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An exploration of the relationship between mode choice and complexity of trip chaining patterns
h [electronic resource] /
by Xin Ye.
260
[Tampa, Fla.] :
University of South Florida,
2004.
502
Thesis (M.S.C.E.)University of South Florida, 2004.
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Includes bibliographical references.
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Text (Electronic thesis) in PDF format.
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System requirements: World Wide Web browser and PDF reader.
Mode of access: World Wide Web.
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Title from PDF of title page.
Document formatted into pages; contains 78 pages.
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ABSTRACT: This thesis investigates the relationship between mode choice and the complexity of trip chaining patterns. An understanding of the causality between these two choice behaviors may aid in the development of tourbased travel demand modeling systems that attempt to incorporate models of trip chaining and mode choice. The relationship between these two aspects of travel behavior is represented in this thesis by considering three different causal structures: one structure in which the trip chaining pattern is determined first and influences mode choice, another structure in which mode choice is determined first and influences the complexity of the trip chaining pattern, and a third structure in which neither is predetermined but both are determined simultaneously. The first two structures are estimated within a recursive bivariate probit modeling framework that accommodates error covariance. The simultaneous logit model is estimated for the third structure that allows a bidirectional simultaneous causality. The analysis and model estimation are performed separately for work tour and nonwork tour samples drawn from the 2000 Swiss Microcensus travel survey. Model estimation results show that the causal structure in which trip chaining precedes mode choice performs best for the nonwork tour sample. For the worktour sample, the findings were less conclusive because two causal structures, one in which trip chaining affects mode choice and the other in which both are determined simultaneously, gave virtually identical goodnessoffit measures. But the structure in which mode choice precedes trip chaining pattern choice gave significantly inferior goodnessoffit measures for the work tour sample. These findings should be reflected in the development of activitybased and tourbased modeling systems.
590
Adviser: Pendyala, Ram M.
653
econometric modeling.
travel behavior.
causal relationships.
mode choice.
simultaneous equations.
trip chains.
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Dissertations, Academic
z USF
x Civil Engineering
Masters.
773
t USF Electronic Theses and Dissertations.
4 856
u http://digital.lib.usf.edu/?e14.417
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An Exploration of the Relati onship between Mode Choice and Complexity of Trip Chaining Patterns by Xin Ye A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Civil Engineering Department of Civil and E nvironmental Engineering College of Engineering University of South Florida Major Professor: Ram M. Pendyala, Ph.D. Manjriker Gunaratne, Ph.D., P.E. John Lu, Ph.D., P.E. Date of Approval: April 22, 2004 Keywords: trip chains, travel behavior, cau sal relationships, mode choice, simultaneous equations, econometric modeling Copyright 2004, Xin Ye
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ACKNOWLEDGEMENTS First, I thank my academic advisor, Dr. Ram M. Pendyala, for his continued support and able guidance in my research. Also I tha nk Dr. Manjriker Gunaratn e and Dr. John Lu for serving on my committee and providing thei r valuable suggesti ons. I would like to acknowledge Dr. Giovanni Gottardi in Je nni+Gottardi AG, Zurich, Switzerland for providing funds and data for this research. Finally, I would like to dedicate my thesis effort to my parents Bangjie Ye and Rong Chen.
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i TABLE OF CONTENTS LIST OF TABLES iii ABSTRACT iv CHAPTER 1. INTRODUCTION 1 1.1 Background 1 1.2 Objectives 3 1.3 Outline 3 CHAPTER 2. LITERATURE REVIEW 5 2.1 Structural Equation Model: Causal Analysis among Continuous Variab les 5 2.2 Discrete Continuous Econometric Modeling Framework: Causal Analysis between Continuous Variable and Discrete Variable 9 2.3 Nested Logit Model : Sequential Discrete Choice Analysis 12 2.4 Summary 14 CHAPTER 3. MODELING METHODOLOGY 15 3.1 Outline 15 3.2 Recursive Simultaneous Bivariate Probit Model 17 3.3 Simultaneous Logit Model 21 CHAPTER 4. DATA SET AND SAMPLE DESCRIPTION 24 4.1 Survey Description 24 4.2 Household Characteristics of Sample and Subsample 25 4.3 Person Characteristics of Sample and Subsample 27 4.4 Trip Chain Analysis of Subsample 29 CHAPTER 5. MODEL ESTIMATION RE SULTS 33 5.1 Outline 33 5.2 Estimation Results for NonWork Tours 33 5.3 Estimation Results for Work Tour Models 40 CHAPTER 6. MODEL PERFORMANCE COMPARISONS 47 6.1 GoodnessofFit Measure 47 6.2 Nonnested Test 49 6.3 Comparison Results 51
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ii CHAPTER 7. DISCUSSION AND CONCLUSI ON 53 7.1 Discussion 53 7.2 Contribution 54 7.3 Future Research 55 REFERENCES 57 APPENDICES 61 Appendix A: Gauss Codes for Simultaneous Logit Model of Nonwork Tours 62 Appendix B: Gauss Codes fo r Simultaneous Logit Model of Work Tours 67
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iii LIST OF TABLES Table 4.1 Household Characteris tics of Swiss Travel Microcensus 2000 25 Table 4.2 Person Characteristics of Swiss Trav el Microcensus 2000 28 Table 4.3 Crosstabulation of Mode Choi ce and Tour Type for Nonwork Tours 30 Table 4.4 Crosstabulation of Mode Choice and Tour Type for Work Tours 31 Table 5.1 Description of Explanatory Va riables Used in Nonwork Tour Models 34 Table 5.2 Nonwork Tour Model (Tour Complexity Auto Mode Choice) 35 Table 5.3 Nonwork T our Model (Auto Mode Choice Tour Complexity) 36 Table 5.4 Nonwork Tour Model Si multaneous Logit Model (Auto Mode Choice Tour Complexity) 37 Table 5.5 Description of Explanatory Variables Used in Work Tour Models 41 Table 5.6 Work Tour Model (Tour Complexity Auto Mode Choice) 42 Table 5.7 Work Tour Model (Auto Mode Choice Tour Complexity) 43 Table 5.8 Work Tour Model Simulta neous Logit Model (Auto Mode Choice Tour Complexity) 44 Table 6.1 Likelihood Ratio Comparis on in Nonwork Tour Models 48 Table 6.2 Likelihood Ratio Comp arison in Work Tour Models 49
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iv AN EXPLORATION OF THE R ELATIONSHIP BETWEEN MODE CHOICE AND COMPLEXITY OF TRIP CHAINING PATTERNS Xin Ye ABSTRACT This thesis investigates the relationship between mode choice and the complexity of trip chaining patterns. An understanding of the causality between these two choice behaviors may aid in the development of tourbased travel demand modeling systems that attempt to incorporate models of trip chaining and mode choice. The relationship between these two aspects of travel behavior is represented in this thesis by considering three different causal structures: one structure in which the trip chaining pattern is determined first and influences mode choice, another structure in which mode choice is determined first and influences the complexity of the trip chaining pattern, and a third structure in which neither is predetermined but both are determin ed simultaneously. The first two structures are estimated within a recursive bivariate probit modeling framework that accommodates error covariance. The simultaneous logit model is estimated for the third structure that allows a bidirectional simultaneous causal ity. The analysis and model estimation are performed separately for work tour and nonwork tour samples drawn from the 2000 Swiss Microcensus travel survey. Model esti mation results show that the causal structure in which trip chaining precedes mode choice performs best for the nonwork tour sample.
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v For the worktour sample, the findings were less conclusive because two causal structures, one in which trip chaining affects mode choice and the other in which both are determined simultaneously, gave virtually identical goodnessoffit measures. But the structure in which mode choice precedes trip chaining pattern choice gave significantly inferior goodnessoffit measures for the work tour sample. These findings should be reflected in the development of activitybas ed and tourbased modeling systems.
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1 CHAPTER 1 INTRODUCTION 1.1 Background Over the past few decades, there has been cons iderable research on peoples trip chaining patterns, i.e., the propensity to link a series of activities into a multistop tour or journey. The analysis of trip chaining activity ma y lead to a better understanding of travel behavior and provide a more appropriate framework for exam ining various transportation policy issues (Strathman & Dueker, 1995). In deed, the profession has seen tourbased models being developed and increasingly app lied in the travel demand forecasting arena in place of the more traditional tripbased models that do not reflect trip chaining behavior and tour formation. In this thesis, the terms trip chain and tour are used synonymously to refer to a sequence of trips that begins at home, involves visits one or more other places, and ends at home. Depending on the number of places visited with in the tour or chain, the tour may be classified into two categories: simple and co mplex. A tour or chain with a single stop or activity outside the home location is defined as a simple tour, whereas a tour or chain with more than one stop outside the home location is defined as a complex tour.
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2 Thus a tour or chain of the form: home shop home is considered a simple tour while a tour of the form: home work shop home is considered a complex tour. As peoples activity patterns become increasingly complex a nd involve interactions with other household and nonhousehold members and as time is a finite resource, it may be conjectured that trip chains are likely to be increasingly complex over time. The ability to chain multiple activities together in a single tour or chain may provide greater efficiency and convenience than a series of si nglestop simple tours (Hensher et al., 2000). There are at least two reas ons as to why this has significant traffic and policy implications. First, complex tours or chains may lead to an increase in automobile usage. If one needed to pursue complex tours or ch ains, then the flexibility afforded by the private automobile is desirable. The abil ity to pursue multiple activities in a single journey is rather limited when constrained by the schedules, ro utes, and uncertainty associated with public transportation. Thus, complex trip chaining may contribute to an increased auto dependency and consequently, automobile traffic. Second, in the case of workers (commuters), the formation of comp lex trip chains may entail the linking of nonwork activities with the work trip (commute). Then, nonwork trips that could have taken place outside the peak periods now occur in the peak periods simply because they are being tied together with the commute. Thus, complex trip chaining patterns may contribute to an increase in peak period travel demand.
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3 1.2 Objective The above discussion clearly points to th e possible interdependency between trip chaining, auto usage, and trip timing. Strathman and Duek er (1995), in an analysis of the 1990 NPTS, found that complex trip chains may tend to be more autooriented. However, the nature of the causal relationship is not uni laterally evident because the availability of an automobile may provide the flexibility and convenience that contributes to the formation of complex trip chains. The flex ibility of the automobile may stimulate the desire to undertake additional activities in one tour. For example, the lower travel times typically associated with the auto mode choice may relax ti me constraints and lead to more stopmaking (Bhat, 1997). Moreover, shared rides, which constitute a portion of total auto mode share, are more likely to involve complex tours due to the variety of trip purposes and destinations between the driver an d passengers. The centr al question that is being addressed in this thesis is: Does mode choice influence the complexity of trip chaining patterns or does the complexity of the trip chai ning patterns influence mode choice?. The ambiguity in the causal relationship between the complexity of trip chains and mode choice motivates this investigati on. This research is aimed at understanding and quantifying the causal relationships between tour complexity and mode choice using econometric methods. 1.3 Outline The rest of this thesis is organized as fo llows. Chapter 2 reviews literature concerning the causal analysis in transportation research. Chapter 3 pres ents the modeling methodology and formulation for the different causal structures considered in this thesis. Chapter 4
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4 introduces the Swiss Travel Microcensus 2000 a nd the process by which the tour data set needed for model estimation was prepared. Model estimation results are discussed in Chapter 5. Chapter 6 presents the performa nce comparison across models representing three different causal structures. Conclusi ons are drawn and some recommendations for future research are provided in Chapter 7.
