Extended Discrete Choice Models: Integrated Framework .

Extended Discrete Choice Models:Integrated Framework, Flexible Error Structures,and Latent VariablesbyJoan Leslie WalkerBachelor of Science in Civil Engineering, University of California at Berkeley (1991)Master of Science in Transportation, Massachusetts Institute of Technology (1994)Submitted to the Department of Civil and Environmental Engineeringin Partial Fulfillment of the Requirements for the Degree ofDoctor of PhilosophyinTransportation Systemsat theMassachusetts Institute of TechnologyFebruary 2001 2001 Massachusetts Institute of TechnologyAll rights reserved.AuthorDepartment of Civil and Environmental EngineeringFebruary 14, 2001Certified byMoshe E. Ben-AkivaEdmund K. Turner Professor of Civil and Environmental EngineeringThesis SupervisorAccepted byOral BuyukozturkChair, Departmental Committee on Graduate Studies

Extended Discrete Choice Models:Integrated Framework, Flexible Error Structures,and Latent VariablesbyJoan Leslie WalkerSubmitted to the Department of Civil and Environmental Engineeringon February 14, 2001 in Partial Fulfillment of the Requirements forthe Degree of Doctor of Philosophy in Transportation SystemsAbstractDiscrete choice methods model a decision-maker’s choice among a set of mutually exclusive andcollectively exhaustive alternatives. They are used in a variety of disciplines (transportation, economics,psychology, public policy, etc.) in order to inform policy and marketing decisions and to better understandand test hypotheses of behavior. This dissertation is concerned with the enhancement of discrete choicemethods.The workhorses of discrete choice are the multinomial and nested logit models. These models rely onsimplistic assumptions, and there has been much debate regarding their validity. Behavioral researchershave emphasized the importance of amorphous influences on behavior such as context, knowledge, andattitudes. Cognitive scientists have uncovered anomalies that appear to violate the microeconomicunderpinnings that are the basis of discrete choice analysis. To address these criticisms, researchers havefor some time been working on enhancing discrete choice models. While there have been numerousadvances, typically these extensions are examined and applied in isolation. In this dissertation, we present,empirically demonstrate, and test a generalized methodological framework that integrates the extensions ofdiscrete choice.The basic technique for integrating the methods is to start with the multinomial logit formulation, and thenadd extensions that relax simplifying assumptions and enrich the capabilities of the basic model. Theextensions include: Specifying factor analytic (probit-like) disturbances in order to provide a flexible covariancestructure, thereby relaxing the IIA condition and enabling estimation of unobserved heterogeneitythrough techniques such as random parameters. Combining revealed and stated preferences in order to draw on the advantages of both types of data,thereby reducing bias and improving efficiency of the parameter estimates. Incorporating latent variables in order to provide a richer explanation of behavior by explicitlyrepresenting the formation and effects of latent constructs such as attitudes and perceptions. Stipulating latent classes in order to capture latent segmentation, for example, in terms of tasteparameters, choice sets, and decision protocols.2

The guiding philosophy is that the generalized framework allows for a more realistic representation of thebehavior inherent in the choice process, and consequently a better understanding of behavior,improvements in forecasts, and valuable information regarding the validity of simpler model structures.These generalized models often result in functional forms composed of complex multidimensional integrals.Therefore a key aspect of the framework is its ‘logit kernel’ formulation in which the disturbance of thechoice model includes an additive i.i.d. Gumbel term. This formulation can replicate all known errorstructures (as we show here) and it leads to a straightforward probability simulator (of a multinomial logitform) for use in maximum simulated likelihood estimation. The proposed framework and suggestedimplementation leads to a flexible, tractable, theoretically grounded, empirically verifiable, and intuitivemethod for incorporating and integrating complex behavioral processes in the choice model.In addition to the generalized framework, contributions are also made to two of the key methodologies thatmake up the framework. First, we present new results regarding identification and normalization of thedisturbance parameters of a logit kernel model. In particular, we show that identification is not alwaysintuitive, it is not always analogous to the systematic portion, and it is not necessarily like probit. Second,we present a general framework and methodology for incorporating latent variables into choice models viathe integration of choice and latent variable models and the use of psychometric data (for example,responses to attitudinal survey questions).Throughout the dissertation, empirical results are presented to highlight findings and to empiricallydemonstrate and test the generalized framework. The impact of the extensions cannot be known a priori,and the only way to test their value (as well as the validity of a simpler model structure) is to estimate thecomplex models. Sometimes the extensions result in large improvements in fit as well as in more satisfyingbehavioral representations. Conversely, sometimes the extensions have marginal impact, thereby showingthat the more parsimonious structures are robust. All methods are often not necessary, and the generalizedframework provides an approach for developing the best model specification that makes use of availabledata and is reflective of behavioral hypotheses.Thesis Supervisor: Moshe E. Ben-AkivaTitle: Edmund K. Turner Professor ofCivil and Environmental Engineering3

