newer tour-based and activity-based microsimulation paradigms. This thesis investigates the relationship between departure time choice and mode choice fo r non-work trips as work trips tend to be constrained with respect to time of day choi ce. Two alternative causal structures are considered in this thesis: one structure in wh ich departure time choice is determined first and mode choice is subsequently influenced by de parture time choice and a second structure in which mode choice is determined first and a ffects departure time choice. These two causal structures are analyzed in a recursive bivariate probit modeling framework that allows random error covariance. The estimation is performed separately for worker and non-worker samples drawn from the 1999 Southeast Florid a Regional Household Travel Survey. For

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vii workers, model estimation results show that the causal structure in which departure time choice precedes mode choice performs signifi cantly better. For non-workers, the reverse causal relationship in which mode choice precedes departure time choice is found to be a more suitable joint modeling structure. These two findings can be reas onably explained from a travel behavior perspective and have important implications for advanced travel demand model development and application.

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1 CHAPTER 1 INTRODUCTION 1.1 Background Departure time choice and mode choice ar e important constituents of traveler behavior [1]. Travel demand models designed to estimate travel not only for the average weekday, but for different periods within the da y (referred to as time-of-day models), are increasingly required to anal yze a broad range of transpor tation policies and initiatives [2]. In addition to the temporal dimension of trip making, mode choice is another facet of trip making that has important implications in the transportation policy context. Understanding the relationships underlying these two facets of travel behavior will, in turn, assist planners in examining the potenti al effectiveness of po licy measures aimed at alleviating traffic congesti on and reducing auto vehicle emissions. Such policies, motivated by recent legislation such as th e Intermodal Surface Transportation Efficiency Act 1991 (ISTEA), Clean Air Act Amendments (CAAAs), and the Tran sportation Equity Act for the 21st Century (TEA-21), call for the de ployment of travel demand models capable of assessing a range of transporta tion control measures (TCMs) such as congestion pricing, peak-period pricing, restrictions on sing le occupancy vehicle (SOV) use during certain time periods in certain pla ces, and incentives that promote ride-sharing and transit use [3, 4].

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2 1.2 Time-of-day Travel Demand Modeling Travel demand modeling systems are increas ingly being enhanced to incorporate time-of-day modeling capabilities. Regardle ss of whether one is implementing time-ofday modeling concepts in a four-step modeli ng paradigm or a newer touror activitybased modeling paradigm, the relationship be tween time-of-day choice or departure time choice and mode choice is an important one In the four step modeling framework, should time-of-day based trip tables be obt ained first and then mode choice models applied to different time-of-day based trip ta bles? Or should mode based trip tables be calculated first and then time-of-day choice mode ls applied to each modal trip table? In tour-based or activity-based modeling syst ems, should time-of-day choice models precede, succeed, or be jointly comb ined with mode choice models? The causality between departure time choice and mode choice is quite important from a transportation planning and policy analysis context. If mode choice precedes departure time choice, then strategies aimed at reducing peak period travel should also focus significantly on people’s mode choice behavior (because the departure time choice is influenced by mode choice). On the othe r hand, if departure time choice affects (and therefore precedes) mode choice, then strate gies aimed at reducing peak period travel demand can focus primarily on departure time as pects of behavior. Besides, strategies aimed at reducing SOV use would have to fo cus significantly on departure time choice aspects as well because mode choice is affect ed by departure time choice. In addition to the causal relationship between these two aspect s of behavior, attentio n must be paid to the potential simultaneity in their nature, in that, unobserved factors affecting each of these may be correlated with one another. Thus, when modeling the relationship between

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3 departure time choice and mode choice, one needs to consider a rigorous simultaneous equations modeling framework. Treating both mode choice (SOV vs non-SOV) and departure time choice (peak vs off-peak period ) as a set of two binary choice variables, the recursive bivariate probit modeling methodology provides a rigorous flexible framework in which to analyze the caus al relationship between them [10]. 1.3 Objective and Scope of the Study The central question addressed in this study is: what is the causal relationship between departure time choice and mode choice for non-work trips? One may conjecture that people engaging in activities in the off-peak period may choose to travel by automobile because of the reduced traffic c ongestion and possibly poore r transit levels of service during such periods. Conversely, peop le choosing to travel by the automobile may arrange their activities such that they can do so in the off-peak periods to avoid congestion. Similar causal relationships may be considered in the context of peak period travel and/or non-auto travel. Thus, one may hypothesize causal relationships between departure time choice and mode choice that are opposite to one another. This study attempts to shed light on this issue by identify ing the causal structure that is statistically supported by travel survey da ta collected in 1999 from a sample of households in the Southeast Florida region consisting of MiamiDade, Broward, and Palm Beach counties. 1.4 Outline of Thesis This thesis is composed of six chapters. This chapter has provided an introduction about the background and the purpose of the st udy as well as literature review. The rest

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4 of the thesis is organized as follows. Chapte r 2 provides a summary of a literature review on the topic of interest. Ch apter 3 presents the model formulation and estimation methodology for the two alternative causal stru ctures. Chapter 4 introduces the Southeast Florida Regional Household Travel Survey and provides a description of the survey sample. Model estimation results are presen ted in chapter 5, including a performance comparison between the models to help iden tify the causal structure(s) supported by the data set from a statistical standpoint. Conc lusions are drawn and some recommendations for future research are given in the sixth and final chapter.

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5 CHAPTER 2 LITERATURE REVIEW 2.1 Need for Time-of-day Modeling Procedures The need for incorporating time-of-day modeling into conven tional travel demand models has been mentioned in the introduction of this thesis. This need for enhancing travel demand models to have the ability of analyzing travel conditi ons at different times of day is driven from the emerging requi rements of recent transportation planning policies on the local and national level. These policies mainly focus on how to deal with the issues of congestion and air quality with in the context of traffic management and transportation planning. It is widely recognized that the magnitude of congestion and vehicle emissions (and poor air quality) are very much rela ted to the extent of peak period auto travel. Developing tr avel demand models that predic t travel at different times of day by different modes of travel, includi ng peak/ off-peak periods and SOV/ Non-SOV modes, may be a way to address the re quirements of contemporary transportation policies. Some of the rising requirements of such policies are outlined below [2]: Vehicle Emissions and Air Qu ality Analysis. Strict ai r quality standards have been established by the Federal Clean Air Act Amendments (CAAA) and State Clean Air Acts. Travel demand models provide necessary variables required for the analysis of vehicle emissions (including traffic volumes,

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6 vehicle speeds, traffic compositions, ve hicle-miles and hours of travel by facility type, by vehicle type, by hour of the day, and by vehicle starting mode). However, because emission leve ls change with different vehicle speeds, variables that describe vehicle volumes and speeds by time-of-day are also required. Congestion Management Programs. Travel demand models are required to be capable of precisely predicting travel speed, congestion, delay, and time-ofday to cope with the rigorous analytic al standards of the Intermodal Surface Transportation Efficiency Act (ISTEA ), and State Congestion Management Programs. In order to justify the replacement of capacity addition and improvement with traffic management strategies on existing transportation facilities, travel demand models must captu re the effect of these strategies on time-of-day travel. Identification of Highway System Pr oblems. Many urban areas are suffering from roadway problems such as rout e diversions caused by peak period congestion. In order to accurately estimate peak travel demands, travel demand models need to account for route diversions because the severity of the peaking and the congestion vary th roughout the urban area and over time. Transit Analysis. Accurately capturing the amount of transit travel has long been a challenge for travel demand m odeling in urban areas. Because mode choice models are commonly applied at the daily level, they do not account for variations in transit service ava ilability throughout the day. As a result, these models are not able to forecast transit mode share in cases where

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7 alternatives may considerab ly change transit ridership trends across peak and off-peak time periods. Analysis of Transportation Demand Ma nagement (TDM) Alternatives. TDM alternatives target such groups as pe ak period travelers (mainly home-to-work commuters) and are aimed at reducing peak traffic congestion, decreasing SOV travel dependency, and dealing with air quality and other environmental issues connected to auto travel. Park ing charges, congest ion pricing, transit subsidies, variable work hours, and telecommuting are some types of TDM policies that involve peak tr avel analysis capabilities. Time-of-Day Travel Choices. These alte rnatives are aimed at significantly changing the times and costs of trave ling during peak periods. Models that deal with the above should be capabl e of capturing the effect of peak spreading, in which many travelers that are more temporary flexible than others try to avoid delays by shifting departure times away from peak hour. Analysis of Intelligent Transportati on Systems (ITS). Many urban areas are considering ITS as a lower-cost altern ative to capital improvements. ITS systems incorporate advanced traffic ma nagement systems, advanced traveler information systems, commercial vehicle operations, and advanced public transportation systems. In order to quan tify the benefits of ITS, models should be enhanced to precisely measure ch anges in the operational context that includes traffic volumes, speed, delay, and queuing by time-of-day.