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CHAPTER 2 LITERATURE REVIEW 2.1 Structural Equation Model: Causal Analysis among Continuous Variables Structural Equations Modeling (SEM) is a powerful modeling methodology that takes a confirmatory hypothesistesting approach to the causal analysis among continuous endogenous variables. A typical structural equations model (with G continuous endogenous variables) is defined by a matrix equation system as shown in Equation 2.1. 2.1 G1G1...BXYY...Y This equation can be rewritten as 2.2 XBYY (or) 2.3 )X()BI(Y1 Where Y: a column vector of endogenous variables, B: a matrix of parameters associated with righthandside endogenous variables, X: a column vector of exogenous variables, : a matrix of parameters associated with exogenous variables, and : a column vector of error terms associated with the endogenous variables. 5
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6 SEM specifies dependent variab les Y as explanatory variables associated with the other exogenous explanatory variables and estimates parameter matrix B to capture inherent causal relationship among dependent variable s Y. The correlations between Y and caused by simultaneous equations disables Ordi nary Least Square (OLS) to consistently estimate the parameter matrix B associated with righthandside Y. Econometrician brought forward 2Stage Least Square (2SLS) and 3Stage Least Square (3SLS) to achieve consistent estimators based on Inst rumental Variable (IV) approach. 3SLS estimator is more efficient than 2SLS estimator, since former accommodates unequal variance of in each single equation. In additi on to Least Square (LS) approach, Maximum Likelihood (ML) method can be applied to consistently estimate the parameters in SEM as well. LimitedInformation Maximum Likelihood (LIML) and FullInformation Maximum Likelihood (FIML) in ML estimators are exactly the counterparts of 2SLS and 3SLS in LS estim ators. With normally distri buted disturbances, FIML is efficient among all the estimators. The othe r advanced estimation approaches, such as AsymptoticallyDistributionFree (ADF), are al so available and app lied in literature. Travel behavior investigators applied SEM in their research in order to analyze complex causal relationship among travelrel ated variables, such as trip frequency, travel time or travel distance, activity duration, etc.. Past research regarding SEM application in travel behavior is briefl y reviewed here. Kitamura, et al. (1992) and Golob, et al (1994) are the first know n application of SEM to joint activity duration and travel time data.
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7 Kitamura (1996) and Pas (1996) are two overviews that include discussions of the role of SEM in activity and timeuse modeling. Lu and Pas (1997) present an SEM of in home activities, outofhome activities (by type), and travel (measured various ways), conditional on socioeconomic variables. Estimation is by normal theorymaximum likelihood, and the emphasis is on interpretation of the direct and indirect effects. The data are derived from the Great er Portland, Oregon metropolitan area. Golob and McNally (1997) present an SEM of the interaction of household heads in activity and travel demand, with data from Portland. Activities are divided into three types, and SEM results are compared usi ng maximum likelihood (ML) and generalized least squares (GLS) estimati on methods. They conclude th at GLS methods should be used to estimate SEM when it is ap plied to activity participation data. Fujii and Kitamura (2000) studied the late nt demand effects of the opening of new freeways. The authors used an SEM to dete rmine the effects of commute duration and scheduling variables on after work discretionary activities and their trips. Data are for the OsakaKobe Region of Japan. Golob (2000) estimated a joint model of work and nonwork activity duration using Portland data.
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8 Kuppam and Pendyala (2000) presented three SEMs estimated by GLS using data from Washington, DC. The models focused on rela tionships between: (1 ) activity duration and trip generation, (2) durations of inhome and outofhome activitie s, and (3) activity frequency and trip chain generation. Simma and Axhausen (2001) developed an SEM that captured relationships between male and female heads of household with regard to activity and travel demands. The dependent variables included car ownership, distances traveled by males and females, and male and female trips by two types of ac tivities using data from the Upper Austria. Meka and Pendyala (2002) investigated the interaction between two adults in one household in their travel an d activity time allocation by SE M using Southeast Florida data. Interesting tradeoff within nonwork travel time and nonwork activity time between two adults was quantified and intera ction of travel decision between household members was verified by SEM. Application of SEM in travel behavior research initiates th e analysis of complex causal relationship among individuals tr avel decisions, however, its limitation is quite apparent. Existing SEM only allows continuous dependent variables, but most travel decisions, such as travel mode choice, destination choice or route choice, are discrete in nature. It is necessary to introduce discrete dependent variables into SE M framework in aim at more comprehensively analyzing the causal relati onship with respect to individuals travel
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decisions. Next subchapter will review the recent research in attempt to integrate discrete dependent variable into SEM framework. 2.2 DiscreteContinuous Econometric Modeling Framework: Causal Analysis between Continuous Variable and Discrete Variable Pendyala and Bhat et. al. (2002) made an attempt to integrate discrete dependent variable into SEMlike modeling framework. Using this discretecontinuous econometric modeling framework, they analyzed the causal relationship between timing and duration of maintenance activities. Details of this methodology are presented as below. Let i be an index for time of day of activity participation (i = 1, 2,, I) and let q be an index for observations (q = 1, 2,, Q). Consider the following equation system: qqqqqiqiqiiqiDxaazu''''* 2.4 qi ~ IID Gumbel(0,1), q ~ N(0, 2 ). where u qi is the indirect (latent) utility associated with the i th time of day for the q th observation, D q is a vector of the time of day dummy variables of length I, is a vector of coefficients representing the effects of different times of the day of activity participation on activity duration, qi is a standard extremevalue (Gumbel) distributed error term assumed to be independently and identically distributed across times of the day and observations. is logarithm of activity duration and is its coefficient. The error term q is assumed to be i.i.d. normally distributed across observations with a mean of zero qa 9
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and variance of 2. In Equation 2.4, the time of day alternative i will be chosen (i.e., Dqi =1) if the utility of that al ternative is the maximum of the I alternatives. Defining 2.5 qi ijI )(u max v* qj },,2,1{j qithe utility maximizing condition for the choice of the ith alternative may be written as: 1 Dqi if and only if i zqi > vqi. Let Fi(vqi) represents the marginal distribution function of vqi implied by the assumed IID extreme value distribution for the error terms qi (i = 1,2,,I) and the relationship in Equation 2. 5. Using the propertie s that the maximum over identically distributed extreme value ra ndom terms is extreme value distributed and the difference of two identically distributed extreme values terms is logistically distributed, the implied distribution for vqi may be derived as: ij q qjj i qiaz y y yFyv ) exp()exp( )exp( )()Pr(' The nonnormal variable vqi is transformed into a standard normal variate using the integral transform result: vqi *= where (.) is the standard cumulative distribution function. ] )v([qi 11iF Equation system 2.4 may now be rewritten as: q q q q qi qii qiDxa azD v' qi 2.6 A correlation i between the error terms vqi* and q is allowed to accommodate common 10
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unobserved factors influencing the time of day choice for activity participation and the duration of the participation. Since a q is partially determined by q and v qi is correlated with q if i is unequal to zero, a q is apparently correlated with random error term v qi in the first equation. Similarly, D q is also correlated with random error term q in the second equation. The endogenous nature of dependent variables D q and a q entails fullinformation maximum likelihood method to jointly estimate their corresponding parameters and Limitedinformation maximum likelihood (sequential estimation) does not provide consistent estimators of the coefficients on endogenous variables. The fullinformation likelihood function for estimating parameters is: QqIiDqiqqiblLL11)()(1 2.7 where (.) is the standard normal density function, and l q and b qi are defined as follows: qqqqDxal'' 211)'(iqiqqiiiqilazFb 2.8 However, they also showed that either or should be equal to zero for logical consistency. It leads to two recursive model system indicating two different causal relationships between discrete dependent variable and continuous dependent variable. If = 0 and 0, then discrete dependent variable, time of day participation, affects continuous dependent variable, the logarithm of activity duration (but not vice versa), inversely, if 0 and = 0, then the continuous dependent variable affects discrete 11
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12 dependent variable (but not vice versa). By comparing the goodnessoffit from the models in two recursive system, the causal relationship between them may be analyzed and identified. The most creative part of this study is to sp ecify the endogenous disc rete and continuous variables as explanatory vari ables into mutual explanator y functions, then by taking advantage of logical consistency to identify two recursive model structures indicating two unidirectional causal relationships. In addition, discretecontinuous econometric modeling approach is ap propriately adopted here to cons istently estimate parameters on endogenous variables with accommodation of correlation between normal error term and Gumbel error terms. 2.3 Nested Logit Model: Sequential Discrete Choice Analysis Hensher et. al. (2000) analyzed trip chaining as a barrier to the propensity to use public transportation using multinomial logit, nested logit and mixed logit model. The theme of that paper is fairly close to the current thesis. Following Strathman & Dueker (1995), they classified trip chains into 7 categories as below: 1) Simple work: h w ( w ) h 2) Complex to work: h nw ( nw/w ) w h 3) Complex from work: h w ( nw/w ) nw h 4) Complex to and from work: h nw ( nw/w ) w ( nw/w ) nw h 5) Complex at work: h w ( nw/w ) nw ( nw/w ) w h 6) Simple nonwork: h nw h
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13 7) Complex nonwork: h nw ( nw ) h h: home, w: work, nw: non work. The bracketed te rms represent additional trips that may be in the chain. On the other side, only two alte rnatives: Car and Public Tran sport are specified in mode choice set. They presumed the sequential ch oice behavior in whic h trip chaining type choice is ahead of trip mode choice, and then imposed 1 on the inclusive value parameter coefficients associated with all the complex chain type choices and equalized the inclusive value parameter coefficients associated with all the rest simple chain type choices. The estimation results showed that inclusive value parameter (0.866) associated with simple chains appeared significant and fe ll into the interval from 0 to 1. This statistical result is consistent with utility maximization theory behi nd nested logit model and validates the presumed sequential choice behavior. From this study, it can be realiz ed that nested logit model (N L) can be applied in dealing with problems regarding the relationship between two discrete dependent variables. Based on the assumption of a sequential choice mechanism, nested logit models representing two alternative tree stru ctures can be formed. By checking the reasonableness of the estimated inclusive valu e parameter coefficients and/or comparing measures of goodnessoffit between models of two different st ructures, the more plausible structure that is supported by the data may be identified. Based on this identification, the causal re lationship between two choice be haviors can be clarified. However, the nested logit model has restrictio n on inclusive value parameter coefficient.
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14 Once estimated inclusive value parameter coe fficients fall outside the allowable range from 0 to 1, the corresponding nested logit structure becomes invali d. Besides, unlike SEM, nested logit model does not provide a set of parameters directly measuring the impact of endogenous variables on the others. 2.4 Summary Chapter 2 extensively reviews the existing methodologies in literature concerned with causal analysis between/among travelrelated variables. These methodologies include Structural Equation Model, DiscreteCon tinuous Econometric Model and Nested Logit Model. As reviewed earlier, SEM only a llows the causal analysis among multiple continuous endogenous variables; NL is potentially applicable in causal analysis evolved with discrete dependent variables but mode ling structure is completely different from SEM and does not provide parameters directly measuring the causal effect. DiscreteContinuous Econometric Model initially introdu ced discrete variable into a SEMlike modeling framework. Following this good start, it seems to be straightforward to generalize this approach from discretecon tinuous situation towards discretediscrete situation. The details of modeling methodology for discretediscrete causal analysis are brought forward in the next chapter.
