Contents. Part I Getting started 1. xxii xxix. List of tables Preface

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1 Table of List of figures List of tables Preface page xvii xxii xxix Part I Getting started 1 1 In the beginning Choosing as a common event A brief history of choice modeling The journey ahead 11 2 Choosing Introduction Individuals have preferences and they count Using knowledge of preferences and constraints in choice analysis 27 3 Choice and utility Introduction Some background before getting started Introduction to utility The observed component of utility Generic versus alternative-specific parameter estimates Alternative-specific constants Status quo and no choice alternatives Characteristics of respondents and contextual effects in discrete choice models Attribute transformations and non-linear attributes Non-linear parameter utility specifications Taste heterogeneity 75 v

2 Table of vi 3.5 Concluding comments 76 Appendix 3A: Simulated data 76 Appendix 3B: Nlogit syntax 78 4 Families of discrete choice models Introduction Modeling utility The unobserved component of utility Random utility models Probit models based on the multivariate normal distribution Logit models based on the multivariate Extreme value distribution Probit versus logit Extensions of the basic logit model Heteroskedasticity A multiplicative errors model The nested logit model Correlation and the nested logit model The covariance heterogeneity logit model Mixed (random parameters) logit model Cross-sectional and panel mixed multinomial logit models Error components model Generalized mixed logit Models estimated in willingness to pay space The latent class model Concluding remarks Estimating discrete choice models Introduction Maximum likelihood estimation Simulated maximum likelihood Drawing from densities Pseudo-random Monte Carlo simulation Halton sequences Random Halton sequences Shuffled Halton sequences Modified Latin Hypercube sampling Sobol sequences 150

3 Table of vii Antithetic sequences PMC and QMC rates of convergence Correlation and drawing from densities Calculating choice probabilities for models without a closed analytical form Probit choice probabilities Estimation algorithms Gradient, Hessian and Information matrices Direction, step-length and model convergence Newton Raphson algorithm BHHH algorithm DFP and BFGS Algorithms Concluding comment 186 Appendix 5A: Cholesky factorization example Experimental design and choice experiments Introduction What is an experimental design? Stage 1: problem definition refinement Stage 2: stimuli refinement Stage 3: experimental design considerations Stage 4: generating experimental designs Stage 5: allocating attributes to design columns Generating efficient designs Some more details on choice experiments Constrained designs Pivot designs Designs with covariates Best worst designs More on sample size and stated choice designs D-efficient, orthogonal, and S-efficient designs Effect of number of choice tasks, attribute levels, and attribute level range Effect of wrong priors on the efficiency of the design Ngene syntax for a number of designs Design 1: standard choice set up Design 2: pivot design set up Design 3: D-efficient choice design Conclusions 287

4 Table of viii Appendix 6A: Best worst experiment 290 Appendix 6B: Best worst designs and Ngene syntax 290 6B.1 Best worst case B.2 Best worst case B.3 Best worst case Appendix 6C: An historical overview 301 6C.1 Louviere and Hensher (1983), Louviere and Woodworth (1983), and others 301 6C.2 Fowkes, Toner, Wardman et al. (Institute of Transport, Leeds, ) 304 6C.3 Bunch, Louviere and Anderson (1996) 305 6C.4 Huber and Zwerina (1996) 306 6C.5 Sándor and Wedel (2001, 2002, 2005) 308 6C.6 Street and Burgess (2001 to current) 309 6C.7 Kanninen (2002, 2005) 312 6C.8 Bliemer, Rose, and Scarpa (2005 to current) 313 6C.9 Kessels, Goos, Vandebroek, and Yu (2006 to current) Statistical inference Introduction Hypothesis tests Tests of nested models Tests of non-nested models Specification tests Variance estimation Conventional estimation Robust estimation Bootstrapping of standard errors and confidence intervals Variances of functions and willingness to pay Delta method Krinsky Robb method Other matters that analysts often inquire about Demonstrating that the average of the conditional distributions aggregate to the unconditional distribution Observationally equivalent respondents with different unobserved influences Observationally different respondents with different unobserved influences Random regret instead of random utility maximization 363