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8 2.2 Time-of-day Modeling in Four-step Modeling Paradigm There are various methods used for time -of-day modeling within the traditional four-step modeling framework. Commonly us ed methods throughout the United States are presented within the context of the Trav el Model Improvement Plan (TMIP) of the U.S. Department of Transportation [2]. TMIP also documents the most innovative methods, and emerging methods to estimate time-of-day travel demands. This section summarizes time-of-day modeling procedures as presented in the TMIP program. 2.2.1 Standard Approaches A first step in time-of-day modeling is to define the peak period or peak hour. This could be done for a weekday trip datase t from local or national surveys. During the average weekday, there are typically two dom inant peak periods: morning (AM) peak and afternoon (PM) peak. A peak period is iden tified by its maximum trip rate in trips per unit time. On the other hand, peak hour is the hour of the day with the highest traffic. “Shoulders of the peak” is a term used to de scribe the segments of the peak before and after the peak hour. In traditional four-s tep modeling, peaking and time of travel are incorporated in a greatly approximate fashion by producing time-of-day factors (TDOF) derived from observed data. The basic assumption, however, is that travel patterns will remain constant over the years. A TDOF is defined as “the ratio of vehicle trips made in a peak period (or peak hour) to vehicle trips in some given base period, usually a day” [2]. TDOF’s, usually fixed and independent of congestion le vels, are either determined separately for each trip purpose form household activity/trave l or on-board transit and intercept auto

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9 surveys, or from traffic data from special surveys (travel su rveys at workplaces or major businesses/ activity centers) depending on the point at which they are applied in the modeling process. Time-of-day factors may be assigned at four points in the four-step model: After trip assignment; Between mode choice an d trip assignment; Between trip distribution and mode choice; and Between trip generation and trip distribution. Time-of-day assignment after trip assi gnment is the most commonly used and simplest method and is used in smaller ur ban areas where there is limited congestion. This method requires minimal labor and data. Data requirements include peak period link-level peak hour factors a nd directional split factors. This method however, does not take into account peak travel times in assignments and congested times are not considered for trip distribution and mode split. Further, it does not account for localized effects of changes in demand. Time-of-day assignment between mode choice and trip assignment is another broadly used method and may be applicable in areas that suffer from least congestion. It requires factors of the trips by purpose and by mode for each hour and direction (production-to-attraction or attrac tion-to-production) as well as directional split factors. Disadvantages of this method include failure to account for congested times in trip distribution and mode split and the lack of se nsitivity to general policy changes, rising congestion, and corridor or subarea-specific changes.

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10 Time assignment between trip distributi on and mode choice is a limited use method applicable in the least congested ar eas. Data required to produce time-of-day factors involves hourly totals of trips by purpose for each direction (production-toattraction or attraction-to-production) and dire ctional split factors. This method fails to account for effects of time-of-da y characteristics such as congestion or transit levels of service in the formation of time-period base d trip tables. Another limitation of this method is that congested times are not accounted for in trip distribution and mode split. Time-of-day assignment between trip gene ration and trip distribution is another limited use method and may be applied in urban areas with minimal congestion. Directional hourly time-of-day factors of trips by purpose a nd mode, and directional split factors are required for this method. A majo r advantage of this approach is its time efficiency in the model application. In addi tion, trip distribution and mode choice may be done according to differences in travel charac teristics by time-of-day. On the other hand, this procedure can not capture the effects of changes in policies, increasing levels of congestion, or congestion management measures. 2.2.2 Innovative Approaches Standard approaches of tim e-of-day modeling, described in the previous section, offer only approximate estimates of time-of -day effects on travel. Various agencies around the U.S. are using innovative methods, w ithin the four-step modeling context, that offer a more realistic approach to time-of-d ay modeling. These methods incorporate peak spreading, a process that deals with the issue that in certain corrido rs projected demand exceeds capacity during the peak period and th at ignoring the effects of excess demand

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11 yields to an inaccurate estimate of future travel conditions. TMIP presents three innovative approaches to improving the time-of-day modeling process: Link-based peak spreading Trip-based peak spreading System-wide peak spreading Link-based peak spreading is a limited-use method developed in Phoenix, AZ that accounts for congestion at the link level and shifts trips to the shoulders of the peak period. The method includes peaking factor func tions by facility type reflecting the peak hour to peak period volume ratio. These func tions are derived by means of a decreasing function of the link three-hour volume-to-cap acity ratio. This me thod, although providing more accurate estimates of regional travel performance measures, does not guarantee continuity of link flow in the peak hour prediction and does not account for further spreading of the peak beyond a three-hour period. Used in Tri-Valley, CA, Boston, MA, and Washington, DC, the trip-based peak spreading method distributes the number of pe ak period or peak hour trips for an origindestination interchange. The method requires in terchange-specific peak hour factors, that may also be trip purpose-specific, that are ap plied to daily trip tables. A disadvantage of this method lies in the fact that it is not e fficient in treating the reduced off-peak trips. Further, it fails to account for changes in traveler behavior associated with congestion. System-wide peak spreading takes into account the system-wide (rather linkspecific or trip-specific) travel demand and delay surplus, and spreads excess travel demand between the separate travel hours of the peak period. It is a limited-use method

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12 implemented by the Volpe National Trans portation System Center (VNTSC) for evaluating Intelligent Transportation Syst ems. The underlying assumption is that a considerable amount of travel information is available to tr avelers through ITS and their reaction to congestion can then be modeled on a system-wide basis. Disadvantages this method lies in the fact that it is not sensitive to different trip purposes or link-specific or origin-destination-sp ecific congestion. 2.2.3 Emerging Approaches The effects of policy changes and TDM pro cedures may not be fully captured by the peak spreading time-of-day procedures described in the prev ious section. The framework of emerging approaches is based on modeling traveler re sponse to congestion in a very similar way that mode choice is modeled within the traditional four-step modeling paradigm. A number of urban areas around the country (including San Francisco, Portland, Sacramento, Jacksonville, and Tampa Bay) are considering such methods and have proposed various approaches including the following: A time of day choice logit model applicable after m ode choice and capable of predicting the period of travel as a functio n of variables that capture free flow and congested travel times, transit level of service, trip purpose, and area type variables. A model predicting whether peak period trips occur in the peak or off-peak hour. This could be in a fo rm of a logit model as pa rt of a “variable demand” multiple vehicle class assignment which guarantees that the outcome of the

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13 peak hour models are in agreement w ith the congestion resulting from the assignment. A model based on the underlying assumpti on that relatively higher congestion levels during peak time tends to increas e the propensity of choosing off-peak departure time. Such model would combine traditional time-of-day factors and a binary time-of-day choice model. Th e choice model would be estimated by congestion variables such peak/off-p eak travel times, delays, etc. 2.3 Previous Studies on Departure Time Choice Early studies involving depa rture time choice have focused mainly on work or commuting trips. Indeed, commuting directly contributes to morning and afternoon peak period congestion. The direct link between wo rk trips and peak tr avel has provided researchers the necessary impetus to undertak e studies that aim at modeling departure time choice of commuters and understand ing the relationship between commuter departure time choice and traffic congestion le vels. Noland and Small [5] used models of commuting time-of-day choice to analyze the eff ect of uncertain travel times, relating this uncertainty in time-of-day choice to the cost of early or late arrival at work. It should be pointed out, however, that most researchers, e.g., Kumar and Levinson [6], do not omit to recognize the interaction of wo rk-trips and non-work trips and the role of non-work trips in travel demand analysis. They state that on weekdays, workers are more likely to pursue shopping and other non-work trips on the way home from work, while nonworkers are more prone to execute such trips during off-peak periods. This study recognizes the rising im portance of non-work trips as a ma jor contributor to urban traffic

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14 congestion and automobile emissions and at tempts to model the relationship between departure time choice and mode choice for su ch trips. As Lockwood and Demetsky [7] note, non-work travel accounts for more than three-quarters of the total trips in urban areas and are growing faster than work trips as suburbanization and ch anges in lifestyles alter travel behavior. The interest in modeling non-work trips also lies in their inhere nt nature of being more flexible than work trips in terms of the individuals’ time-of-day choice and mode choice. For certain types of non-work activ ities, such as shopping, the departure time flexibility is evident and th erefore travelers may have a greater tendency to shift departure times than shift modes in response to transportation control measures [1]. Similarly, social-recreation trips may be pursu ed at various times of the day unless the activity involves rigid time and space constraint s such as those associated with concerts, sporting events, and movies. With respect to mode choice, non-work activities and trips tend to be undertaken jointly with other household members or friends [8, 9]. Such joint coupling constraints may make mode sw itching quite difficult; on the other hand, departure time shifts may still be feasible, pa rticularly in today’s context of real-time activity scheduling using cellula r communications technology.

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15 CHAPTER 3 MODELING METHODOLOGY 3.1 The Recursive Simultaneous Bivariate Probit Model The recursive simultaneous bivariate probit model, which allows the analysis of one-way causal relationshi ps between two choice behaviors, is employed in this study. In this formulation, the random error terms in the simultaneous equation system are assumed to follow the bivariate normal dist ribution. The bivariate normality assumption implies that two endogenous dummy variable s may not coexist in mutual functional relations. The existence of an endogenous du mmy variable in eith er function corresponds to two different causal structures as illustrated later in this section. Intuitivel y, this feature of the bivariate probit model provides an appropriate approach to distinguish the causality between departure time choice and mode choice. However, it should be noted that this approach also entails an underlying assump tion that an explicit unidirectional causal relationship (or at least the te ndency of such a unidirectional causal relationship) exists in the population being studied. 3.2 Model Structure and Formulation Two different possible caus al structures are cons idered in this study: Mode choice Departure time choice (recurs ive bivariate probit model) Departure time choice Mode choice (recursive bivariate probit model)

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16 Through a performance comparison of models between the two causal structures, it is envisaged that the relationship between departure time choice and mode choice may be discussed and clarified. If the departure time choice (peak vs off-peak) and SOV/non-SOV mode choice are treated as two binary choices, the bivariat e probit model can be formulated at the trip level to simultaneously analyze their probab ilities with accommoda tion of random error correlation. The general formula tion is as follows: q q q q q q q qM x T T z M '* (3.1) where, q is an index for observations of trips ( q = 1, 2, … Q) Mq is a latent variable represen ting the mode choice for trip q Tq is a latent variable representing the departure time choice for trip q Mq = 1 if Mq > 0, = 0 othe rwise, i.e., Mq is a dummy variable indicating whether trip q uses the SOV mode Tq = 1, if Tq > 0, = 0 otherwise, i.e., Tq is a dummy variable indicating whether trip q is made in the peak period zq is a vector of explanatory variables for Mq xq is a vector of expl anatory variables for Tq are two vectors of model coefficien ts associated with the explanatory variables zq and xq, respectively

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17 is a scalar coefficient for Tq to measure the impact of departure time choice on mode choice is a scalar coefficient for Mq to measure the impact of mode choice on departure time choice q andq are random error terms, which are standard bivariate normally distributed with zero means, unit variances, and correlation i.e., q q ~) 1 1 0 0 (2 Based on this normality assumption, one can derive the probability of each possible combination of binary choices for trip q : ] ' [ ) 0 0 (2 x z T M prob (3.2) ] ), ( [ )] ( [ ) 0 1 (2 1 x z x T M prob (3.3) ] ), ( [ )] ( [ ) 1 0 (2 1 x z z T M prob (3.4) )] ( [ )] ( [ 1 ) 1 1 (1 1 x z T M prob ] ), ( ), ( [2 x z (3.5) where, ] [1 is the cumulative distribution f unction for standard univariate normal distribution ] [2 is the cumulative distribution f unction for standard bivariate normal distribution.