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15 CHAPTER 3 MODELING METHODOLOGY 3.1 Outline As discussed in last chapter, the causal re lationship between tour type choice and mode choice cannot be analyzed in SEM or DiscreteContinuous Econometric Model since dependent variables are both disc rete in nature. In this th esis, two different econometric modeling methods are employed to analyze the relationship between two discrete variables. The first is the recursive simu ltaneous bivariate probit model, which allows the analysis of oneway causa l relationships between two c hoice behaviors. In this formulation, the random error terms are assumed to follow the bivariate normal distribution. The bivariate normality a ssumption implies that two endogenous dummy variables may not coexist in mutual functiona l relations. The existence of an endogenous dummy variable in either function corresponds to two different ca usal structures (see Section 3.2 for details). Intuitively, this f eature of the bivariate probit model provides an appropriate approach to disti nguish the causality between tour complexity and auto mode choice. However, this approach also enta ils an underlying assumption that an explicit unidirectional causal relationshi p (or at least the tendency of such a unidirectional causal relationship) exists in the population being studied. A unidirectional causal relationship may exist in a specific tour, but the nature of the causal relationship may vary across individuals and across tours for the same individual. Macros copically, the presence of a
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16 bidirectional causality would possibly appear in the population if neither unidirectional causal relationship dominates the other. In order to address the possibility of a si multaneous bidirectional causality, this thesis also uses the simultaneous logit model fo rmulation presented by Schmidt and Strauss (1975) and initially introduced in the transpor tation context by Ouyang, et.al. (2002). This model formulation enables the modeling of bidirectional causality that might exist in tour complexity and mode choice. Essen tially, the simultaneous logit model may be considered an extension of the more co mmonly known multinomial logit model, where two endogenous dummy variables can be incorpor ated into the mutual utility functions simultaneously. The only restriction on these two dummy variables is that their model coefficients must be identical for logical consistency (see Section 3.3 for details). Thus, three different possibl e causal structures are cons idered in this thesis: 1) Mode choice Trip chain complexity (recursive bivariate probit model) 2) Trip chain complexity Mode choice (recursive bivariate probit model) 3) Trip chain complexity Mode choice (simulta neous logit model) Through a performance comparison of models across the three causal structures, it is envisaged that the relationship between t our complexity and mode choice may be discussed and clarified.
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3.2 Recursive Simultaneous Bivariate Probit Model If the tours complexity/simplicity and auto/nonauto mode choice are treated as two binary choices, the bivariate probit model can be formulated at the tour level to simultaneously analyze their probabilities with accommodation of random error correlation. The general formulation is as follows: qqqqqqqqMxTTzM''** 3.1 where q is an index for observations of tour (q = 1, 2, Q) M q is a latent variable representing the mode choice for tour q T q is a latent variable representing the complexity of tour q M q = 1 if M q > 0, = 0 otherwise i.e., M q is a dummy variable indicating whether tour q uses the auto mode T q = 1, if T q > 0, = 0 otherwise i.e., T q is a dummy variable indicating whether tour q is complex z q is a vector of explanatory variables for M q x q is a vector of explanatory variables for T q are two vectors of model coefficients associated with the explanatory variables z q and x q respectively is a scalar coefficient for T q to measure the impact of tours complexity on mode choice is a scalar coefficient for M q to measure the impact of mode choice on the choice of tour complexity 17
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q and q 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 tour q: ],','[)0,0(2 xzTMprob 3.2 ]),'(,'[)]'([)0,1(21 xzxTMprob 3.3 ],'),'([)]'([)1,0(21 xzzTMprob 3.4 )]'([)]'([1)1,1(11 xzTMprob ]),'(),'([2 xz 3.5 where ][1 is the cumulative distribution function for standard univariate normal distribution, ][2 is the cumulative distribution function for standard bivariate normal distribution. 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( TMprobTMprobTMprobTMprob 3.6 Substituting equations 3.2 through 3.5 into equation 3.6, it can be shown that ]),'(),'([],','[22 xzxz ],'),'([]),'(,'[22 xzxz 3.7 18
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This equation does not hold unless either or is equal to zero. This requirement, known as the logical consistency condition similar to the situation in DiscreteContinuous Econometric Model, will lead to two different recursive simultaneous modeling structures (Maddala, 1983) suggesting two different causal relationships: 1) 0 0 (Mode Choice Tour Complexity) qqqqqqqMxTzM''** 3.8 In this structure, mode choice is predetermined as per the first functional relationship. Then, the choice of mode is specified as a dummy variable in the second functional relationship for tour complexity to directly measure the impact of mode choice on the complexity of the trip chain or tour. 2) 0 0 (Tour Complexity Mode Choice) qqqqqqqxTTzM''** 3.9 Conversely, one may consider the alternative structure in which tour complexity is predetermined as per the second functional relationship. The complexity of the tour is specified as an explanatory variable influencing mode choice as per the first functional relationship. 19 Thus, the desirable feature of the bivariate probit model in which the coefficients of two endogenous dummy variables do not coexist in both functional relationships provides an
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appropriate modeling framework to analyze the unidirectional causality between tour complexity and mode choice. The endogenous nature of one of the dependent variables in the simultaneous equation system can be ignored in formulating the likelihood function. To facilitate formulating likelihood functions, equations 3.2 through 3.5 can be rewritten in a format including only the cumulative distribution function of the standard bivariate normal distribution. ],','[)0,0(2 xzTMprob 3.10 ]),'(,'[)0,1(2 xzTMprob 3.11 ],'),'([)1,0(2 xzTMprob 3.12 ],','[)1,1(2 xzTMprob 3.13 Equations 3.10 through 3.13 and the corresponding likelihood functions can be summarized by the following general formulations for the two different unidirectional causal structures (Greene, 2003): 1) 0 0 (Mode Choice Tour Complexity) ]),'(,'[2 qqqqqqqqMxzprob 3.14 QqqqqqqqqMxzL12),'(,' 3.15 20
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2) 0 0 (Tour Complexity Mode Choice) ],'),'([2 qqqqqqqqxTzprob 3.16 QqqqqqqqqxTzL12,'),'( 3.17 where and 12qqM 12qqT As the likelihood functions of the recursive 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. 3.3 Simultaneous Logit Model 21 One may also consider the possibility where neither of the two unidirectional causal structures is dominant within the population, i.e., both causal structures are prevalent in the population. In addition, one may consider the possibility where the choices regarding tour complexity and mode are made simultaneously. To accommodate such plausible bidirectional causality, the simultaneous logit model is applied in this thesis. The simultaneous logit model may be considered an extension of the multinomial logit model commonly used in transportation modeling practice. In the simultaneous logit model, the logarithm of the ratio of probabilities for two alternatives to be selected from one choice set is assumed to equal a linear combination of a set of explanatory variables. One dummy variable indicating the choice of tour complexity may be added into the set of explanatory variables for mode choice; similarly, one dummy variable indicating mode choice may be added into the set of explanatory variables for tour complexity. The
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formulations may be written as follows (all of the symbols have the same meaning as in Section 3.2): qqqTzTMPTMP')0()1(log 3.18 qqqMxMTPMTP')0()1(log 3.19 By rewriting equations 3.18 and 3.19 across two possible values that T q and M q can take, one gets: qqzTMPTMP')0,0()0,1(log 3.20 qqzTMPTMP')1,0()1,1(log 3.21 qqxMTPMTP')0,0()0,1(log 3.22 qqxMTPMTP')1,0()1,1(log 3.23 The sum of the probabilities for the four combinations of binary choices should be equal to one, i.e., 1)1,1()1,0()0,1()0,0( qqqqTMPTMPTMPTMP 3.24 22
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By converting simultaneous equations 3.20 through 3.23, it can be shown that )''exp()0,0()1,1( qqqqxzTMPTMP )''exp()0,0( qqqxzTMP 3.25 For logical consistency, must be equal to Endogenous dummy variables T q and M q are allowed to coexist in the simultaneous equation system. By replacing with and solving the simultaneous equations 3.20 through 3.24, the probability for each combination is formulated as follows: qqqTMPP /1)0,0(00 3.26 qqqqzTMPP /)'exp()0,1(10 3.27 qqqqxTMPP /)'exp()1,0(01 3.28 qqqqqxzTMPP /)''exp()1,1(11 3.29 where )''exp()'exp()'exp(1 qqqqqxzxz 3.30 Finally, the likelihood function may be formulated as follows: qqqqqqqqTMqTMqTMqQqTMqPPPPL)()()()(11)1(01)1(101)1)(1(00 3.31 Model estimation is performed using the Gauss programming language (see Gauss codes in Appendix). 23
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24 CHAPTER 4 DATA SET AND SAMPLE DESCRIPTION 4.1 Survey Description The data set used for analysis and model estimation is extr acted from the Swiss Travel Microcensus 2000. A very detail ed description of the survey and the survey sample can be found in Ye and Pendyala (2003). Only a brief description of the survey sample is provided in this thesis. The survey res pondent sample consists of 27,918 households from 26 cantons in Switzerland. The person sample was formed by randomly selecting one person over 6 years old from each household with less than 4 household members and two persons over 6 years old from each ho usehold with 4 or mo re members. As a result of this sampling scheme, the person re spondent sample consisted of 29,407 persons. All of the persons in the person sample were as ked to report their travel in a oneday trip diary. The resulting trip data set include s 103,376 trips reported by 29,407 interviewed persons (including the possibility of some respondents making zero trips on the survey day). The household and pers on characteristics of these sa mples are respectively shown in Tables 4.1 and 4.2. Da ta corresponding to respondents fro m the Canton of Zurich was extracted to reduce the data to a more mana geable size and to control for possible area specific effects. Tables 4.1 and 4.2 also in clude summary statistics for the subsample of respondents from Zurich in addition to those of the overall
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25 Swiss sample. The Zurich subsample includes 5,128 hou seholds from which 5,241 persons provided travel information. 4.2 Household Characteristics of Sample and Subsample Table 4.1 Household Characteristic s of Swiss Travel Microcensus 2000 Characteristic Swiss Sample Zurich Subsample Sample Size 27918 5128 Household Size 2.43 2.20 1 person 27.5% 31.0% 2 persons 35.1% 37.0% 3 persons 14.0% 12.6% 4 persons 23.4% 19.5% Monthly Income Low (Fr 8K) 18.4% 21.5% Vehicle Ownership 1.17 1.09 0 auto 19.8% 23.8% 1 auto 50.5% 49.5% 2 autos 24.5% 21.8% 3 autos 5.2% 4.9% Family Type Single 27.2% 30.6% Unmarried couple (no child) 27.9% 29.3% Married 43.6% 37.8% Presence of Children Child <6 years old 10.6% 8.7% Child 6~17 years old 22.5% 18.9% Household Location Major city 42.4% 55.1% Surrounding areas of city 30.4% 35.2% Rural 26.1% 8.9%
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26 Table 4.1 lists sample size, average household size and its distribution, household income distribution, average household vehicle owne rship and its distribution, family type distribution, proportion of households with children a nd household location distribution by total Swiss household sample and Zurich household subsample. As expected, the proportion of households without automobile s in this Swiss sample is substantially higher than in a typical samp le from the United States. This may be reflective of the higher level of public transport service in Switzerland that enables mobility and accessibility without the same leve l of auto dependence. As a result, one might expect the automobile to play a smaller role in the Swiss travel environment than in the US environment. In general, the Zurich subsam ple exhibits characteristics rather similar to the overall Swiss sample but to some degree reflects the ur ban characteristics of Zurich from various angles. Average household size in Zurich subs ample is smaller than the average in Swiss sample in accord with the common sense th at urban residents tend to live more independently. Monthly income distribution apparently shows that Zurich has 3.1% more families falling into highincome category but 3.3% less families into lowincome category than the nation leve l distribution, which also reflects Zurichs urban characteristics. Average vehicle ownership in Zurich subsample is somewhat smaller than in Swiss sample and there are 4.0% more households in Zurich without vehicle than nationlevel distribution. It may be conjectured that advanc ed public transit system in Zurich enables more people live without vehicl es in household. Sta tistics also shows that
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27 Zurich has substantially less married families and less families with children, which may account for smaller average household size. Finally, the household location distribution in Zurich subsample shows le ss than 10% households are loca ted in rural area and around 55% in major city, as expected. 4.3 Person Characteristics of Sample and Subsample The person characteristics are shown separa tely for commuters and noncommuters. The statistics shows personal da ily trip rates is less than 4.0 for both commuters and noncommuters, whereas personal daily trip rates in US are typically more than 4.0. Because noncommuter is defined as those people who make work trips at least twice per week, work trips rates for noncommuter are not exactly equal to zero but fairly close to zero, as shown in Table 4.2. Auto mode share within work trips and nonwork trips is less than 60% in accordance with the lower vehicl e ownership in comparison with US. Person characteristics show similarities between the overall Swiss sample and the Zurich subsample. As expected, noncommuters sh ow a greater proportion of elderly (retired) and young persons than commuter samples. On average, commuters make about 1.4 trip chains per day where the trip chain is defined as a complete hometohome tour. Noncommuters make, on average, about 1.2 trip chains per day. Commuters make nearly four trips per day while noncommuters make fe wer trips at about th ree trips per day. The difference in trip making between commute rs and noncommuters is primarily due to
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28 Table 4.2 Person Characteristics of Swiss Travel Microcensus 2000 Swiss Sample Zurich Subsample Characteristic Commuters NonCommuters Commuters NonCommuters Sample Size 13296 16111 2504 2737 Age (in years) 40.7 (Mean) 46.5 (Mean) 41.0 (Mean) 49.0 (Mean) Young (6~29) 20.8% 31.8% 20.4% 28.1% Middle (30~59) 73.5% 26.3% 73.1% 25.3% Old ( 60) 5.7% 41.8% 6.5% 46.6% Sex Male 54.8% 39.3% 56.4% 39.6% Female 45.2% 60.7% 43.6% 60.4% Employment Status Full time 71.8% 8.9% 72.8% 8.7% Part time 24.3% 6.0% 23.0% 7.5% Licensed 87.7% 50.7% 87.3% 51.4% #Chains/day 1.43 1.24 1.32 1.20 #Trips/day 3.98 3.13 3.77 3.13 Work trips 0.91 0.08 0.87 0.08 Nonwork trips 3.07 3.05 2.90 3.05 Work Trip Mode Share Auto 57.1% 54.8% 51.8% 46.6% NonAuto 42.9% 45.2% 48.2% 53.4% NonWork Trip Mode Share Auto 58.4% 41.1% 52.6% 37.0% NonAuto 41.6% 58.9% 47.4% 63.0% Notes: Commuters are those who make work trips at least twice per week. All others are noncommuters. Incomplete chains, defined as a series of trips that does not end at ho me, are not included.