5 Table of ix 8.3 Endogeneity Useful behavioral outputs Elasticities of choice Partial or marginal effects Willingness to pay 378 Part II Software and data Nlogit for applied choice analysis Introduction About the software About Nlogit Installing Nlogit Starting Nlogit and exiting after a session Starting the program Reading the data Input the data The project file Leaving your session Using Nlogit How to Get Nlogit to do what you want Using the Text Editor Command format Commands Using the project file box Useful hints and tips Limitations in Nlogit Nlogit software Data set up for Nlogit Reading in and setting up data The basic data set up Entering multiple data sets: stacking and melding Handling data on the non-chosen alternative in RP data Combining sources of data Weighting on an exogenous variable Handling rejection: the no option Entering data into Nlogit 414

6 Table of x 10.6 Importing data from a file Importing a small data set from the Text Editor Entering data in the Data Editor Saving and reloading the data set Writing a data file to export Choice data entered on a single line Data cleaning 427 Appendix 10A: Converting single line data commands 431 Appendix 10B: Diagnostic and error messages 432 Part III The suite of choice models Getting started modeling: the workhorse multinomial logit Introduction Modeling choice in Nlogit: the MNL command Interpreting the MNL model output Determining the sample size and weighting criteria used Interpreting the number of iterations to model convergence Determining overall model significance Comparing two models Determining model fit: the pseudo-r Type of response and bad data Obtaining estimates of the indirect utility functions Handling interactions in choice models Measures of willingness to pay Obtaining utility and choice probabilities for the sample 465 Appendix 11A: The labeled choice data set used in the chapter Handling unlabeled discrete choice data Introduction Introducing unlabeled data The basics of modeling unlabeled choice data Moving beyond design attributes when using unlabeled choice data 478 Appendix 12A: Unlabeled discrete choice data Nlogit syntax and output Getting more from your model Introduction 492

7 Table of xi 13.2 Adding to our understanding of the data Descriptive output (Dstats) ;Show ;Descriptives ;Crosstab Adding to our understanding of the model parameters Starting values ;effect: elasticities Elasticities: direct and cross extended format Calculating arc elasticities Partial or marginal effects Partial or marginal effects for binary choice Simulation and what if scenarios The binary choice application Arc elasticities obtained using ;simulation Weighting Endogenous weighting Weighting on an exogenous variable Willingness to pay Calculating change in consumer surplus associated with an attribute change Empirical distributions: removing one observation at a time Application of random regret model versus random utility model Nlogit syntax for random regret model The Maximize command Calibrating a model Nested logit estimation Introduction The nested logit model commands Normalizing and constraining IV parameters Specifying IV start values for the NL model Estimating a NL model and interpreting the output Estimating the probabilities of a two-level NL model Specifying utility functions at higher levels of the NL tree Handling degenerate branches in NL models Three-level NL models Elasticities and partial effects Covariance nested logit 593

8 Table of xii 14.9 Generalized nested logit Additional commands Mixed logit estimation Introduction The mixed logit model basic commands Nlogit output: interpreting the ML model Model 2: mixed logit with unconstrained distributions Model 3: restricting the sign and range of a random parameter Model 4: heterogeneity in the mean of random parameters Model 5: heterogeneity in the mean of selective random parameters Model 6: heteroskedasticity and heterogeneity in the variances Model 7: allowing for correlated random parameters How can we use random parameter estimates? Starting values for random parameter estimation Individual-specific parameter estimates: conditional parameters Conditional confidence limits for random parameters Willingness to pay issues WTP based on conditional estimates WTP based on unconditional estimates Error components in mixed logit models Generalized mixed logit: accounting for scale and taste heterogeneity GMX model in utility and WTP space SMNL and GMX models in utility space Recognizing scale heterogeneity between pooled data sets Latent class models Introduction The standard latent class model Random parameter latent class model A case study Results Conclusions Nlogit commands Standard command structure 724