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18 The sum of the probabilities for the four combinations of two binary choices should be equal to one, i.e., 1 ) 1 1 ( ) 1 0 ( ) 0 1 ( ) 0 0 ( T M prob T M prob T M prob T M prob (3.6) Substituting equations (3.2) through (3.5) in to equation (3.6), it can be shown that ] ), ( ), ( [ ] ' [2 2 x z x z ] ), ( [ ] ), ( [2 2 x z x z (3.7) This equation does not hold unless either or is equal to zero. This requirement, known as the logical consistenc y condition, will lead to two different recursive simultaneous modeling structures [11] suggesting two different causal relationships: 0 0 (Mode Choice Departure Time Choice) q q q q q q qM x T z M '* (3.8) In this structure, mode choice is pr edetermined as per the first functional relationship. Then, the choice of mode is specified as a dummy variable in the second functional relationship for departure time choice to directly measure the impact of mode choice on time-of-day choice. 0 0 (Departure Time Choice Mode Choice) q q q q q q qx T T z M '* (3.9)

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19 Conversely, one may consider the altern ative structure in which departure time choice is predetermined as per the second func tional relationship. The trip departure time is specified as an explanatory variable influe ncing mode choice as pe r the first functional relationship. Thus, the desirable feature of the bivariat e probit model in which the coefficients of two endogenous dummy variables do not co exist in both functional relationships provides an appropriate mode ling framework to analyze th e unidirectional causality between trip departure time and mode choice. 3.3 Formulation of Likelihood Functions The endogenous nature of one of the de pendent variables in the simultaneous equation system can be ignored in formul ating the likelihood func tion. To facilitate formulating likelihood functi ons, equations (3.2) through (3 .5) can be rewritten in a format including only the cumulative distri bution function of the standard bivariate normal distribution. ] ' [ ) 0 0 (2 x z T M prob (3.10) ] ), ( [ ) 0 1 (2 x z T M prob (3.11) ] ), ( [ ) 1 0 (2 x z T M prob (3.12) ] ' [ ) 1 1 (2 x z T M prob (3.13) Equations (3.10) through (3.13) and th e corresponding likelih ood functions can be summarized by the following general formulati ons for the two different unidirectional causal structures [12]:

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20 0 0 (Mode Choice Departure Time Choice) ] ), ( [2 q q q q q q q qM x z prob (3.14) Q q q q q q q q qM x z L1 2), ( (3.15) 0 0 (Departure Time Choice Mode Choice) ] ), ( [2 q q q q q q qx T z prob (3.16) Q q q q q q q qx T z L1 2, ), ( (3.17) where, 1 2 q qM and 1 2 q qT As the likelihood functions of the recu rsive bivariate probit model and the common bivariate probit model are virtually identical, parameter estimation can be accomplished using readily available software such as LIMDEP 8.0 [13].

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21 CHAPTER 4 DATA SET AND SAMPLE DESCRIPTION 4.1 The Southeast Florida Regi onal Household Travel Survey The dataset used in this study is draw n from the Southeast Florida Regional Household Travel Survey which was conduc ted during 1999 in the Southeast Florida region consisting of Miami-Dade, Broward, a nd Palm Beach counties. The travel survey consisted of three parts: A CATI (computer aided telephone interv iew) recruitment, a mail-out of survey instruments and travel di aries, and a CATI retrieval of the survey responses. Households agreeing to particip ate in the survey we re mailed a survey package including a travel diary for each me mber of the household. As with most household travel surveys, this survey colle cted detailed socio-demographic and trip information for each person in the household. The 24-hour travel diary was organized around tours to minimize potential under-reporting of short trip s. A tour was defined as a series of trips that began at home, visite d other locations, and ended at home. More details about the survey a nd sampling methodology and an extensive description and graphical presentation of the survey inst ruments are provided by The Corradino Group [14]. The sampling procedure employed was based on a geographically stratified random sampling methodology in order to ensure that the survey sample had adequate geographic coverage for the entire Southeast Florida region. Surveys were collected from

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22 households in Broward, Miami, and Palm Be ach counties. Each of these counties was further subdivided into survey districts a nd a stratified random sample was drawn to obtain appropriate geographi c coverage. A total of 5,168 households completed the survey, and out of these households, 5,067 had valid addresses within the tri-county region. Approximately 34 percent of the surv eys were collected in Broward County, and 33 percent each in Miami-Dade and Palm Beach counties. The surveys provided a respondent sample of 11,426 persons repor ting a total of 33,082 trips. The socioeconomic, demographic, and travel characte ristics of the respondent sample were generally consistent with those of the population in the region. 4.2 Household Characteristics of the Survey Sample A summary description of house hold characteristics of the survey data is shown in Table 4.1. The average household size is a bout 2.6 persons per hous ehold with nearly 30 percent of the households reporting household sizes of 4 or more persons. About twothirds of the households have annual incomes greater than $30,000 per year. On average, households own about 1.8 vehicles per househ old with only four pe rcent reporting no vehicles. More than 60 percent have two or more vehicles in the household. Likewise, about 60 percent of the households live in a single-family dwelling unit. The average number of licensed drivers, at nearly two drivers per househol d, is consistent with the average household size and vehicle owne rship figures. About 60 percent of the households report having no ch ild under the age of 18 years. The average number of workers is about 1.6 workers per household.

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23Table 4.1. Household Characteristics of Southeast Florida Household Travel Survey Characteristic Statistic Sample Size 5067 Household Size 2.66 1 person 17.7% 2 persons 34.2% 3 persons 18.3% 4 persons 29.8% Annual Income $15 K or less 12.2% $15 K $30 K 19.9% $30 K $50 K 27.8% Greater than $50 K 40.1% Vehicle Ownership 1.80 0 auto 3.9% 1 auto 33.3% 2 autos 45.5% 3 autos 17.3% Dwelling Unit Type Single-family dwelling unit 59.4% Apartment 27.1% Mobile Home 1.8% Condo 11.1% Other 0.5% Average No. of Licensed Drivers 1.95 0 licensed drivers 1.6% 1 licensed driver 27.0% 2 licensed drivers 53.8% 3 licensed drivers 12.8% 4+ licensed drivers 4.8% Average No. of Children (under 18) 0.75 0 children 58.3% 1 child 18.0% 2 children 15.9% 3+ children 7.8% Average No. of Workers 1.6 0 workers 18.7% 1 worker 30.2% 2 workers 38.2% 3+ workers 12.9%

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244.3 Departure Time, Mode Choice, and Travel Patterns of the Sample A set of figures and tables, describing the nature of trips, time-of-day and mode choice population characteristics of the Southe ast Florida Region are presented in this chapter. These figures are useful in understand ing the travel patterns of the particular region of interest. Further, they are impor tant in understanding and comparing travel patterns between different population groups w ithin the dataset and have helped in drawing useful conclusions for the further ti me-of-day/ mode choice analysis of this study. 4.3.1 All Trips Figures 4.1 through 4.4 and Table 4.2 show characteri stics for all trips drawn from the original trip file (33,082 trips). A distribution of trips by purpose (Figure 4.2) shows that the majority of trips are work related (home-based work) and home-based other, each having a share of about 23%. SOV combined with car-pool constitute of the highest mode share (81%) with an almost negligible percentage of public transit trips (1%) (Table 4.2). A time-of-day distribution (Figure 4.1) shows two peaks, as expected, representing morning (7:00 am – 9:00 am ) and afternoon (4:00 pm – 6:00 pm) peak periods. The afternoon peak period seems to be not as distinct as the morning peak extending two hours to the left shoulder of the peak (2:00 pm – 4:00 pm). This is indicative of the peak-spreading phenomenon e xplained in Chapter 2 and later in Chapter 5 of this thesis. In Figure 4.3 the peak periods are clearer for SOV and car-pool modes as opposed to non-motorized and “oth er” travel modes in which af ternoon trips peak in the early afternoon rather than during the typical 4:00 pm – 6:00 pm period. The distribution

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25 of public transit trips indicate service stari ng at 5:00 am and ending at 11:00 pm with a better service during morning commute. Gene rally, non-SOV trips demonstrate a longer afternoon peak period (2:00 pm – 6:00 pm) than SOV trips (Figure 4.4). Fi g ure 4.1. Time-of-Da y Distribution of All Trips (N = 28889)0 2 4 6 8 10 12 14 01234567891011121314151617181920212223 Time of Day (Hour)Percent of Trips Note: missing values are excluded Table 4.2. Mode Share of All Trips (N = 33082) Mode Share SOV 46.2 Pool 35.1 Public Transit 1.1 Non-Motorized 3.4 Other 1.5 Missing 12.7 Total 100.0 Note: modes are categorized: SOV (car, motor-cycle), Pool (car/van pool, multi-passenger auto), Public Transit (bus, train, jitney), Non-motorized (walk, bi ke, run, roller-blade), Other (taxi, school-bus, airplane), and Missing (don't know, refused and missing)