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29 the work trip as nonwork trip generation is virtually identical between commuters and noncommuters. Finally, it is seen that the Zurich subsamples are less dependent on the auto mode as they exhibit a smaller auto mode share compared to the overall Swiss sample. This is presumably due to the high le vel of transit service av ailable in the Zurich area. 4.4 Trip Chain Analysis of Subsample In this thesis, the unit of analysis and modeling is the tour or trip chain. A trip chain is defined in this thesis as a complete homet ohome journey where the origin of the first trip is home and the destination of the last trip is home. No intermediate home stop is present within the trip chain. Whenever the home location is reached, a chain is formed. A tourlevel data set was formed by aggregatin g the trip data set to the tour level. All person and household characteristic s were merged into the tour level data set. In most cases, a single mode was prevalent for the trip chain. In cases where multiple modes were prevalent within the same trip chain or tour, a single mode was assigned based on the whether or not the auto mode was used in the chain. If the auto mode was used for any segment in the trip chain, then the ch ain was assigned an auto mode and vice versa. Each tour was classified as a simple or complex tour depending on whether it had one intermediate stop or more than one inte rmediate stops within the chain. In addition, tours were also classified as workbased tours and nonworkbased tours. Any tour that included a work stop (regardless of the presence of other types of stops) was classified as a workbased tour while an y tour that included only nonwork stops was
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30 classified as a non workbased tour. It was felt that the causal relationships governing workbased tours may be differe nt from those governing non wo rkbased tours. This is because the presence of a work stop may impose a certain amount of spatial and temporal rigidity on the activity/travel behavior of the individual in the context of that tour. The constraints associated with the work activit y may lead to a different causal structure underlying trip chain formati on and mode choice. Table 4.3 Crosstabulation of Mode C hoice and Tour Type for Nonwork Tours Tour Type Mode Choice Simple Complex Total Frequency Nonauto 2685 661 3346 Auto 1030 525 1555 Total 3715 1186 4901 Column Percent Nonauto 72.3% 55.7% 68.3% Auto 27.7% 44.3% 31.7% Total 100.0% 100.0% 100.0% Row Percent Nonauto 80.2% 19.8% 100.0% Auto 66.2% 33.8% 100.0% Total 75.8% 24.2% 100.0% As the model estimation was performed only on the Zurich subsample, all further analysis presented in the thesis pertains on ly to this subsample. The Zurich subsample included 4,901 nonwork tours and 1,711 work t ours. Tables 4.3 and 4.4 offer simple crosstabulations of tour complexity agai nst mode choice. Table 4.3 examines the distribution of tour comple xity by mode choice for nonwork tours while Table 4.4 examines the distribution for work tours.
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31 Table 4.4 Crosstabulation of Mode Choice and Tour Type for Work Tours Tour Type Mode Choice Simple Complex Total Frequency Nonauto 436 355 791 Auto 397 523 920 Total 833 878 1711 Column Percent Nonauto 52.3% 40.4% 46.2% Auto 47.7% 59.6% 53.8% Total 100.0% 100.0% 100.0% Row Percent Nonauto 55.1% 44.9% 100.0% Auto 43.2% 56.8% 100.0% Total 48.7% 51.3% 100.0% An examination of columnbased percentages in Table 4.3 indi cates that about 28 percent of simple nonwork tours involve the use of the automobile as the primary mode of transportation. This value is considerably higher at 44 percent for complex nonwork tours. Thus it appears that there is a correlation (at least) between mode choice and tour complexity. Clearly, the auto mode is util ized to a greater degree in the context of complex multistop trip chains. Similarly, examining the rowba sed percentages shows that 80 percent of nonwork nonauto tours are simple in nature (i nvolve only one stop). On the other hand, only 66 percent of nonwork auto tours are simple in nature. Thus it appears that nonauto tours tend to be mo re simple than autobased tours. Table 4.4 offers similar indications, albeit th e tendencies are not as strong as those seen in Table 4.3. In the case of work tours, it is found that a majority of simple tours are non autobased (52 percent) while a majority of complex tours are autobased (60 percent). Similarly, a majority of non autobased work tours tend to be si mple in nature (55
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32 percent), while a majority of autobased tours tend to be complex in nature (57 percent). Once again, a clear correlation between auto use and trip chain complexity is seen in these cross tabulations. Give n the difference in the percen t distributions between work and nonwork tours, it was considered pr udent to examine th e causal relationship between tour complexity and mode choice for work and nonwork tours separately.
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33 CHAPTER 5 MODEL ESTIMATION RESULTS 5.1 Outline This chapter presents estimation results for th e models developed in this thesis. Tables 5.1 and 5.5 present a description of the vari ables used in model estimation for nonwork and work tours respectively. The variables are listed in alphabetical order and mostly constitute dummy variable indicators that take a value of one if the condition is satisfied and zero otherwise. Estimation results for nonwork tour models are provided in Tables 5.2 through 5.4 and estimation results for work tour models are provided in Tables 5.6 through 5.8. 5.2 Estimation Results for NonWork Tours Table 5.2 provides estimation results for th e causal structure where tour complexity affects mode choice, Table 5.3 provides estimation results for the causal structure where mode choice affects tour complexity, and Table 5.4 provides estimation results for the simultaneous logit model that is intended to capture simultaneous causality between the two variables. In Table 5.2, the coefficient for tour complexity is statistically significant and positive in the mode choice model. This lends credence to th e hypothesis that the need to make a complex tour is likely to increase dependency on the auto mode.