9 Table of xiii Command structure for the models in Table Other useful latent class model forms Binary choice models Introduction Basic binary choice Stochastic specification of random utility for binary choice Functional form for binary choice Estimation of binary choice models Inference-hypothesis tests Fit measures Interpretation: partial effects and simulations An application of binary choice modeling Binary choice modeling with panel data Heterogeneity and conventional estimation: the cluster correction Fixed effects Random effects and correlated random effects Parameter heterogeneity Bivariate probit models Simultaneous equations Sample selection Application I: model formulation of the ex ante link between acceptability and voting intentions for a road pricing scheme Application II: partial effects and scenarios for bivariate probit Ordered choices Introduction The traditional ordered choice model A generalized ordered choice model Modeling observed and unobserved heterogeneity Random thresholds and heterogeneity in the ordered choice model Case study Empirical analysis Nlogit commands Combining sources of data Introduction 836

10 Table of xiv 19.2 The nested logit trick Beyond the nested logit trick Case study Nlogit command syntax for Table 19.2 models Even more advanced SP RP models Hypothetical bias Key themes Evidence from contingent valuation to guide choice experiments Some background evidence in transportation studies Pivot designs: elements of RP and CE Conclusions 893 Part IV Advanced topics Frontiers of choice analysis Introduction A mixed multinomial logit model with non-linear utility functions Expected utility theory and prospect theory Risk or uncertainty? The appeal of prospect theory Case study: travel time variability and the value of expected travel time savings Empirical application Empirical analysis: mixed multinomial logit model with non-linear utility functions NLRPLogit commands for Table 20.6 model Hybrid choice models An overview of hybrid choice models The main elements of a hybrid choice model Attribute processing, heuristics, and preference construction Introduction A review of common decision processes Embedding decision processes in choice models Two-stage models Models with fuzzy constraints Other approaches 952

11 Table of xv 21.4 Relational heuristics Within choice set heuristics Between choice set dependence Process data Motivation for process data collection Monitoring information acquisition Synthesis so far Case study I: incorporating attribute processing heuristics through non-linear processing Common-metric attribute aggregation Latent class specification: non-attendance and dual processing of common-metric attributes in choice analysis Evidence on marginal willingness to pay: value of travel time savings Evidence from self-stated processing response for common-metric addition Case study II: the influence of choice response certainty, alternative acceptability, and attribute thresholds Accounting for response certainty, acceptability of alternatives, and attribute thresholds The choice experiment and survey process Empirical results Conclusions Case study III: interrogation of responses to stated choice experiments is there sense in what respondents tell us? The data setting Investigating candidate evidential rules Derivative willingness to pay Pairwise alternative plausible choice test and dominance Influences of non-trading Dimensional versus holistic processing strategies Influence of the relative attribute levels Revision of the reference alternative as value learning A revised model for future stated choice model estimation Conclusions The role of multiple heuristics in representing attribute processing as a way of conditioning modal choices 1058 Appendix 21A: Nlogit command syntax for NLWLR and RAM heuristics 1062

12 Table of xvi Appendix 21B: Experimental design in Table Appendix 21C: Data associated with Table Group decision making Introduction Interactive agency choice experiments Case study data on automobile purchases Case study results Nlogit commands and outputs Estimating a model with power weights Pass 1, round 1 (agent 1) and round 2 (agent 2) ML model Pass 1, round 1 (agent 1) and round 2 (agent 2) agree model Sorting probabilities for two agents into a single row Creating cooperation and non-cooperation probabilities for the pairs Removing all but line 1 of the four choice sets per person in pair Getting utilities on 1 line (note: focusing only on overall utilities at this stage) Writing out new file for power weight application Reading new data file Estimating OLS power weight model (weights sum to 1.0) Pass #2 (repeating same process as for pass#1) Pass #3 (same set up as pass#1) Group equilibrium Joint estimation of power weights and preference parameters 1113 Select glossary 1116 References 1128 Index 1163