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26 Figure 4.2. Distribution of All Trips by Purpose (N = 33082)0 5 10 15 20 25 Trip PurposePercent of Trips HB Work HB Shop HB Soc. Rec. HB School HB Other HB Unknown Non-HB Work Non-HB Other Figure 4.3. Time-of-Day Distribution of All Trips by Mode (N = 24677) 0 5 10 15 20 25 30 01234567891011121314151617181920212223 Time of Day (Hour)Percent of Trips SOV Pool Public Transit Non-motorized Other Note: missing values are excluded

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27 Note: missing values are excluded 4.3.2 Work Trips Figure 4.5 shows a time-of-day distribution of all work trips made by adults of 18 years of age or older. By looking at the chart someone can clea rly distinguish both morning and afternoon peak periods a ssociated with commute travel. The 7th and 17th hours combined constitute of more than 30% of trips indicating hi ghest commute activity during those hours. The mode share of work tr ips (Table 4.3) also appears to be in agreement with expectations. The vast majori ty of work trips (more than 75%) are made by drive-alone mode while car-pooling falls fa r behind with only around 11%. It is not a surprise that public transit a nd non-motorized travel are almo st negligible and in accord with national numbers. Consid ering the fact that Southeas t Florida is a very autoFigure 4.4. Time-of-Day Distribution of All Trips by Mode: SOV vs Non-SOV (N = 24677) 0 2 4 6 8 10 12 14 01234567891011121314151617181920212223 Time of Day (Hour)Percent of Trips SOV Non-SOV

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28 dependant region and public transit service is limited (despite the existence of the relatively new Miami metro) the above numbers make sense. As indicated in the above discussi on and corresponding figures, work-related travel behavior seems to be rather predictable in nature. Work travel is auto-oriented revolving around the typical peak periods. This is one reas on for choosing to analyze non-work travel behavior for the purposes of this study, as mentioned in the introduction. Since this thesis is not aimed in analyzing wo rk trip patterns, the discussion on work trips is limited. Figure 4.5. Time-of-Day Distribution of Work Trips (N = 6638)0 2 4 6 8 10 12 14 16 18 20 01234567891011121314151617181920212223 Time of Day (Hour)Percent of Trips Note: missing values are excluded

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29Table 4.3. Mode Share of Work Trips (N = 9788) Note: modes are categorized: SOV (car, motor-cycle), Pool (car/van pool, multi-passenger auto), Public Transit (bus, train, jitney), Non-motorized (walk, bi ke, run, roller-blade), Ot her (taxi, school-bus, airplane), and Missing (don't know, refused and missing) 4.3.3 Non-work Trips Figures 4.6 through 4.8 and Table 4.4 pres ent general characteristics of all nonwork trips made by adults of 18 years of age or older. Unlike work trips, the distribution of non-work trips by time-of-day (Figure 4. 6) is described by one major peak point (morning peak period) and a substantial conc entration of trips along the early to late afternoon hours. The majority of non-work trips are made by SOV mode (Table 4.6). However, there is a substantial percentage of ride-sharing trips (46%) which may be explained by the general tendency of non-wo rk trips to be undertaken jointly in accommodating obligations of households of di fferent auto-availability. A time-of-day distribution by SOV vs. Non-S OV modes (Figure 4.8) shows a strong morning peak for car-pooling trips. This peak may be associated with the presence of drop-off school trips and other non-work trips linked with the mo rning commute. On the other hand, drivealone non-work travel seems to be more temp orally flexible with most trips occurring uniformly during the course of the day. Mode Share (%) SOV 75.4 Pool 12.3 Public Transit 1.3 Non-Motorized1.8 Other 0.02 Missing 9.2 Total 100.0

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30 Figure 4.6. Time-of-Day Dist ribution of Non-Work Trips (N = 22251)0 2 4 6 8 10 12 01234567891011121314151617181920212223 Time of Day (Hour)Percent of Trips Note: missing values are excluded Table 4.4. Mode Share of Non-Work Trips (N = 14727) Note: modes are categorized: SOV (car, motor-cycle), Pool (car/van pool, multi-passenger auto), Public Transit (bus, train, jitney), Non-motorized (walk, bi ke, run, roller-blade), Ot her (taxi, school-bus, airplane), and Missing (don't know, refused and missing) Mode Share (%) SOV 49.9 Pool 45.0 Public Transit 0.9 Non-Motorized3.9 Other 0.3 Total 100.0

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31 Figure 4.7. Time-of-Day Distributi on of Non-Work Trips by Mode (N = 22251)0 2 4 6 8 10 12 14 01234567891011121314151617181920212223 Time of Day (Hour)Percent of Trips SOV Pool Public Transit Non-motorized Note: missing values are excluded Fi g ure 4.8. Time-of-Da y Distribution of Non-Work Trips b y Mode: SOV vs Non-SOV (N = 14727)0 2 4 6 8 10 12 01234567891011121314151617181920212223 Time of Day (Hour)Percent of Trips SOV Non-SOV Note: missing values are excluded

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324.4 Preparation of Datasets for Modeling In preparing the available survey data for modeling, all origin and destination locations in the original trip file were ge ocoded to latitude/longitude and to the traffic analysis zone (TAZ) of the Southeast Regi onal Planning Model. The household travel survey trip data set was therefore augmented with secondary data. Modal level of service (LOS) data was extracted from th e Southeast Regional Planning Model. This data provided information on travel times, distances, and costs between each pair of TAZ’s in the Southeast Florida Region for both peak and off-peak periods. The LOS data was merged into the trip file producing a new da taset with added moda l LOS characteristics by time-of-day for each origin-destination TAZ pair. The merging process as well as the descriptive analysis of the data was performed with the aid of SPSS Version 11.5 statistical software [18]. This study focuses on the relationship between time-of-day choice and mode choice for non-work trips made by adults. Fo r this reason, all non-work trips made by persons 18 years of age or older were extracted from the original dataset. In addition, this study distinguishes between workers (employe d) and non-workers (unemployed) in an attempt to capture the effect of potential differences in temporal and modal choice flexibility between these two groups. For example, workers might link their non-work trips to the commute while non-workers might make use of their travel flexibility to avoid congestion during peak hours. From the original trip data set, all non-work trips that had complete information including household and person socio-economic da ta, trip attribute data, and modal LOS data were extracted. Th is subsample of trips included a total of

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33 14,410 non-work trips of which 7,947 were ma de by 2,710 workers and 6,463 were made by 1,741 non-workers. Non-work trips include the following trip categories: Home-based Shopping/Personal Business Home-based Social Recreation Home-based School Home-based Other Non-home-based Non-work 4.5 Workers and Non-workers Sample Characteristics Table 4.5 offers a description of person characteristics for the subsamples of workers and non-workers used in this study. In general, the non-worker sample includes a large proportion of elderly and retired people, thus pushing the average age up to 57 years. The corresponding average age for work ers is 41 years. A bout 80 percent of the worker sample is employed full time while th e remainder is employed part time. A vast majority of the persons in both samples are full time residents of the area. As expected, average daily trip rate for wo rkers is slightly higher than non-workers presumably due to the presence of commute trips for workers. On average, workers make about five trips per day while non-workers make a lit tle over four trips per day. Time-of-day distributions of non-work trips are shown in Figure 4.9 for both worker and non-worker samples. The differe nces between the two graphs are rather striking. The time-of-day distribution for wo rkers shows two peaks that are coincident with the commute peak periods. This dist ribution suggests that workers may be more

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34 inclined to link their non-work trips with their work trips. However, the peaks are not as well defined as one might encounter in the cas e of work trips suggesting that there is a substantial portion of non-wo rk travel occurring during offpeak hours as well. The timeof-day distribution pattern for non-workers is consistent with expectations and quite different from that of workers. The dist ribution shows that non-workers tend to make non-work trips during the midday period. There may be several reasons for this distributional pattern including th e desire to avoid traveling in the peak periods for trips that are flexible in the temporal dimensi on. A time-of-day distri bution by mode (Figure 4.10) shows that workers may utilize the be tter transit service during the morning and afternoon peak periods to accommodate nonwork activities within their commute. Further, the majority of non-motorized trips by workers tend to be associated with the morning commute while a significant amount of such trips is concen trated in the early evening hours. In general, workers traveli ng alone tend to take on their non-work trips throughout the course of day looking to a void the peak hour, while those who use alternative modes (mostly ride-sharing) ar e more temporally constraint around the commute peak periods (Figure 4.11). On the other hand, non-workers, being more temporally flexible than workers due to the absence of work schedule, are more likely to try to avoid the peak hour weather they ar e driving alone, ride-sharing, or walking/ bicycling (figures 4.12 and 4. 13). There seems to be an exception for transit use however, where more frequent service during the morni ng hours may be a stronger factor than peak traffic for special groups of non-workers who are dependent on transit (Figure 4.12).