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34 In addition, it was found that demographic and socioeconomic charact eristics, the tours prim ary purpose, and timeofday signifi cantly influence mode choice and tour complexity. For example, larger household si zes, lower income, and school tours tend to be associated with a lower propens ity to use the automobile mode. Table 5.1 Description of Explanatory Vari ables Used in Nonwork Tour Models (N = 4901) Variable Name Variable Description Mean Std Dev AD1_YOU1 Household is composed of one adult and one child who is over 6 but below 17 years old 0.01 0.09 AMPEAK Tour starts in AM p eak period (7:00~8:59) 0.17 0.37 AUTO Auto mode choice for tour 0.32 0.47 CARGE2 Number of autos in household 2 0.29 0.45 COMPLEX Tour is complex (multistop) 0.24 0.43 HHSIZE Number of hous ehold m embers 2.72 1.46 HHSIZE1 Single person household 0.25 0.44 HHSIZE4 Number of household members 4 0.36 0.48 HIGH_INC Monthly household incom e > Fr10000 0.14 0.34 LOWINC Monthly household income < Fr4000 0.18 0.38 OLD Person > 60 years old 0.27 0.45 MALE Person is male 0.46 0.50 PMPEAK Tour starts in PM peak period (16:00~17:59) 0.10 0.30 SCHOOL Primary purpose of the tour is school 0.11 0.32 SERVICE Primary purpose of the tour is service 0.06 0.23 SHOPPING Primary purpose of th e tour is shopping 0.30 0.46 TOURDIST Total distance that th e tour covers (km ) 26.32 86.15 Note: Primary purpose of a tour is defined as the tr ip purpose other than return home that accounts for the longest cumulative distance within the tour. If two different trip purposes account for equal distances within the tour, then the primary purpose is defined based on the following priority sequence: work>school>service>shopping>recreation>other On the other hand, higher income, higher car ow nership levels, males, and tours primarily involving service (serve passenger) stops increa se the propensity to use the automobile. In the tour complexity model, it is found th at individuals in single person households tend to make complex tours as opposed to individuals in larger hous eholds. This is a rather
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surprising result as it was expected that indi viduals in larger households would have to make complex tours to serve the needs of multiple household members. Table 5.2 Nonwork Tour Model (Complex Tour Auto Mode Choice) Variable Parameter ttest Auto Mode Choice Model Constant 0.8035 16.344 HHSIZE 0.0790 5.135 HIGHINC 0.1075 2.195 LOW_INC 0.3315 6.842 CARGE2 0.5050 12.077 MALE 0.3169 9.153 SERVICE 0.3684 4.583 SCHOOL 1.1255 10.622 COMPLEX 1.6323 23.151 Complex Tour Choice Model Constant 0.5231 13.638 HHSIZE1 0.1099 2.467 AD1YOU1 0.3843 1.998 HHSIZE4 0.1314 2.597 OLD 0.1620 3.737 YOUNG 0.6122 9.464 SERVICE 0.5172 6.279 SHOPPING 0.2089 5.230 AMPEAK 0.2879 5.933 PMPEAK 0.2372 3.568 (Error Correlation) 0.8083 19.744 Sample Size 4901 Number of parameters 20 Loglikelihood At convergence 5179.689 At market share 5734.170 At zero 6794.229 35
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Table 5.3 Nonwork Tour Model (Auto Mode Choice Complex Tour) Variable Parameter ttest Auto Mode Choice Model Constant 0.3797 7.247 HHSIZE 0.1502 9.542 HIGHINC 0.1710 2.941 LOW_INC 0.3951 6.891 CARGE2 0.6317 13.577 MALE 0.3630 9.079 TOURDIST 0.0005 3.361 SERVICE 0.8842 10.815 SCHOOL 1.3619 12.936 Complex Tour Choice Model Constant 0.9301 17.228 HHSIZE1 0.2534 5.142 HHSIZE4 0.1784 3.613 SERVICE 0.3623 3.866 SHOPPING 0.2518 5.531 AMPEAK 0.3032 5.621 PMPEAK 0.3263 4.399 AUTO 0.7593 6.168 (Error Correlation) 0.2473 3.158 Sample Size 4901 Number of parameters 18 Loglikelihood At convergence 5207.736 At market share 5734.170 At zero 6794.229 36
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Table 5.4 Nonwork Tour Model Simultaneous Logit Model (Auto Mode Choice Complex Tour) Variable Parameter ttest Auto Mode Choice Model Constant 0.8028 8.814 HHSIZE 0.2384 8.476 HIGHINC 0.2472 2.531 LOW_INC 0.6879 6.955 CARGE2 1.0678 13.417 MALE 0.6399 9.495 SERVICE 1.3552 9.600 SCHOOL 2.6113 10.818 Complex Tour Choice Model Constant 1.2239 15.641 HHSIZE1 0.3812 4.529 AD1YOU1 0.5977 1.686 HHSIZE4 0.3168 3.224 OLD 0.1727 2.052 YOUNG 0.4019 3.454 SERVICE 0.7508 5.486 SHOPPING 0.4656 5.746 AMPEAK 0.5479 6.024 PMPEAK 0.5577 4.200 (Joint Dependence) 0.6390 8.885 Sample Size 4901 Number of parameters 19 Loglikelihood At convergence 5203.343 At market share 5734.170 At zero 6794.229 37
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38 On the other hand, one may conjecture that the possibility of task allocation present in a multiperson household may reduce the need to perform multistop trip chains (Strathman et al., 1994). Single parents, as expected, ar e more prone to engage in multistop trip chains. Compared to the middle age group, th e older and younger individuals tend to be less prone to making multistop trip chains. This is possibly due to household and other obligations reaching their peak for many indivi duals during the middle age lifecycle stage. It is also rather surprising that tours undert aken in the AM peak show a greater propensity to involve multiple stops than those undertaken in the PM peak period. However, in the context of nonwork tours, this may be a plau sible result in that people combine a series of errands and school activities in the morni ng and complete their activities by midday. Another possible explanation is that time constraints towards the end of the day (PM period) limit the number of activities that an individual can pursue at that time. Another interesting finding is that gende r does not significantly influence tour complexity in the case of nonwork tours. Other studies have suggested that females tend to make more complex trip chains than males (McGuckin et al., 1999). The analysis in this thesis does not support that finding in the Swiss travel context. The tours primary purpose appears to affect tour complexity. While service (serve passenger) tours tend to be complex in nature, shopping tours do not tend to be comp lex in nature. Thus it appears that the shopping activity may be more prone to being a standalone activity within a tour. The error correlation is found to be statistically sign ificant and this is indi cative of the validity of the assumption that nonwork tour complex ity and mode choice should be modeled in a simultaneous equations framework. The ne gative sign associated with the error correlation indicates that the unobserved fact ors influencing these two variables are
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39 negatively correlated. Further analysis is warranted to fully explain the implications of the negative error correlation. Table 5.3 provides estimation results for the causal structure where mode choice affects tour complexity for nonwork tours. In terestingly, it is found that mode choice significantly affects tour complexity and that the choice of auto is positively associated with the formation of complex tours. Thus it appears from this m odel that the choice of the automobile mode for a tour contributes positively to the formation of multistop trip chains. In addition, the error correlation is significant and ne gative as in Ta ble 5.2. All of the other indications provide d by the model system are similar to those seen in Table 5.2. The tour length (distance in km) is f ound to significantly contri bute to the choice of the auto mode. Tables 5.2 and 5.3 appear to support the no tion that there is a bidirectional causality between mode choice and tour complexity. In both models (representing two different causal structures), the coefficient associated with the endogenous variable on the right hand side is statistically significant and consis tent with expectations and trends in the data set. In addition, both models offe r significant and negative error correlation supporting the simultaneous equations formul ation for representing the relationship between mode choice and tour complexity. In light of these findings, Ta ble 5.4 provides estimation resu lts of the simultaneous logit model for nonwork tours in which mode c hoice and tour complexity influence each
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other simultaneously and bidirectional causality is allowed. The significantly positive joint dependence parameter, shows the presence of significant positive correlation between auto mode choice and tour complexity. The other explanatory variables provide similar indications as those in Table 5.2. As all of the estimation results in Tables 5.2 through 5.4 offer plausible and similar interpretations, a more rigorous performance comparison must be conducted among the models to potentially identify the causal structure underlying the data set. This performance comparison is presented in Chapter 5 following the discussion of the estimation results for the work tour models. 5.3 Estimation Results for Work Tour Models Estimation results for work tour models are provided in Tables 5.6 through 5.8. Table 5.6 provides estimation results for the causal structure where tour complexity affects mode choice, Table 5.7 provides estimation results for the causal structure where mode choice affects tour complexity, and Table 5.8 provides estimation results for the simultaneous logit model that is intended to capture simultaneous causality between the two variables. In Table 5.6, it is found that tour complexity has a positive impact on auto mode choice. This is consistent with expectations, trends in the data, and the models of nonwork tours. The coefficient associated with tour complexity variable in the mode choice model is positive and statistically significant. 40
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41 Thus the model supports the notion that a com plex tour or trip chaining pattern contributes to the choice of auto as the mo de for the tour. In addition, the error correlation is negative and statistica lly significant, once again supporting the simultaneous equations formulation of the relationship between tour complexity and mode choice. Table 5.5 Description of Explanatory Va riables Used in W ork Tour Models (N = 1711) Variable Na me Variable Description Mean Std Dev AUTO Auto mode choice for tour 0.54 0.50 BEG13_14 Tour starts in time pe riod from 13:00 to 14:59 0.11 0.31 BEG68 Tour starts in time period from 6:00 to 8:59 0.67 0.47 COMPLEX Tour is complex (multistop) 0.51 0.50 COUNTRY Residence is locat ed in rural area 0.11 0.31 DISWORK Distance between reside nce and work place (km ) 11.02 15.02 END12 Tour ends in time period from 12:00 to 12:59 0.12 0.32 FREEPARK Reserved parking lot at the work place is free 0.33 0.47 FULLTIME Person is fulltime employed 0.77 0.42 HHSIZE1 Single person household 0.30 0.46 HIGHINC Monthly household incom e > Fr10000 0.21 0.41 OWN_BUS Person owns enterprise/business 0.14 0.35 OWNRES Person owns the residence 0.30 0.46 MALE Person is male 0.61 0.49 SWISS Person is of Swiss Nationality 0.85 0.36 With respect to other variable s, it is found that free parki ng, longer commutes, full time employment, and rural residence are all positiv ely influencing the choice of auto as the mode choice for work tours. All of these findings are consistent w ith expectations. In the tour complexity model, it is found that single persons tend to engage in multistop trip chains possibly due to the inability to sh are or allocate tasks among multiple household members.
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Table 5.6 Work Tour Model (Complex Tour Auto Mode Choice) Variable Parameter ttest Auto Mode Choice Model Constant 1.0013 8.757 FREEPARK 1.2859 15.278 DISWORK 0.0062 2.673 COUNTRY 0.5123 4.469 FULLTIME 0.2458 3.094 COMPLEX 0.8106 3.723 Complex Tour Choice Model Constant 0.4812 4.844 HHSIZE1 0.1859 2.640 HIGHINC 0.3173 4.000 OWNBUS 0.3312 3.660 SWISS 0.2529 2.833 OWN_RES 0.1592 2.222 BEG68 0.3096 4.180 BEG1314 0.3678 3.238 END12 0.7236 7.384 (Error Correlation) 0.3481 2.404 Sample Size 1711 Number of parameters 16 Loglikelihood At convergence 2076.249 At market share 2354.340 At zero 2371.950 42
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Table 5.7 Work Tour Model (Auto Mode Choice Complex Tour) Variable Parameter ttest Auto Mode Choice Model Constant 0.6690 8.596 MALE 0.1269 1.671 FREEPARK 1.3003 16.783 DIS_WORK 0.0081 3.546 COUNTRY 0.5346 4.541 FULLTIME 0.2229 2.519 Complex Tour Choice Model Constant 0.5924 4.765 HHSIZE1 0.1465 2.085 HIGHINC 0.3003 3.693 OWN_BUS 0.2465 2.637 SWISS 0.2997 3.358 BEG68 0.3193 4.183 BEG1314 0.4198 3.541 END12 0.7380 7.319 AUTO 0.2715 2.003 (Error Correlation) 0.0050 0.054 Sample Size 1711 Number of parameters 16 Loglikelihood At convergence 2078.843 At market share 2354.340 At zero 2371.950 43
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Table 5.8 Work Tour Model Simultaneous Logit Model (Auto Mode Choice Complex Tour) Variable Parameter ttest Auto Mode Choice Model Constant 1.2268 9.351 MALE 0.2470 2.022 FREEPARK 2.1867 16.104 COUNTRY 0.9025 4.689 FULLTIME 0.3679 2.592 Complex Tour Choice Model Constant 1.0245 5.996 HHSIZE1 0.2917 2.498 HIGHINC 0.4818 3.671 OWNBUS 0.4424 2.967 SWISS 0.4495 3.076 OWNRES 0.1666 1.401 BEG68 0.5174 4.184 BEG1314 0.6688 3.498 END12 1.2212 7.286 (Joint Dependence) 0.4859 4.906 Sample Size 1711 Number of parameters 15 Loglikelihood At convergence 2079.840 At market share 2354.340 At zero 2371.950 44
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45 Individuals owning their business enterprise and place of residence are found to be more prone to engage in multistop trip chains, presumably for seeing multiple clients, visiting to office or supply stores, etc. A few variables were found to be statistically significant, but are potentially more difficult to interpret. For example, individuals of Swiss Nationality are more likely to engage in comp lex work tours. It is possible that these individuals have occupational ch aracteristics that lead to the formation of complex trip chains. Another interesting find ing is that timeofday indica tors play an important role in influencing tour complexity. Tours endi ng within the lunch hour are less prone to be complex possibly due to time constraint s and the presence of a single lunch stop/destination. However, th ose beginning in the morning pe riod of 6 to 9 AM are more prone to being multistop trip chains, possibl y due to the linking of a nonwork activity with the work activity in the overall tour. A more detailed timeofday based analysis of trip chain formation is warra nted to fully understand the re lationship between trip chain complexity and time of day choice behavior. Within the context of this study, time of day choice is assumed exogenous to the mode l system. However, one may argue that time of day choice is endogenous to trip chain complexity and mode choice. The study of the simultaneous causal relationships among trip chain formation, mode choice, and time of day choice (three e ndogenous entities) remains a future research effort. Table 5.7 gives estimation resuls for the m odel where mode choice affects work tour complexity. As before, the coefficient associat ed with the auto mode choice variable in the tour complexity equation is statistically significant and positive indicating that the choice of auto mode contributes positively to the formation of complex multistop trip