AcknowledgmentsI am indebted to a great number of people who generously offered advise, encouragement, inspiration, and friendshipthroughout my time at MIT.I offer my sincere gratitude to my advisor and mentor, Professor Moshe Ben-Akiva, with whom it has been an honorand a pleasure to work. I thank him for a great number of things: for sharing his knowledge, for treating me as acolleague, for the opportunities he has provided me, for forcing me to dig deeper into my research and then helpingme find the solutions, for his patience, his accessibility, his encouragement, and his invaluable ideas, which form thebackbone of this thesis.Thank you to the members of my doctoral thesis committee. Professor Nigel Wilson, who provided input on myresearch as well as truly valued advice, and to whom I am grateful for looking out for me throughout my tenure atMIT. Professor Denis Bolduc, who provided vital assistance with my estimation programs and the empirical casestudies, as well as instrumental guidance for Chapter 2. Dr. Dinesh Gopinath, whose thorough reading of the thesisdraft greatly improved the final product, and whose command of econometrics proved over and over again to beinvaluable. Fred Salvucci, whose wealth of fascinating insight and stories never ceases to amaze me, and whogenerously offered nothing but encouragement when my research headed away from his primary interests.Thank you to the MIT faculty and staff who have enriched my experience. Professor Cynthia Barnhart who is anincredible role model and a tremendous asset to the program. Professor Ismail Chabini for his enthusiastic supportand for bringing such energy to the department. Professor Joseph Sussman for his continued support that started thefirst day I arrived at MIT. Dr. Joseph Coughlin for his cheerful encouragement. My honorary committee members, Dr.Shlomo Bekhor and Professor Ikki Kim, for their interest in my research and useful comments. To the staff of CTS andCEE, especially Cynthia, Ginny, Jan and Sydney, who provide immeasurable assistance to the students in their care.Thanks to Nora, who cheerfully checked in on me on many a late nights. I also gratefully acknowledge the numeroussources from which my education has been funded, including Tren Urbano, the National Science Foundation, theUniversity Transportation Centers Program, the United Parcel Service, the US Department of Transportation, and theCenter for Transportation Studies at MIT.Thank you to all the friends and colleagues who have made the process a whole lot more enjoyable. Leanne forproviding endless entertainment and support. Sarah for her empathy, wonderful conversations, and inspiration.Denise for her encouragement and the fun. Jon for making the long hours in the office much more bearable and oftenenjoyable. Fani for her laughter and stories. My fellow modelers Scott and John, for the conversations aboutstatistics and, thankfully, other topics as well. Salal for doing his best to teach me not to sweat the small stuff, and forlistening so well when I forgot this lesson. Julie for her friendship and kindness. Neal, Paul, Emmanuelle, and Benoitfor providing great escapes from MIT. Kristie and Rob, who were with me when I entered the doctoral program andtouched me by returning for the conclusion. Mary, who has been influencing and supporting my academic pursuitsfor as long as I can remember. Alberta and Linda for their continuous support and interest in my endeavors. And Raj,for his great wisdom and unending encouragement.Finally, thanks to my amazing family, who provide me with more love, support, and friendship then I would otherwisethink possible. To my siblings, Kathy, Jeff, and Sue, who have done such a good job looking out for their little sister.They have each had a tremendous influence on who I am. To the recent additions to the family: kind and fun Arne;sweet and generous Judy; and beautiful, smart, and perfect little Julia. And to my parents, who have taught mecountless philosophies of life, many of which I found to be invaluable during this process! To my dad, who hasinspired me through his passion and dedication to both his family and his work. And to my mom, my biggest fan, towhom I hope I have given back a fraction of what I have received.4

Table of ContentsABSTRACT . 2TABLE OF CONTENTS. 5LIST OF FIGURES. 9LIST OF TABLES .10CHAPTER 1: INTRODUCTION .12MOTIVATION .12The Foundation of Quantitative Models of Discrete Choice Behavior. 13Qualitative Concepts of Behavioral Theory. 14The Gap Between Behavioral Theory and Discrete Choice Models. 17The State of the Practice in Discrete Choice Modeling and Directions of Research. 18Specification of the Disturbances.20Incorporating Methods from Related Fields .22Preference and Behavior Indicators.22Choice Process Heterogeneity.23Data, Estimation Techniques, and Computational Power.23OBJECTIVES.23OVERVIEW OF THE GENERALIZED FRAMEWORK .24OUTLINE OF THE DISSERTATION .25CONTRIBUTIONS .26CHAPTER 2: FLEXIBLE ERROR STRUCTURES AND THE LOGIT KERNEL MODEL.28INTRODUCTION .28Terminology. 29Organization of the Chapter. 29RELATED LITERATURE .29THE LOGIT KERNEL MODEL .31The Discrete Choice Model . 31The Logit Kernel Model with Factor Analytic Form. 32Model Specification .32Response Probabilities .33IDENTIFICATION AND NORMALIZATION.34Comments on Identification of Pure Probit versus Logit Kernel.34Overview of Identification.35Setting the Location .37Order Condition.38Rank Condition.39Positive Definiteness.40SPECIAL CASES .44Heteroscedastic . 45Identification .45Nesting & Cross-Nesting Error Structures. 46Identification .46Models with 2 Nests .465