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35Table 4.5. Person Characteristics of So utheast Florida Household Travel Survey Statistics Characteristic Workers Non-workers Sample Size 2710 1741 Average Age (in years) 41 57 18 to 24 years 10.2% 8.0% 25 to 54 years 73.9% 29.4% 55 to 64 years 9.9% 14.2% 65+ 4.2% 45.4% Employment Status Full time 81.3% Part time 18.6% Resident Status Full time 98.7% 92.0% Part time 1.3% 7.9% #Trips per day 5.08 4.32 Notes: Workers are defined as those who indicated that they are employed. Non-workers are defined as those who indicated that they are unemployed. Fi g ure 4.9. Time-of-da y Distribution of Non-Work Trips: Workers vs Non-Workers0 2 4 6 8 10 1201234567891011121314151617181920212223Time of Day (Hour)Percent of Trips Non-Workers (N=6463) Workers (N=7947)

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36 Figure 4.10. Time-of-Day Distribution of Workers Non-Work Trips by Mode (N = 7947)0 2 4 6 8 10 12 14 16 18 01234567891011121314151617181920212223 Time of Day (Hour)Percent of Trips SOV Pool Public Transit Non-motorized Figure 4.11. Time-of-Day Distribution of Workers Non-Work Trips by Mode: SOV vs Non-SOV (N = 7947)0 2 4 6 8 10 12 14 01234567891011121314151617181920212223 Time of Day (Hour)Percent of Trips SOV Non-SOV

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37 Figure 4.12. Time-of-Day Distribution of Non-Workers Non-Work Trips by Mode (N = 6463)0 2 4 6 8 10 12 14 01234567891011121314151617181920212223 Time of Day (Hour)Percent of Trips SOV Pool Public Transit Non-motorized Figure 4.13. Time-of-Day Distribution of Non-Workers Non-Work Trips by Mode SOV vs Non-SOV (N = 6463)0 2 4 6 8 10 12 14 01234567891011121314151617181920212223Time of Day (Hour)Percent of Trips SOV Non-SOV

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38 Crosstabulations of time-of-day choice w ith mode choice are shown in Tables 4.6 and 4.7. Both choice variables are represen ted in a binary format to facilitate the development of the crosstabulation in a ma nner consistent with the treatment of the variables in the model specificati on. In Table 4.6, it is found that a majority of off-peak non-work trips (56 percent) by workers are made by SOV mode. On the other hand, a majority of peak non-work trips (54 pe rcent) are made by non-SOV mode. An examination of the row percentages shows that while 72 percent of SOV trips are made in the off-peak period, the corresponding percen tage for non-SOV trips is only 64 percent. These tendencies suggest that there is a negative relations hip between SOV mode choice and travel in the peak period. Similar trends are seen in Table 4.7 fo r non-workers, although the tendencies do not appear to be as strong. More than 75 percent of non-workers trips occur in the offpeak period. A slightly higher percentage of SOV trips occur in the off-peak period. Similarly, it is found that about 48 percent of off-peak trips are made by SOV while a slightly smaller percent of p eak period trips (44 percent) are made by SOV. Thus, even for non-workers, it appears that there is a s light inverse relationship between SOV mode choice and peak period travel.

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39Table 4.6. Crosstabulation of Depart ure Time Choice by Mode Choice: Worker Sample (N = 7947) Departure Time Choice Mode Choice Non-Peak Peak Total Frequency Non-SOV 2399 1350 3749 SOV 3041 1157 4198 Total 5440 2507 7947 Column Percent Non-SOV 44.1 53.8 47.2 SOV 55.9 46.2 52.8 Total 100 100 100 Row Percent Non-SOV 64.0 36.0 100 SOV 72.4 27.6 100 Total 68.5 31.5 100 Table 4.7. Crosstabulation of Depart ure Time Choice by Mode Choice: Non-worker Sample (N = 6463) Departure Time Choice Mode Choice Non-Peak Peak Total Frequency Non-SOV 2563 831 3394 SOV 2404 665 3069 Total 4967 1496 6463 Column Percent Non-SOV 51.6 55.5 52.5 SOV 48.4 44.5 47.5 Total 100 100 100 Row Percent Non-SOV 75.5 24.5 100 SOV 78.3 21.7 100 Total 76.9 23.1 100

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40 CHAPTER 5 RESULTS 5.1 Model Estimation Results Model estimation results are presented in th is section. Tables 5.1 and 5.2 offer descriptions of the variables used in the m odels. The variables constitute a series of dummy variables describing socio-economic ch aracteristics on the household and person levels as well as modal LOS’s. Both causal structures, i.e., mode choice affects departure time choice and departure time choice affects mode choice, are estimated separately for the worker and non-worker samples.

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41Table 5.1. Description of Variables Used in Workers Non-work Trip Models (Sample Size = 7947) Variable Name Variable Description Mean Std Dev AGE18_24 Person is between 18 and 24 years of age 0.09 0.29 CHILD2P Number of children in the household is equal to or greater than 2 0.31 0.46 COMMUT15 One-way commute time for person is equal to or greater than 15 minutes 0.36 0.48 FTJOB Person has a full-time job 0.77 0.42 HHSIZE1 Single person household 0.10 0.30 HHSIZE3P Household size is equal to or greater than 3 0.61 0.49 HWRUN30 Peak-period highway run time without HOV lane is equal to or greater than 30 minutes 0.13 0.34 INC_100K Annual income of household is equal to or greater than $100,000 0.15 0.35 NOCHILD Household has no children 0.48 0.50 PEAK Departure time of trip is in peak period (7:00am-9:00am or 4:00pm-6:00pm) 0.32 0.53 PT_RES Person is a part-time resident 0.02 0.14 SCHOOL Primary purpose of trip is school 0.05 0.22 SOV Trip mode is single-occu pancy vehicle (SOV) 0.46 0.50 TERMTI2P Peak-period highway terminal time is equal to or greater than 2 minutes 0.20 0.40 VEHICL2P Number of autos owned by household is equal to or greater than 2 0.74 0.44 WALK5 Peak-period transit walk time is equal to or less than 5 minutes 0.34 0.48

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42 Table 5.2. Description of Variables Used in Non-workers Non-work Trip Models (Sample Size = 6463) Variable Name Variable Description Mean Std Dev DIST30 Peak-period highway distance without HOV lane is equal to or greater than 30 minutes 0.02 0.13 FARE125 Peak-period one-way transit fare is equal to or greater than $1.25 0.13 0.33 FARE150 Peak-period one-way transit fare is equal to or greater than $1.50 0.05 0.22 HBREC Trip purpose is home-based social recreation 0.07 0.25 HBSHOP Trip purpose is home-based shopping 0.11 0.31 HHSIZE1 Single person household 0.14 0.35 HHSIZE2 Household size is equal to two persons 0.47 0.50 INC_100K Annual income of household is equal to or greater than $100,000 0.12 0.32 NOCHILD Household has no children 0.70 0.46 NOVEHICL Household has no autos 0.02 0.15 PALM_BCH Person is a reside nt in Palm Beach 0.46 0.50 PEAK Departure time of the trip is in peak period (7:00am-9:00am or 4:00pm-6:00pm) 0.23 0.42 SOV Trip mode is single-occu pancy vehicle (SOV) 0.47 0.50 T1WAIT30 Peak-hour transit first wait time is equal to or greater then 30 minutes 0.24 0.42 TERMTI2P Peak-period highway terminal time is equal to or greater than 2 minutes 0.22 0.41 VEHICL2P Number of autos owned by the household is equal to or greater than 2 0.56 0.50 WALK15 Peak-hour transit walk time is equal to or less than 15 minutes 0.59 0.49

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435.1.1 Estimation Results for Workers Non-work Trips Tables 5.3 and 5.4 offer estimation result s of the bivariate probit model for both causal structures for the worker sample. In Table 5.3, departure time choice is hypothesized to affect mode choice. Firs t, it is found that the dummy variable representing peak period depa rture time choice (PEAK) signi ficantly affects the choice of SOV as the mode for non-work trips. The coefficient is negative indicating that a departure time choice in the peak period tends to lower the propensit y to drive alone for non-work trips. There are two important possi ble explanations for this. First, it is possible that peak period non-work trips pr imarily serve passenger trips where a worker is dropping off or picking up a child at school or daycare on the way to and from work. As nearly one-half of the households in the sample have at least one child, this is likely to be a strong explanation for this relationship. Second, it is possible that some workers are choosing to use alternative modes of transpor tation for their non-work trips to avoid the frustration of driving alone in congested c onditions during the peak period. Thus, the negative coefficient associated with the peak period departure time variable in the mode choice model is both reasonable and plausible. In addition, it is found that the random error correlation is stat istically significant, thus supporti ng the paradigm of simultaneity embodied in the bivariate probit model sp ecification adopted in this study. The constant term in the departure time choice model is negative indicating that the general propensity is to pursue non-work trips in th e off-peak period. Younger workers and those without children tend to pur sue their non-work trips in the off-peak period as demonstrated by the negative coeffici ents associated with these variables. The finding that absence of children contributes to more off-peak departure time choice lends

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44 credence to the explanation offered in the pr evious paragraph. As expected, school trips also tend to occur in the peak period. The model also indicates that highway level of service affects departure time choice. Peak period travel time variables (HWRUN30 and TERMTI2P) are found to have negative coeffici ents indicating that higher peak period travel times lead to a greater propensity to engage in non-work tr ips in the off-peak period. This finding is sugge stive of the presence of peak spreading where individuals pursue their trips outside the peak pe riod to avoid the worst congestion. With respect to the mode choice model, it is found th at the constant term is positive indicating a general tendency toward s the use of the SOV mode for non-work trips. As expected, larger households cont ribute to a lower prope nsity to use SOV for non-work trips presumably due to ride shar ing and serving passenger trips associated with larger households. Holding a full time j ob, having access to mo re vehicles (higher car ownership levels), and high income are a ll found to contribute posit ively to the use of SOV mode for non-work trips. All of these indications are c onsistent with expectations. School trips show a propensity to be undert aken by SOV mode. Young adults driving to college and university may do so alone, possi bly because they are from small one and two person households. Also, part time resi dents who live in the area for less than six months of the year are found to show a negativ e propensity to drive alone. This may be due to the fact that these residents tend to be elderly retired people whose driving abilities may be diminished. They may also have lim ited auto availability thus contributing to a greater propensity to use tran sit or share rides with others The model also suggests that small transit walk access times contribute nega tively to the choice of SOV as the travel mode.