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chains. However, unlike other models, the error correlation is statistically insignificant. Thus, this model suggests that tour complexity and mode choice can be modeled as two independent equations where mode choice affects tour complexity in a recursive unidirectional causal structure. While this may be possible, it is highly unlikely to be true given the findings suggested by the previous models where the error correlation is consistently significant and negative in value. Thus, this model is suggesting that the unobserved factors in the two equations are uncorrelated and challenging the assumption of simultaneity in the relationship between auto mode choice and tour complexity. Given that this model contains no additional explanatory variables or power than the other previous models, the authors feel that a rejection of the assumption of simultaneity is not warranted. Despite the very different value of the error correlation between models presented in Tables 5.6 and 5.7, virtually all of the other variables show similar indications between the two model structures. Table 5.8 furnishes estimation results of the simultaneous logit model for work tours. The joint dependence parameter, is found to be statistically significant and positive. This model supports the notion that there is a significant and positive bidirectional causal relationship between tour complexity and auto mode choice. All of the other explanatory variables are found to offer indications very similar to those seen in Tables 5.6 and 5.7. 46
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47 CHAPTER 6 MODEL PERFORMANCE COMPARISONS 6.1 GoodnessofFit Measure The model estimation results presented in Chap ter 5 generally offer plausible indications for alternative causal paradigms. The only model that may be rejected on qualitative grounds is that in Table 5.7 where the mode choice decision precedes the tour complexity decision. The statistically in significant random e rror correlation which implies that there are no correlated unobserv ed factors between mode choice and tour complexity appears difficult to explain and defend in light of the simultaneity shown by the other models. This chapter presents a more rigorous compar ison across models to see if it is possible to identify the most likely causal structure gove rning the relationship between mode choice and trip chaining. A goodnessoffit comparison among the models of different causal structures is conducted first. The adjusted likelihood ratio index as a goodnessoffit measure can be used for testing and comparing nonnested re lationships in discrete choice models. The indices are given as follows:
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)0()(1020LKL 6.1 )()(12cLKLcc 6.2 20 : Adjusted likelihood ratio index at zero 2c : Adjusted likelihood ratio index at market share )( L : Loglikelihood value at convergence )0(L : Loglikelihood value at zero )(cL : Loglikelihood value at market share (model including only the constant term) K 0 and K c : the number of parameters in the corresponding model. The adjusted likelihood ratio indices for all of the models are presented in Tables 6.1 and 6.2. Table 6.1 Likelihood Ratio Comparison in Nonwork Tour Models (N = 4901) Causal Structure Number of Parameters (K) 20 2c 20 2c Complexity Auto 20 0.238 0.097 0.235 0.093 Auto Complexity 18 0.234 0.092 0.231 0.089 Complexity Auto 19 0.234 0.093 0.231 0.089 48
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Table 6.2 Likelihood Ratio Comparison in Work Tour Models (N = 1711) Causal Structure Number of Parameters (K) 20 2c 20 2c Complexity Auto 16 0.125 0.118 0.118 0.111 Auto Complexity 16 0.124 0.117 0.117 0.111 Complexity Auto 15 0.123 0.117 0.117 0.110 6.2 Nonnested Test Likelihood ratio test, a statistical test of the goodnessoffit between two models, is widely applied for selecting more appropriate models estimated by maximum likelihood method. A relatively more complex model is compared to a simpler model to see if it fits the dataset significantly better. If so, the more complex model is considered as the better one. The likelihood ratio test is given as below. LR = 2 (lnL R lnL U ) ~ 2 (N) 6.3 under the null hypothesis that the restrictions on unrestricted model are jointly valid. LR: Loglikelihood Ratio lnL R : Loglikelihood function value for restricted model lnL u : Loglikelihood function value for unrestricted model N: number of restrictions imposed on the parameters in unrestricted model to achieve restricted model. However, likelihood ratio test is only valid if it is used to compare hierarchically nested models. That is, the more complex model must differ from the simple model only by the 49
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additional restrictions on the existing parameters in complex model. Restricted model should be developed by imposing restriction on the more general unrestricted model. In this thesis, the models in three different causal structures need to be compared one another, but no pair models of them are hierarchically nested since none model can be formed from either of the other two models with additional restriction. The adjusted likelihood ratio index 20 as a goodnessoffit measure can be used for testing nonnested hypothesis of discrete choice modes. To choose between two models (say, 1 and 2), Benakiva and Lerman (1985, p. 172) provide a test where under the null hypothesis that model 1 is the true specification, the following holds asymptotically: 0},)]()0(2[{)Pr(2/1122122zKKzLz 6.4 where 2i : the adjusted likelihood ratio index at zero for model i = 1, 2 K i : the number of parameters in model i : the standard normal cumulative distribution function )0(L : loglikelihood value at zero; if all N observations in the sample have all J alternatives, L(0) = N ln(1/J). The probability that the adjusted likelihood ratio index of model 2 is greater by some z > 0 than that of model 1, given that the latter is the true model, is asymptotically bounded by the righthand side of equation 6.4 above. If the model with the greater 2 is selected, then this bounds the probability of erroneously choosing the incorrect model over the true 50
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51 specification. Using this procedure, models of alternative causa l structures can be compared against one another. 6.3 Comparison Results For nonwork tour models, the difference in adjusted likelihood ratios is approximately 0.004 between the models in Table 5.2 and the models in Tables 5.3 and 5.4. According to equation 6.4, the calculated bounding probability on the right hand side of the expression is almost zero. Thus, it may be c oncluded that the model of Table 5.2 is more closely capturing the causal st ructure underlying the relatio nship between mode choice and tour complexity. The significantly bett er goodnessoffit of the model in Table 5.2 suggests that the causal structur e where the complexity of th e tour affects mode choice (tour complexity auto mode choice) is statisti cally, and possibly behaviorally, dominant in the population for nonwork tour s. One must be careful when drawing inferences regarding behavioral causa lity from statistical indicators. For work tour models, however, the situation is not as clear. In comparing the models, the seemingly better model of Table 5.6 has an adjusted likelihood rati o index that is only 0.001 greater than those of th e models in the other two causal structures. The bounding probabilities, as per the right hand side of equation 6.4, are calculated to be 0.036 and 0.067, respectively. The statistic al test rejects the model of Table 5.7, i.e., the causal structure where auto mode choice drives the complexity of the work tour (auto mode choice tour complexity). However, the test fails to reject the simultaneous logit model, i.e., bidirectional simultaneous causality, at the 0.05 level of significance. In addition to
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52 this nonnested test, the insignificance of the random error correlation in the model of auto mode choice affecting tour complexity s uggests that the assumed causal structure in that joint model may not be valid and may be indicative of the irrationality of causality in that direction. Thus, for work tours, two possible causal stru ctures can not be rejected from this analysis. Either, th e decision to make a complex work tour tends to result in the choice of the auto mode or both of thes e decisions are made contemporaneously. From the viewpoint of activity based travel behavior theory where travel choices are considered to be derived from activity patter ns (and activity needs th at are distributed in time and space), one may consider the findings of this thesis to be quite consistent with expectations. For nonwork tours, the statistical model estimation resu lts show that tour complexity (which is reflective of the activ ity pattern) drives mode choice. For work tours, the statistical model estimation results reject the notion that auto mode choice drives tour complexity. Once ag ain, either tour complexity drives auto mode choice or both decisions are simultaneously related to one another.
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53 CHAPTER 7 DISCUSSION AND CONCLUSION 7.1 Discussion Mode choice behavior is a f undamental element of travel be havior that has significant implications for transportation planning. Estim ates of public transit ridership and the use of alternative modes of transportation ar e largely based on studi es of mode choice behavior and modal split models. Public transport agencies face increasing competition from the automobile as automobiles become increasingly affordable and the road infrastructure becomes increasingly ubiquitous. Undoubtedly, the automobile is considered to provide greater flexibility a nd convenience when compared with public transport modes that are generally cons trained with respect to schedules and routes/destinations. This study examines the interrelationship between the complexity of peoples activitytravel patterns and their mode choice. In order to conduct the analysis, this thesis examines mode choice behavior in the cont ext of multistop (complex) vs singlestop (simple) trip chains. Through a series of econometric model formula tions, this thesis presents a rigorous analysis of the most likely causal relationship between these two phenomena at the level of the i ndividual trip chain or tour. It should be emphasized that
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54 the analysis in this thesis does not attempt to replicate causality at the level of the individual traveler, but rather at the macrosc opic level to identify the causal tendency that appears to be dominant in the population. Using data derived from the 2000 Swiss Trav el Microcensus, the thesis estimates bivariate probit models and simultaneous logit models that provide a rigorous analytical framework for analyzing and testing alternat ive causal structures. In the case of nonwork tours (i.e., tours that do not involve any work stops), the analysis suggests that the causal structure where the complexity of the trip chaining pattern dr ives mode choice is the dominating causal trend in th e population. In the case of work tours (i.e., tours that involve at least one work stop) the analysis sugges ts that the causal structure where the auto mode choice drives the complexity of the tour can be rejected statistically. Thus, either tour complexity drives mode choi ce or the two phenomena occur simultaneously. 7.2 Contribution These findings have important implications fo r public transport serv ice providers who are interested in attracting choice riders. If mode choice decisions precede activity pattern/agenda decisions, then it may be possibl e for public transport service providers to simply attract choice riders by improving amenities, schedule, route coverage, safety and security, and comfort. On the other hand, if the formation of the ac tivity agenda precedes mode choice decisions, then th e public transport industry has a greater challenge before it. Trip chaining and tour complexity serve as impediments to public transport usage. The analysis in this thesis suggests that this is the predominant relationship in the data set.
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55 Then, not only do public transport service providers have to improve service amenities, but they also have to try a nd cater to a multitasking oriented complex activity agenda. This is extremely difficult to do with a fi xed route fixed schedule system. As activitytravel patterns and tours become increasingly complex, it is likely that public transport agencies will have to develop new types of se rvices to try and retain existing riders in addition to attracting new riders. The analysis and findings of this thesis are also useful from an activitybased and tourbased model development standpoint. Most activitybased and tourbased travel demand model systems consist of hierarchical structures involving activity agenda or tour formation, mode choice, destination choice, and time of day choice. The development and application of these model systems calls for the ability to accurately represent causal relationships that are prevalen t in the population. This thes is suggests that the activity agenda or tour formation step may precede the mode choice step for both nonwork and work tours, although the hierarchy is less clea r for the latter. 7.3 Future Research Future research efforts should focus on analyzing whether these findi ngs regarding causal relationships between tour comple xity and mode choice hold in ot her data sets as well. In addition, the modeling framework can be extended to consider multinomial choice situations as opposed to pure binary choice variables consider ed in this thesis. Mode choice can be expanded to consider multiple modes including SOV, shared ride, public transit, and nonmotorized modes. Similarl y, tour complexity can be expanded to
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56 consider different levels of tour complexity or different tour types su ch as that presented in Strathman and Dueker (1995). Another cons ideration that merits further investigation is the extent to which findings such as those presented in this thesis are sensitive to model specification. It is possible that statistical indicators of model performance will change depending on the model specification chosen. Such efforts would further aid in understanding important causal relations hips underlying tr avel behavior. Finally, it must be noted that causal relati onships are being extracted and examined in this thesis from statistical relationships estimated on revealed outcome data. While such data provides insights into what people have done, it does no t provide true insights into the decision mechanisms and behavioral proc esses underlying the revealed outcomes. In order to truly understand and identify causal relationships, data regarding processes and decision mechanisms are needed. Future research into the development of microsimulation models of activity and travel behavior should include attempts to collect and analyze such data.
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57 REFERENCES Aptech (1996) GAUSS 3.2, Aptech Systems, Maple Valley, Washington. BenAkiva, M. and Lerman, S.R. (1985) Discrete Choice Analysis: Theory and Application to Travel Demand. The MIT Press, Cambridge, MA. Bhat, C.R. (1997) Work Travel Mode Choice and Number of Nonwork Commute Stops. Transportation Research B 31(1), pp. 4154. Dissanayake, D. and Morikawa, T. (2002) Ho usehold Travel Behavi or in Developing Countries: Nested Logit Model of Vehicle Own ership, Mode Choice, and Trip Chaining, Transportation Research Record 1805, Journal of the Transportation Research Board, National Research Council, Washington, D.C., pp. 4552. Fujii, S., Kitamura, R., and Kishizawa, K. ( 1999) Analysis of Individuals Joint Activity Engagement Using a Model System of Activitytravel Behavior and Time Use, Transportation Research Record 1676, pp. 1119. Fujii, S. and Kitamura, R. (2000) Evaluati on of Tripinducing Effects of New Freeways Using a Structural Equations Model System of Commuters' Time use and Travel, Transportation Research B 34, pp. 339354. Golob, T.F. and E.R. Zondag (1984). A causal model of mobility. Presented at the Tenth Transportation Planning Research Colloquium. Zandvoort, the Netherlands. Golob, T.F. and H. Meurs (1987). A structural model of te mporal changes in multimodal travel demand. Transportation Research A, 21: 391400. Golob, T.F. and L.J. van Wissen (1989). A jo int household travel di stance generation and car ownership model. Transportation Research B 23: 471491. Golob, T.F., R. Kitamura and G. Occhiuzzo (1991). An attitudeb ehavioral intention model of the market potential for alternativefuel vehicles: the "green" segment and the role of information. Presented at Annual Meeting of Transportation search Board, Washington, D.C.
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58 Golob, T.F. and D. Brownstone (1992). A dynamic attitudebehavior model of consumer reactions to incentives for restricting solo driving trips for environmental reasons. Presented at 6th World Conference on Transport Research, Lyon, France, June 29July 3. Golob, T.F. R. Kitamura and C. Lula ( 1994). Modeling the Effect s of Commuting Time on Activity Duration and NonWork Travel. Presented at Annual Meeting of Transportation Research Board, Washington, D.C. Golob, T.F. and McNally, M. G. (1997) A Model of Activity Particip ation and Travel Interactions Between Household Heads, Transportation Research B 31(3), pp. 177194. Golob, T.F (2000). A Simultane ous Model of Household Activ ity Participation and Trip Chain Generation. Transportation Research B 34, pp. 355376. Golob T.F. (2000) A Simultaneous Model of Household Activity Part icipation and Trip Chain Generation, Transportation Research B 34, pp. 355376. Greene, W.H. (2003) Econometric Analysis, Fifth Edition, Pearson Education, Inc., NJ. Greene, W.H. (2002) LIMDEP Version 8.0: User's Manual, Econometric Software, Inc., 2002, Plainview, NY. Hensher, D.A. and Reyes A.J. (2000) Trip Ch aining as a Barrier to the Propensity to Use Public Transport. Transportation 27, pp. 341361. Kitamura, R. (1988). An evaluation of activitybased tr avel analysis. Transportation 15 pp. 934. Kitamura, R., J.P. Robinson, T.F. Golob, M.A. Bradley, J. Leonard and T. van der Hoorn (1992). A comparative analysis of time use data in the Neth erlands and California. In Proceedings of the 20 th PTRC Summer Annual Meeting: Transportation Planning Methods, pp. 127138. Kitamura, R. (1996). Activitybased travel demand forecasting and policy analysis. Presented at the TMIP Conference on ActivityBased Travel Forecasting, New Orleans, LA, June 25. Kitamura, R., C. Chen, and R.M.Pendyala (1997). Generation of Synthetic Daily ActivityTravel Patterns. Transportation Research Record 1607, pp. 154162. Kitamura, R., Fujii, S. and Pas, E.I. (1997) Timeuse Data, Analysis and Modeling: Toward the Next Generation of Tr ansportation Planning Methodologies. Transport Policy 4(4), pp. 225235.
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59 Kitamura, R., C. Chen, and R. Narayanan (1998 ). The Effects of Time of Day, Activity Duration and Home Location on Travelers Destinati on Choice Behavior. Paper Presented at the 77 th Annual Meeting of Transportation Research Board, Washington, D.C. Koppelman, F.S. and Wen, C. (1998) Altern ative Nested Logit Models: Structure, Properties and Estimation, Transportation Research B 32(5), pp. 289298. Kuppam, A.R. (1999). A Limited Dependent Va riable Structural Equations Model of Travel Behavior for Transportation Policy Evaluation. PhD Di ssertation, Department of Civil and Environmental Engineering, Univer sity of South Florida, Tampa, FL. Kuppam, A.R. and R.M. Pendyala (2000). An ex ploratory analysis of commutersactivity and travel patterns. Presented at the 79 th Annual Meeting of the Transportation research Board, Jan. 913, Washington, DC. Lu, X. and E.I. Pas (1997). A structural e quations model of the relationships mong sociodemographics, activity participation and travel behavior. Presented at 76th Annual Meeting of the Transportation Research Board, January 1216, Washington, DC. Lu, X. and Pas, E.I. (1999). Sociodemogr aphics, Activity Participation and Travel Behaviour, Transportation Research A 33, pp. 118. Maddala, G.S. (1983) Limiteddependent and Qualitative Variables in Econometrics, Cambridge University Press, Cambridge, MA. McGuckin, N. and Murakami, E. (1999) Examining TripChaining Behavior: A Comparison of Travel by Men and Women, Transportation Research Record 1693, Journal of the Transportation Research Board, National Research Council, Washington, D.C., pp. 7985. Meka, S. (2003). A Structural Equations Analysis of W ithinHousehold Activity and Time Allocation Between Two Adults, Mast er Thesis, Department of Civil and Environmental Engineering, University of South Florida, Tampa, FL. Misra, R., Bhat, C. and Srinivasan, S. ( 2003) A Continuous Time Representation and Modeling Framework for the Analysis of Nonworker ActivityTravel Patterns: Tour and Episode Attributes. CDROM of the 82nd Annual Meeting of the Transportation Research Board, National Research Council, Washington, D.C. Ouyang, Y., Shankar, V. and Yamamoto, T. (2002) Modeling the Simu ltaneity in Injury Causation in Multivehicle Collisions. CDROM of the 81st Annual Meeting of the Transportation Research Board, National Research Council, Washington, D.C.
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60 Pas, E.I. (1996). Recent advances in activityb ased travel demand modeling. Presented at the TMIP Conference on ActivityBased Travel Forecasting, New Orleans, LA, June 25. Pas, E. & Harvey. A.S. (1997). Understanding travel behavior in an era of change. (Eds.) Peter R. Stopher.and Martin LeeGosselin. New York: Pergamon Press. Pendyala, R.M., Bhat, C., Parashar, A. and Mu thyalagari, G.R. (2001) An Exploration of the Relationship between Timing and Duration of Maintenance Activities. CDROM of the 81st Annual Meeting of the Trans portation Research Board, National Research Council, Washington, D.C. RDC, Inc. (1995). ActivityBased Modeli ng System for Travel Demand Forecasting, TMIP. Schmidt, P. and Strauss, R.P. (1975) Es timation of Models with Jointly Dependent Qualitative Variables: A Simultaneous Logit Approach. Econometrica 43(4), pp. 745755. Shiftan, Y. (1998) Practical Appr oach to Model Trip Chaining, Transportation Research Record 1645, Transportation Research Board, Na tional Research Council, Washington, D.C., pp. 1723. Simma, A. and Axhausen, K.W. (2001). With inHousehold Allocation of Travel: The Case of Upper Austria. Presented at the 80 th Annual Meeting of the Transportation Research Board, Washington, D.C. Strathman J.G. and Dueker K.J. (1994) Effe ct of Household Structure and Selected Characteristics on Trip Chaining. Transportation 21, pp. 2345. Strathman, J.G. and Dueker, K.J. (1995) Understanding Trip Chaining, Special Reports on Trip and Vehicle Attributes, 1990 NPTS Reports Series, Publication No. FHWAPL95033, U.S. Department of Tr ansportation, pp. 11 127. Ye, X. and Pendyala, R.M. (2003) Description of the Switzerland Microcensus 2000 Travel Survey Sample. Research Report prepared for Jenni + Gottardi AG, Department of Civil and Environmental E ngineering, University of S outh Florida, Tampa, FL.