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45 Table 5.4 shows model estimation results in which mode choice is assumed to affect departure time choice. The results show that the SOV mode choice contributes negatively to peak period departure time choice as evidenced by the negative coefficient associated with the SOV choice variable in th e departure time choice model. In addition, it is found that the random error correlation is statistically significant. These indications are consistent with those found in Table 5.3. All of the other variables pr ovide indications in Table 5. 4 that are very similar to those found in Table 5.3. The signs of the coefficients are virtua lly identical for the different explanatory variable s in the two models. Model estimation results suggest that those with full time jobs te nd to make their non-work tr ips in the peak period as evidenced by the positive coefficient. This is po ssibly due to the desire to efficiently link non-work activities with the commute trip that typically tends to take place in the peak period. Another noteworthy finding is that the constant term in the SOV mode choice model shows a negative value. This is in dicative of a general tendency in the worker sample to avoid using the S OV mode for non-work trips. However, an examination of Table 4.6 shows that a majority of the nonwork trips by workers are made by SOV (53 percent). While the constant term in the S OV mode choice model of Table 5.3 is positive and consistent with this higher percentage of SOV non-work trips, the negative constant term seen here in Table 5.4 is not easily explained. In addition, the random error correlation term is not as statistically significa nt as in Table 5.3. These findings provide the first indication that the model in which mode choice affects de parture time choice may not be as well supported by the data as the one in which departure time choice affects mode choice. Indeed, one would expe ct that workers are more constrained with

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46 respect to their departure time choice due to scheduling constraints imposed by the work activity. Thus, workers determine their time-of-day choice for non-work activities (around the work activity/schedu le) and then determine the mode choice based on a host of factors including the time-of-day choice.

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47 Table 5.3. Workers Non-work Trip Model (Departure Time Choice Mode Choice) Variable Parametert-test Peak Period Departure Choice Model Constant -0.2997-14.124 AGE18_24 -0.2171-4.514 SCHOOL 0.590238.693 NOCHILD -0.3226-11.288 TERMTI2P -0.2129-6.459 HWRUN30 -0.0806-2.163 SOV Mode Choice Model Constant 0.29607.0560 HHSIZE1 0.564010.3350 HHSIZE3P -0.2263-6.5660 CHILD2P -0.1077-3.5230 SCHOOL 0.61139.1220 PTRES -0.3617-4.5200 FTJOB 0.04701.7110 VEHICL2P 0.376910.9840 INC100K 0.11983.6240 WALK5 -0.0786-3.2420 PEAK -1.4558-22.1550 (Error Correlation) 0.827516.2600 Sample Size 7947 Number of parameters 18 Log-likelihood At convergence -9912.779 At market share -10417.222 At zero -11016.881

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48Table 5.4. Workers Non-work Trip Model (Mode Choice Departure Time Choice) Variable Parametert-test Peak Period Departure Choice Model Constant -0.1907-2.9210 AGE18_24 -0.2447-4.3740 SCHOOL 0.68509.5990 FTJOB 0.13093.5800 NOCHILD -0.1958-4.9510 TERMTI2P -0.2339-6.0030 HWRUN30 -0.1035-2.3430 SOV -0.4903-3.9000 SOV Mode Choice Model Constant -0.1668-4.0040 HHSIZE1 0.739012.4890 HHSIZE3P -0.3913-10.2100 CHILD2P -0.2273-6.2310 COMMUT15 0.20446.7360 SCHOOL 0.41776.0930 PTRES -0.3588-3.5030 VEHICL2P 0.515413.7610 INC100K 0.15253.6790 WALK5 -0.0897-2.9330 TERMTI2P 0.10432.8350 (Error Correlation) 0.19752.4680 Sample Size 7947 Number of parameters 20 Log-likelihood At convergence -9908.679 At market share -10417.222 At zero -11016.881

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495.1.2 Estimation Results for Non-workers Non-work Trips Estimation results for non-workers non-work trips are shown in Tables 5.5 and 5.6. In Table 5.5, estimation results corres pond to the model where departure time choice is predetermined and affects mode choice. Th is model appears to reject the paradigm of simultaneity in the relationship between de parture time choice and mode choice. The coefficient of the dummy endogenous variable (PEAK) in the model choice model is negative, but not at all statis tically significant. Moreover, the random error correlation is also not statistically significant at all. Bo th of these findings indicate that this model specification does not support the notion of simultaneity in departure time and mode choice for non-work trips made by non-worker s. As these findings are quite counterintuitive, the authors feel that this causal structure is not appropr iate to describe the behavior of non-workers. As far as the other explanat ory variables are concerned, the model offers plausible and reasonable indications. The constant te rm in the departure time choice model is negative indicating a negative pr opensity to undertake non-work trips in the peak period. As non-workers are not constrained by the schedul e of work activities, this is consistent with expectations. Those with no children tend to avoid the peak period; this may be due to the fact that people with children need to drop off and pick up children at school and daycare and these serve-child trips may occu r in or around the peak periods. While shopping trips tend to be outside the peak pe riod (negative coefficient associated with HB_SHOP), recreational trips tend to be occurring in the peak period (positive coefficient for HB_REC). These findings are also plausible in that recreational trips may involve household member participation an d therefore occur in the peak periods

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50 depending on the availability and constraint s of the household worker and school children. As far as LOS vari ables are concerned, non-worker s seem to be sensitive to transit walk time in their departure time choi ce. The variable representing a peak period transit walk access time of less than 15 minut es has a positive influence on peak period departure time choice. This finding may be attr ibuted to the better transit service that is provided during the peak period. The mode choice model shows a negative c onstant indicating an overall tendency to avoid using the SOV mode for non-work trips. Smaller household sizes and the absence of children positively influence SOV mode choice, presumably due to the lower possibility of sharing ride s with other household member s. As expected, vehicle ownership affects mode choice for non-work trip s. Consistent with the findings in the departure time choice model, home-based shoppi ng trips show a greater propensity to be drive-alone while home-based r ecreational trips show a grea ter propensity to be non-SOV trips. Once again, this may be due to the tendency to pursue recreational trips together with other household members leading to more shared ride trips. Three LOS variables appear to affect the mode choice of non-work ers. A highway distance greater than 30 miles appears to discourage driving-alone wh en pursuing non-work trips. It is possible that longer trips are recr eational trips undertaken with other household members and friends, thus contributing to a lower proport ion of drive-alone mode usage. Greater transit waiting times and higher fares appear to discourage transit use and have positive impact on SOV mode choice. In Table 5.6, estimation results corres pond to the model where mode choice is predetermined and affects time-of-day choice. The most noteworthy fi nding in this table

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51 is that this model (causal structure) s upports the hypothesis of simultaneity between departure time choice and mode choice. Th e coefficient of mode choice (SOV) in the departure time choice model is negative and st atistically significant at the 0.05 level of significance. In addition, the random erro r correlation is positive and statistically significant at the 0.05 level of significance. In general, the model indicates that nonworkers are likely to avoid traveling in th e peak period (negative constant in the departure time choice model) a nd using the SOV mode further contributes to avoiding the peak period. In general, it appears that non-workers undertake shopping and personal business trips using the drive alone mode during the off-peak periods. The positive coefficient associated with HB_SHOP variable in the mode choice model further supports this conjecture. In the departur e time choice model, a longer out-of-vehicle travel time has a negative effect on peak pe riod departure time choice. This finding is consistent with that observed in the worker mo dels. All of the other findings in this model are consistent with those reported in Table 5.5. Thus, from a qualitative and intuitive standpoint, it appears that the causal model in which departure time choice precedes mode choice is more applicable to workers nonwork trips while the opposite causal structur e in which mode choice precedes departure time choice is more applicable to the non-worker sample.

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52Table 5.5. Non-workers Non-work Trip Model (Departure Time Choice Mode Choice) Variable Parametert-test Peak Period Departure Choice Model Constant -0.4935-12.1370 NOCHILD -0.3299-8.6340 INC100K 0.09331.7550 PALMBCH -0.1010-2.8240 HB_SHOP -0.1807-3.9670 HBREC 0.09321.7620 WALK15 0.06761.8970 SOV Mode Choice Model Constant -0.8498-3.5730 HHSIZE1 1.240515.3950 HHSIZE2 0.12072.2890 NOCHILD 0.28092.9340 NOVEHICL -2.4143-11.6130 VEHICL2P 0.703616.8100 HB_SHOP 0.24044.0300 HBREC -0.1167-2.0960 DIST30 -0.3676-3.1500 T1WAIT30 0.07071.7140 FARE150 0.21082.8660 PEAK -0.2655-0.4110 (Error Correlation) 0.14390.3800 Sample Size 6463 Number of parameters 20 Log-likelihood At convergence -7448.404 At market share -7964.838 At zero -8959.620

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53Table 5.6. Non-workers Non-work Trip Model (Mode Choice Departure Time Choice) Variable Parametert-test Peak Period Departure Choice Model Constant -0.3666-6.2420 NOCHILD -0.2824-6.8980 INC100K 0.12552.3540 PALM_BCH -0.0992-2.7880 HBSHOP -0.1746-3.8270 TERMTI2P -0.1551-3.6200 WALK15 0.06341.7790 SOV -0.2431-2.3260 SOV Mode Choice Model Constant -0.9562-20.9490 HHSIZE1 1.258717.2300 HHSIZE2 0.13502.5560 NOCHILD 0.30885.7960 NOVEHICL -2.4405-12.6390 VEHICL2P 0.705518.4520 HBSHOP 0.25546.1560 HB_REC -0.1239-2.3640 DIST30 -0.3365-2.9250 T1WAIT30 0.08212.1010 FARE125 0.15653.1790 (Error Correlation) 0.13722.0430 Sample Size 6463 Number of parameters 20 Log-likelihood At convergence -7440.233 At market share -7964.838 At zero -8959.620

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545.2 Performance Comparisons The model estimation results presented in section 5.1 of this chapter generally offer plausible indications for alternative cau sal paradigms. The only model that may be rejected on qualitative grounds is that in Table 5.5 where the departure time choice decision precedes the mode c hoice decision for the non-worker sample. The statistically insignificant random error correlation whic h implies that there are no correlated unobserved factors between mode choice and de parture time choice appears difficult to explain and defend in light of the simultaneit y shown by the other models. In addition, the coefficient reflecting the influence of departure time choice on mode choice is also statistically insignificant. In order to furt her help clarify the causal structure(s) most supported by the data, this section presents a more rigorous comparison across models to better understand the relationshi p between mode choice and de parture time choice. A goodness-of-fit comparison among the models of different causal structures is conducted first. The adjusted likelihood ratio index as a goodness-of-fit measure can be used for testing and comparing non-nested re lationships in discrete choice models. The indices are given as follows: ) 0 ( ) ( 12 0L K L (5.1) ) ( ) ( 12c L K Lc (5.2) where, 2 0: Adjusted likelihood ratio index at zero

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55 2 c: Adjusted likelihood ratio index at market share ) ( L : Log-likelihood value at convergence ) 0 ( L : Log-likelihood value at zero ) ( c L : Log-likelihood value at market share (model including only the constant term) K: the number of parameters in model. The adjusted likelihood ratio indices for a ll of the models are presented in Tables 5.7 and 5.8. To choose between two models (say, 1 and 2), Ben-akiva and Lerman [15, p. 172] provide a test where under th e null hypothesis that model 1 is the true specification, the following holds asymptotically: 0 }, )] ( ) 0 ( 2 [ { ) Pr(2 / 1 1 2 2 1 2 2 z K K zL z (5.3) where 2 i= the adjusted likelihood rati o index at zero for model i = 1, 2 Ki = the number of parameters in model i = the standard normal cumulative distribution function ) 0 ( L = log-likelihood value at zer o; if all N observations in the sample have all J alternatives, L (0) = N ln(1/J).