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61 APPENDICES
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62 Appendix A: Gauss Codes for Simultaneo us Logit Model of Nonwork Tours library maxlik; maxset; load data[4901,131] = "C:\\swiss\\multicho ice\\nonwork_tours_zurich_4901.dat"; one=ones(4901,1); intnr = data[., 1 ]; tournum = data[., 2 ]; hhnr = data[., 3 ]; tripdist = data[., 4 ]; tripdur = data[., 5 ]; beg_time = data[., 6 ]; end_time = data[., 7 ]; nsegment = data[., 8 ]; trip_pur = data[., 9 ]; mode_dur = data[., 10 ]; mode_dis = data[., 11 ]; person = data[., 12 ]; targetpn = data[., 13 ]; intdur = data[., 14 ]; weekday = data[., 15 ]; day = data[., 16 ]; season = data[., 17 ]; age = data[., 18 ]; sex = data[., 19 ]; employed = data[., 20 ]; study = data[., 21 ]; auto_lic = data[., 22 ]; motr_lic = data[., 23 ]; live_st = data[., 24 ]; national = data[., 25 ]; study16 = data[., 26 ]; edu_lev = data[., 27 ]; emp_sit = data[., 28 ]; school = data[., 29 ]; emp_reg = data[., 30 ]; worktime = data[., 31 ]; occ_posi = data[., 32 ]; dis_work = data[., 33 ]; pklot_wk = data[., 34 ]; n_trp_wk = data[., 35 ];
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63 Appendix A: (Continued) dis_schl = data[., 36 ]; pklot_sc = data[., 37 ]; n_tr_sch = data[., 38 ]; av_bike = data[., 39 ]; av_egbik = data[., 40 ]; av_motor = data[., 41 ]; av_auto = data[., 42 ]; weather = data[., 43 ]; workday = data[., 44 ]; leavehom = data[., 45 ]; why_nlv = data[., 46 ]; when_lv = data[., 47 ]; comp_pwk = data[., 48 ]; kilo_pwk = data[., 49 ]; y_ljny_r = data[., 50 ]; n_jny_3m = data[., 51 ]; m_ljny_r = data[., 52 ]; d_ljny_r = data[., 53 ]; n_nights = data[., 54 ]; means_r = data[., 55 ]; ds_jny_i = data[., 56 ]; ds_jny_e = data[., 57 ]; air_12m = data[., 58 ]; air_5y = data[., 59 ]; n_air_5y = data[., 60 ]; y_l_air = data[., 61 ]; air_pur = data[., 62 ]; hol_trp = data[., 63 ]; pck_tour = data[., 64 ]; mn_airpt = data[., 65 ]; y_tkoff = data[., 66 ]; m_tkoff= data[., 67 ]; d_tkoff = data[., 68 ]; nair_12m = data[., 69 ]; n_ck_12m = data[., 70 ]; hhld_w = data[., 71 ]; canton = data[., 72 ]; hhdate = data[., 73 ]; language = data[., 74 ]; city_typ = data[., 75 ]; city_rur = data[., 76 ]; hhsize = data[., 77 ];
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64 Appendix A: (Continued) hh6plus = data[., 78 ]; n_targtp = data[., 79 ]; hhincome = data[., 80 ]; perm_add = data[., 81 ]; add_swit = data[., 82 ]; y_in_add = data[., 83 ]; faml_typ = data[., 84 ]; rent_own = data[., 85 ]; n_apartm = data[., 86 ]; n_2ndhom = data[., 87 ]; own_park = data[., 88 ]; n_park = data[., 89 ]; n_auto = data[., 90 ]; n_motor = data[., 91 ]; n_smotor = data[., 92 ]; n_engbik = data[., 93 ]; n_bike = data[., 94 ]; n_bik_lc = data[., 95 ]; bad_ch_1 = data[., 96 ]; nwk_ch_1 = data[., 97 ]; work_c_1 = data[., 98 ]; sim_comx = data[., 99 ]; pr_mode4 = data[., 100 ]; uni_mult = data[., 101 ]; kid = data[., 102 ]; kid5 = data[., 103 ]; kid6_17 = data[., 104 ]; dri_lic = data[., 105 ]; age0_5 = data[., 106 ]; age6_17 = data[., 107 ]; age18_24 = data[., 108 ]; age25_34 = data[., 109 ]; age35_44 = data[., 110 ]; age45_54 = data[., 111 ]; age55_64 = data[., 112 ]; age65_74 = data[., 113 ]; age75 = data[., 114 ]; male = data[., 115 ]; female = data[., 116 ]; pr_pur = data[., 117 ]; nwf_firs = data[., 118 ]; nwf_mid = data[., 119 ];
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65 Appendix A: (Continued) nwf_last = data[., 120 ]; chain_tp = data[., 121 ]; beg_c = data[., 122 ]; end_c = data[., 123 ]; pmode5 = data[., 124 ]; mode3 = data[., 125 ]; auto = data[., 126 ]; complx = data[., 127 ]; tourmode = data[., 128 ]; m_sov = data[., 129 ]; m_hov = data[., 130 ]; m_other = data[., 131 ]; /* dummy variables definition */ shopping = (pr_pur .==4) ; leisure = (pr_pur .==5) ; service = (pr_pur .==3) ; pschool = (pr_pur .==2) ; business = (pr_pur .==1) ; pmale = (sex .==1) ; old = (age.>60) ; young = (age.<18 .and age.>0) ; high_inc = (hhincome.>=6) ; car_0 = (n_auto .==0) ; car_1 = (n_auto .==1) ; car_ge2 = (n_auto.>=2) ; low_inc = (hhincome .<3 .and hhincome.>0) ; with_kid = ((hhsizehh6plus).>0) ; hhsize1 = (hhsize .==1) ; hhsize2 = (hhsize .==2) ; hhsize3 = (hhsize .==3) ; hhsize4 = (hhsize.>3) ; high_edu = (EDU_LEV .==6 .or EDU_LEV .==7) ; with_kid = (kid5.>0) ; with_you = (kid6_17.>0) ; weekend = (weekday .==5) ; bad_weat = (weather.>=4 .and weather.<=7) ; rain = (weather .==5) ; working = (workday .==1) ; ad1_you1= (kid6_17.>0 .and hhsize.==2) ; ampeak=(beg_c.==7 .or beg_c.==8); pmpeak=(beg_c.==16 .or beg_c.==17);
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66 Appendix A: (Continued) proc lpr(b,z); local x,y,ux,uy,alpha,delta,p00,p01,p10,p11; x = one~hhsize~high_inc~low_inc~ car_ge2~pmale~service~pschool; y = one~hhsize1~ad1_you1~hhsize4~old~y oung~service~shopping~ampeak~pmpeak; ux=x*b[1:8,.]; /* utility for auto */ uy=y*b[9:18,.]; /* utility for complex chain */ alpha=b[19,.]; /* joint dependence */ delta= 1 + exp(ux) + exp(uy) + exp(ux + uy + alpha) ; p00=one./delta; /* probability of nonauto & simple */ p01=exp(uy)./delta; /* probabili ty of nonauto & complex */ p10=exp(ux)./delta; /* probability of auto & simple */ p11= exp(ux+uy+alpha)./delta; /* probability of auto & complex */ retp ( (1auto) .* (1complx).*ln( p00 ) + (1auto) .* complx.*ln( p01 ) + auto .* (1complx).*ln( p10 ) + auto .* complx.*ln( p11 ) ) ; endp; b0={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}; {b,f,g,cov,ret}=maxlik(data,0,&lpr,b0); call maxprt(b,f,g,cov,ret);
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67 Appendix B: Gauss Codes for Simultaneous Logit Model of Work Tours library maxlik; maxset; load data[1711,131] = "C:\\swiss\\multicho ice\\work_tours_zurich_1711.dat"; one=ones(1711,1); intnr = data[., 1 ]; tournum = data[., 2 ]; hhnr = data[., 3 ]; tripdist = data[., 4 ]; tripdur = data[., 5 ]; beg_time = data[., 6 ]; end_time = data[., 7 ]; nsegment = data[., 8 ]; trip_pur = data[., 9 ]; mode_dur = data[., 10 ]; mode_dis = data[., 11 ]; person = data[., 12 ]; targetpn = data[., 13 ]; intdur = data[., 14 ]; weekday = data[., 15 ]; day = data[., 16 ]; season = data[., 17 ]; age = data[., 18 ]; sex = data[., 19 ]; employed = data[., 20 ]; study = data[., 21 ]; auto_lic = data[., 22 ]; motr_lic = data[., 23 ]; live_st = data[., 24 ]; national = data[., 25 ]; study16 = data[., 26 ]; edu_lev = data[., 27 ]; emp_sit = data[., 28 ]; school = data[., 29 ]; emp_reg = data[., 30 ]; worktime = data[., 31 ]; occ_posi = data[., 32 ]; dis_work = data[., 33 ]; pklot_wk = data[., 34 ]; n_trp_wk = data[., 35 ]; dis_schl = data[., 36 ]; pklot_sc = data[., 37 ]; n_tr_sch = data[., 38 ];
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68 Appendix B: (Continued) av_bike = data[., 39 ]; av_egbik = data[., 40 ]; av_motor = data[., 41 ]; av_auto = data[., 42 ]; weather = data[., 43 ]; workday = data[., 44 ]; leavehom = data[., 45 ]; why_nlv = data[., 46 ]; when_lv = data[., 47 ]; comp_pwk = data[., 48 ]; kilo_pwk = data[., 49 ]; y_ljny_r = data[., 50 ]; n_jny_3m = data[., 51 ]; m_ljny_r = data[., 52 ]; d_ljny_r = data[., 53 ]; n_nights = data[., 54 ]; means_r = data[., 55 ]; ds_jny_i = data[., 56 ]; ds_jny_e = data[., 57 ]; air_12m = data[., 58 ]; air_5y = data[., 59 ]; n_air_5y = data[., 60 ]; y_l_air = data[., 61 ]; air_pur = data[., 62 ]; hol_trp = data[., 63 ]; pck_tour = data[., 64 ]; mn_airpt = data[., 65 ]; y_tkoff = data[., 66 ]; m_tkoff= data[., 67 ]; d_tkoff = data[., 68 ]; nair_12m = data[., 69 ]; n_ck_12m = data[., 70 ]; hhld_w = data[., 71 ]; canton = data[., 72 ]; hhdate = data[., 73 ]; language = data[., 74 ]; city_typ = data[., 75 ]; city_rur = data[., 76 ]; hhsize = data[., 77 ]; hh6plus = data[., 78 ]; n_targtp = data[., 79 ]; hhincome = data[., 80 ];
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69 Appendix B: (Continued) perm_add = data[., 81 ]; add_swit = data[., 82 ]; y_in_add = data[., 83 ]; faml_typ = data[., 84 ]; rent_own = data[., 85 ]; n_apartm = data[., 86 ]; n_2ndhom = data[., 87 ]; own_park = data[., 88 ]; n_park = data[., 89 ]; n_auto = data[., 90 ]; n_motor = data[., 91 ]; n_smotor = data[., 92 ]; n_engbik = data[., 93 ]; n_bike = data[., 94 ]; n_bik_lc = data[., 95 ]; bad_ch_1 = data[., 96 ]; nwk_ch_1 = data[., 97 ]; work_c_1 = data[., 98 ]; sim_comx = data[., 99 ]; pr_mode4 = data[., 100 ]; uni_mult = data[., 101 ]; kid = data[., 102 ]; kid5 = data[., 103 ]; kid6_17 = data[., 104 ]; dri_lic = data[., 105 ]; age0_5 = data[., 106 ]; age6_17 = data[., 107 ]; age18_24 = data[., 108 ]; age25_34 = data[., 109 ]; age35_44 = data[., 110 ]; age45_54 = data[., 111 ]; age55_64 = data[., 112 ]; age65_74 = data[., 113 ]; age75 = data[., 114 ]; male = data[., 115 ]; female = data[., 116 ]; pr_pur = data[., 117 ]; nwf_firs = data[., 118 ]; nwf_mid = data[., 119 ]; nwf_last = data[., 120 ]; chain_tp = data[., 121 ]; beg_c = data[., 122 ];
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70 Appendix B: (Continued) end_c = data[., 123 ]; pmode5 = data[., 124 ]; mode3 = data[., 125 ]; auto = data[., 126 ]; complx = data[., 127 ]; tourmode = data[., 128 ]; m_sov = data[., 129 ]; m_hov = data[., 130 ]; m_other = data[., 131 ]; /* dummy variables definition */ pmale = (sex .==1) ; old = (age.>60) ; young = (age.<18 .and age.>0) ; high_inc = (hhincome.>=6) ; car_0 = (n_auto .==0) ; car_ge2 = (n_auto.>=2) ; low_inc = (hhincome .<3 .and hhincome.>0) ; with_kid = ((hhsizehh6plus).>0) ; hhsize1 = (hhsize .==1) ; hhsize2 = (hhsize .==2) ; hhsize3 = (hhsize .==3) ; hhsize4 = (hhsize.>3) ; high_edu = (EDU_LEV .==6 .or EDU_LEV .==7) ; with_kid = (kid5.>0) ; with_you = (kid6_17.>0) ; weekend = (weekday .==5) ; bad_weat = (weather.>=4 .and weather.<=7) ; rain = (weather .==5) ; working = (workday .==1) ; freepark= (pklot_wk .==1); country= (city_rur.==2); fulltime=(emp_sit .==1); independ= (occ_posi .==1); swiss= (national .==1); beg6_8=(beg_c .==6 .or beg_c .==7 .or beg_c .==8); beg13_14=(beg_c .==13 .or beg_c .==14); end12 = (end_c .==12) ; owner= (rent_own.==3);
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71 Appendix B: (Continued) proc lpr(b,z); local x,y,ux,uy,alpha,delta,p00,p01,p10,p11; x=one~pmale~freepark~country~fulltime; y = one~hhsize1~high_inc~independ~swiss~owner~beg6_8~beg13_14~end12; ux=x*b[1:5,.]; /* utility for auto */ uy=y*b[6:14,.]; /* utility for complex chain */ alpha=b[15,.]; /* joint dependence */ delta= 1 + exp(ux) + exp(uy) + exp(ux + uy + alpha) ; p00=one./delta; /* probability of nonauto & simple */ p01=exp(uy)./delta; /* probabili ty of nonauto & complex */ p10=exp(ux)./delta; /* probability of auto & simple */ p11= exp(ux+uy+alpha)./delta; /* probability of auto & complex */ retp ( (1auto) .* (1complx).*ln( p00 ) + (1auto) .* complx.*ln( p01 ) + auto .* (1complx).*ln( p10 ) + auto .* complx.*ln( p11 ) ) ; endp; b0={0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0}; {b,f,g,cov,ret}=maxlik(data,0,&lpr,b0); call maxprt(b,f,g,cov,ret);