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56 The probability that the adjusted likeli hood ratio index of model 2 is greater by some z > 0 than that of model 1, given that th e latter is the true model, is asymptotically bounded by the right-hand side of equation (5.3) above. If the model with the greater 2 is selected, then this bounds the probability of erroneously choosing the in correct model over the true specification. Using this procedur e, models of alternative causal structures can be compared against one another. Table 5.7 shows the comparis on between the two models for the worker sample. The difference between the adjusted likelihood ra tio indices for the two models is 0.0002 with the model in which departure time choice precedes mode choice showing the better fit. Applying equation (5.3) yields a bounding probability of almost zero; therefore, it can be said with a high degree of confiden ce (99 percent confidence or better) that the model of Table 5.3 better fits the data than the model of Table 5.4. The significantly better goodness-of-fit measure suggests that th e causal structure “departure time choice mode choice” is statistically dominant in the worker sample (for non-work trips). This may be behaviorally explained by considering the typical work schedule constraints faced by workers. As workers tend to link their nonwork trips with the commute to and from work, the departure time choice is predetermi ned in conjunction with the work schedule that takes precedence over all else. The mode choice is then simply determined by the mode that has been chosen for the commute trip as the non-work trips are part of a larger trip chaining mechanism.

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57Table 5.7. Likelihood Ratio Co mparison for Worker Models (Sample Size = 7947) Model Number of Parameters (K) 2 0 2c 2 0 2c Departure Time Mode 18 0.1002 0.0484 0.0986 0.0467 Mode Departure Time 20 0.1006 0.0488 0.0984 0.0465 For non-workers, the model presented in Ta ble 5.5 in which departure time choice precedes mode choice may be considered susp ect on qualitative intuitive reasoning as explained earlier. In addi tion, Table 5.8 shows that the model where mode choice precedes departure time choice exhibits a high er adjusted likelihood ratio index. The difference between adjusted likelihood ratios is 0.001 and the non-nested test shown in equation (5.3) rejects the joint structure of Ta ble 5.5 at the 0.01 leve l of significance. That the most appropriate causal structure fo r non-workers is opposite to that of workers is also quite reasonable. For non-workers, work-related scheduli ng constraints are not there. However, mode availability constrai nts may occur. If the worker has taken the automobile, then auto availability may be constrained particularly in multi-person households. Then, the non-worker must firs t think about the decision regarding mode and can then determine the most suitable time-of-day for pursuing the non-work activity. Table 5.8. Likelihood Ratio Comp arison for Non-worker Models (Sample Size = 6463) Model Number of Parameters (K) 2 0 2 c 2 0 2 c Departure Time Mode 20 0.1298 0.0648 0.1664 0.0623 Mode Departure Time 20 0.1308 0.0659 0.1674 0.0634

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58 In summary, this study points to the po ssible behavioral mechanism where people tend to first make choices that are subject to constraints and then make choices that are less constrained. Thus, for workers, departur e time choice is determ ined first because of work schedule constraints, while for non-wo rkers, mode choice is determined first because of possible modal availability constr aints and greater departure time flexibility. These conclusions are reasonabl e and consistent with exp ectations regarding travel behavior. 5.3 Model Application Travel demand models are important tools in forecasting future travel demand. In order to make educated decisions regarding tr ansportation infrastructu re planning, travel demand models must be capable of predictin g the response of the transportation system and its users to changing demand. It is quite challenging however for travel demand models to accurately predict future demand. In order to achieve that, travel demand models should incorporate realistic represen tations of individual and household activity and travel decision making [17]. The traditional urban transportation m odeling system (UTMS), widely used in regional-level studies, incorporat es aggregate trip making leve ls, rather than trip making on the individual level. As all discrete choice models, the bivariate probit model is based on the concept of utility maximization which assumes that the traveler will select the alternative that maximizes his or her benefit. In this sense, discrete choice attributes such as mode choice and departure time choice can be modeled on the aggregate trip level. In terms of forecasting however, probit models are much less applicable compared to logit

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59 models and very limited literature exists that discusses incorporating probit models in travel demand forecasting. 5.3.1 Comparison of Predictions between Causal Structures In the context of this study, estimating predictions of travel er mode choice and departure time choice based on the estimated stru ctural models may be useful in further supporting the validity of the models. Comp aring predicted values across the two different directional relationshi ps featured in this study can be helpful in assessing the importance of the proposed causal relations hips for workers and non-workers. If the predictions are very different across the two opposite causa l structures for workers or non-workers, then it can be stated that the outcome of this study makes a major contribution in the context of time-of-day mode ling. That is to say, in order to have a realistic representation of traveler behavior in terms of time-of-day and mode choice, the modeling effort must be capable of ac hieving the right cau sal structure. In achieving predictions, for each subsample (workers and non-workers) of nonwork trips, new random seeds must be genera ted that reflect randomness for all cases in the dataset and produce independe nt random variables with sta ndard normal distribution. For this purpose, the Monte-Carlo method is used to generate the bivariate normal random seeds for the error terms that are inde pendent random variables with a standard normal distribution [12]. The met hodology is illust rated below: The Monte-Carlo method will generate independent random variables, suppose U and V, each with the standard normal distribution.

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60 Based on the normal distribution the random error terms are defined by: U d X1 1 V d U d Y ) 1 (2 2 2 2 (5.4) The joint distribution of ( X, Y ) is called the bivariate normal distribution with zero means (1 ,2 = 0), unit variances (1d,2d= 1), and correlation in [-1, 1] Based on the specifications of this study, the error terms definition becomes: ) 1 ( ,2 V U Uq q q q (5.5) where, q and q are random error terms, which are standard bivariate normally distributed with zero means, unit variances, and correlation which is an estimator of correlation in the different estimated bivariat e probit models, i.e. q ,q ~) 1 1 0 0 (2 The two different causal structures fo r prediction then become as follows: 0 0 (Mode Choice Departure Time Choice) q q q q q q qM x T z M '* In the first functional relationship, if Mq > 0, i.e. the predicted probability (Mq *) > 0.5 then Mq = 1 (otherwise equal to zero), and the mode choice model is selected.

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61 Accordingly, in the second functional relationship, if Tq > 0, i.e. the predicted probability (Tq *) > 0.5 then Tq = 1 (otherwise equal to zero), and the departure time choice model is selected. 0 0 (Departure Time Choice Mode Choice) q q q q q q qx T T z M '* In the first functional relationship, if Mq > 0, i.e. the predicted probability (Mq *) > 0.5 then Mq = 1 (otherwise equal to zero), and the mode choice model is selected. Accordingly, in the second functional relationship, if Tq > 0, i.e., the predicted probability (Tq *) > 0.5 then Tq = 1 (otherwise equal to zero), and the departure time choice model is selected. Given the above model definitions, prediction estimations can be computed using LIMDEP 8.0 [13]. 5.3.2 Prediction Results Tables 5.9 through 5.12 illustrate crosstabulations of predicted values and percentages of departure time choice with mode choice. A first look in the tables indicates four fairly different causal re lationships across workers and non-workers samples. In tables 5.9 and 5.10 there seems to be a strong indication of two very different casual structures. The values across the two causal relationships are indeed dissimilar. For example, the predicted number of worker s non-SOV trips made in the off-peak hour

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62 is 1679. On the other hand, only 512 of th e off-peak hour trips are made by non-SOV mode. A comparison of tables 5.11 and 5.12 show s that, even in the case of non-workers there seems to be a notable difference betw een the two causal stru ctures, although this difference is not as evident as in the case of workers. For example, the predicted number of workers SOV trips made in the peak hour is 3844. On the other hand, 3175 of the total peak hour trips are made by SOV mode. Table 5.9. Crosstabulation of Departure Time Choice Mode Choice: Worker Sample Predicted Values (N = 7947) Departure Time Choice Mode Choice Non-Peak Peak Total Frequency Non-SOV 1679 2928 4607 SOV 2131 1209 3340 Total 3810 4137 7947 Table 5.10. Crosstabulation of Mode Choice Departure Time Choice: Worker Sample Predicted Values (N = 7947) Departure Time Choice Mode Choice Non-Peak Peak Total Frequency Non-SOV 512 1860 2372 SOV 2260 3315 5575 Total 2772 5175 7947

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63Table 5.11. Crosstabulation of Departure Time Choice Mode Choice: Non-worker Sample Predicted Values (N = 6463) Departure Time Choice Mode Choice Non-Peak Peak Total Frequency Non-SOV 220 732 952 SOV 1667 3844 5511 Total 1887 4576 6463 Table 5.12. Crosstabulation of Mode Choice Departure Time Choice: Non-worker Sample Predicted Values (N = 6463) Departure Time Choice Mode Choice Non-Peak Peak Total Frequency Non-SOV 439 922 1361 SOV 1927 3175 5102 Total 2366 4097 6463 As a conclusion, it can be stated that at least in the case of workers, the evident distinct differences of the pr ediction results across the two different causal relationships further support the advocated variability between mode-cho ice/ departure-time-choice patterns of this group. Hence, when mode ling workers non-work trips by time-of-day, one should be very careful in achieving the correct causal structure that portrays the relationship of mode choice a nd departure time choice. In the case of non-workers, the above can not be stated with high level of confidence. However, a dominant causal relationship between mode choice and depa rture time choice for non-workers still seems to hold as supported by the model es timation results of this study.

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64 CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS 6.1 Conclusions and Future Research New microsimulation models of travel a nd activity behavior attempt to predict travel and activity patterns at the level of th e individual decision-make r or traveler. The development of such models calls for a deeper understanding of the causal decision mechanisms that govern travel and activity pa rticipation decisions. Two major elements of travel and activity behavior include depart ure time choice and mode choice as planners would undoubtedly expect such advanced mo del systems to offer information about travel demand by mode and time-of-day. This study attempts to shed considerable light on the relationship between these two elements of behavior by considering alternative formulations of joint model systems of departure time choice and mode choice for nonwork trips. As departure time choice for work trips tends to be governed largely by work schedules and constraints, studies of work trip departure time choice have largely examined the issue with respect to travel er sensitivity to congestion, travel time reliability, and arrival/departure time window sizes. On the other hand, less attention has been paid to the issue of departure time c hoice for non-work trips, a growing segment of trip making that is accounting for a larger share of trips at all times of day. This study considers two alternative formulations of joint model systems indicating two possible altern ative causal relationships be tween departure time choice

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65 and mode choice for non-work trips. The analysis employs the 1999 Southeast Florida Regional Travel Characteristics Study hous ehold travel survey data. The model estimation effort was conducted separately for workers and non-workers due to the different scheduling and time constraints under which thes e demographic groups make activity and travel decisions. Both mode choice and depart ure time choice were treated as binary choice variables with mode repr esented as a choice between SOV and non-SOV and departure time represented as a choice between peak and off-peak periods. Under this scheme, the bivariate probit modeling fr amework was applied to estimate the model systems and clarify the direction of causal relationships between these dimensions of behavior. Undoubtedly, this effo rt can be extended in future research efforts to treat departure time as a continuous choice process (along the continuous time axis) and mode as a multinomial choice among several modes. The model results suggest that peopl e generally make decisions on choice variables that are more constr ained first. For the worker sample, it was found that the data better supporting th e causal relationship where depart ure time choice preceded mode choice. For the non-worker sample, on the ot her hand, the analysis and modeling results suggested that the data s upport the causal relationship wh ere mode choice decisions preceded departure time choice. These findi ngs are consistent with the notion that choices on constrained dimensi ons are made first. Workers are time constrained due to work activity schedules. Then, workers firs t determine when they can pursue their nonwork activities and trips and then choose the mode for those trips depending on the timeof-day, modal availability, and other factors. Non-workers, on the other hand, are not as time constrained as workers. They may be more mode constrained than time-of-day

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66 constrained due to the modal avai lability issue, need to enga ge in non-work activities that serve household members and other household ob ligations (leading to more shared ride trips), and the absence of typi cally rigid work schedules. M odels of activity and travel behavior should incorporate rela tionships such as those iden tified in this study to more accurately portray the decision mechanisms that may be driving traveler patterns. As with most research efforts of this type, limitations appl y to this study and additional research is warranted. First a nd foremost, it must be recognized that the identification of true causal relationships based on a statis tical analysis of revealed behavior data is extremely difficult and challenging. This study provides a framework by which alternative hypotheses regarding causal re lationships can be te sted, but true causal relationships may be best id entified by collecting and analyz ing behavioral process data that collects information about the thought proc ess that went into a certain decision or behavioral choice. Also, despite the best e fforts of the author, research results may be sensitive to model specificati on and choice of explanatory va riables. Finally, additional research should examine whether the relations hips found to be more suitable in this study extend to other data sets a nd geographical contexts. 6.2 Implications on Four-step Modeling Paradigm Application on time time-of-day based factors within the traditional UTMS fourstep modeling process has been discussed in th e introduction of this thesis. Based on the outcome of this study someone could consid er applying time-of-day factors at two different points in the four-step process. If indeed departure time choice precedes mode choice then time-of-day modeli ng could be performed before mode choice (between trip

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67 distribution and mode choice) to account for variations of traveler mode choice across peak/off-peak periods. On the other hand, if the opposite scenario is true, that is, mode choice precedes departure time choice, then TDOF’s may well be applied after mode choice (between mode choice a nd traffic assignment). Two important problems seem to arise however: First and foremost, the implica tions of this study ar e constrained to nonwork trips. Non-work travel may indeed accoun t for the majority of all trips in an urban area, but commuting has its own share in urban daily travel. Second, the findings of this study are contradicting across two equally important market segments: workers and nonworkers. Applying TDOF’s before mode choice would not account for non-worker departure time travel patterns while the opposite may be conjectured for workers. Deciding how time-of-day assignment should be treated in the contex t of the four-step process, given the implications of th is study, is therefore a challenge. Essentially, someone may consider differe nt models for different trip purposes and different market segments across an ar ea-wide dataset. A co mmon dataset including all person trips may be used for the first two steps of the modeling process: trip generation and trip distribution. Then, non-work trips may be separated from work trips and treated differently for worker and non-work er subsets. This process would eventually yield different link-level non-work trip a ssignments for workers and non-workers. The procedure could be implemented within the f our-step modeling proces s as illustrated in Figure 6.1.

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68Figure 6.1. Time-of-Day Modeling Procedure for Non-work Trips GENERATION DISTRIBUTION Work trips Non-work trips MODE SPLIT (Workers) MODE SPLIT (Non-workers) TOD ASSIGNMENT (Workers) ASSIGNMENT (Non-workers) TOD

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69 REFERENCES 1. Bhat, C.R. (1998) Analysis of Travel M ode and Departure Time Choice for Urban Shopping Trips, Transportation Research 32B(6), pp. 361-371. 2. Cambridge Systematics, Inc. (1997) Time-o f-Day Modeling Proce dures: State-of-thePractice, State-of-the-Art. Final Report Travel Model Improvement Program, U.S. Department of Transportation, Washington, D.C. 3. Stopher, P.R. (1993) Deficienci es of Travel Forecasting Methods Relative to Mobile Emissions. ASCE Journal of Transportation Engineering 119(5), pp. 723-741. 4. Weiner, E. and Ducca, F. (1996) Upgradi ng Travel Demand Forecasting Capabilities: USDOT Travel Model Improvement Program. TR News 186, Transportation Research Board, National Research Council, Washington, D.C., pp. 2-6. 5. Noland, R.B. and Small, K.A. (1994) Tr avel-Time Uncertainty, Departure Time Choice, and the Cost of Morning Commutes, Transportation Research Record 1439, Transportation Research Board, National Research Council, Washington, D.C., pp. 150-158. 6. Kumar, A. and Levinson, D. (1994) Tem poral Variations on A llocation of Time. Transportation Research Record 1439, Transportation Research Board, National Research Council, Washington, D.C., pp. 118-127. 7. Lockwood, P.B. and Demetsky, M.J. (1994) Non-work Travel A Study of Changing Behavior. Presented at th e 73rd Annual Meeting of th e Transportation Research Board, January 9-13, Washington, D.C. 8. Bhat, C.R. (1998) Accommodating Flexible Substitution Patterns in Multidimensional Choice Modeling: Formulation and Application to Travel Mode and Departure Time Choice, Transportation Research 32B(7), pp. 455-466. 9. Steed, J.L. and Bhat, C.R. (2000) On M odeling Departure Time Choice for HomeBased Social/Recreatio nal and Shopping Trips, Transportation Research Record 1706, Transportation Research Board, Nati onal Research Council, Washington, D.C., pp. 152-159.

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70 10. Ye, X. and Pendyala, R.M. (2003) An Explor ation of the Relationship between Auto Mode Choice and Complexity of Trip Chaining Patterns. Working Paper, Department of Civil and Environmental E ngineering, University of South Florida, Tampa, FL. 11. Maddala, G.S. (1983) Limited-dependent and Qualitative Variables in Econometrics, Cambridge University Press, Cambridge, MA. 12. Greene, W.H. (2003) Econometric Analysis, Fifth Edition Pearson Education, Inc., NJ. 13. Greene, W.H., LIMDEP Version 8.0: Reference Guide Econometric Software, Inc., Plainview, NY, 2002. 14. The Corradino Group (2000) Southeast Flor ida Travel Characteristics Study: Household Travel Characteristics Survey Pl an and Findings. Fina l Report prepared for Florida Department of Transportati on, Miami MPO, Broward MPO, and Palm Beach MPO. 15. Ben-Akiva, M. and Lerman, S.R. (1985) Discrete Choice Analysis: Theory and Application to Travel Demand The MIT Press, Cambridge, MA. 16. Pendyala, R.M., Bhat, C., Parashar, A. and Muthyalagari, G.R. (2001) An Exploration of the Relationship between Timing and Duration of Maintenance Activities. CD-ROM of the 81st Annual Meeting of the Transportation Research Board, Transportation Research Board, Nati onal Research Council, Washington, D.C. 17. Bhat, C. R. and K. T. Lawton. (2000) Passenger Travel Demand Forecasting. Millenium Paper, Transportation Resear ch Board, National Research Council, Washington D. C. 18. SPSS Version 11.5 for Windows, Users’ Guide