Modeling Ordered Choices: A Primer

by William H. Greene , David A. Hensher

• ISBN13: 9780521142373
• ISBN10: 0521142377
• Edition: 1st
• Format: Paperback
• Copyright: 2010-05-17
• Publisher: Cambridge University Press

Summary

It is increasingly common for analysts to seek out the opinions of individuals and organizations using attitudinal scales such as degree of satisfaction or importance attached to an issue. Examples include levels of obesity, seriousness of a health condition, attitudes towards service levels, opinions on products, voting intentions, and the degree of clarity of contracts. Ordered choice models provide a relevant methodology for capturing the sources of influence that explain the choice made amongst a set of ordered alternatives. The methods have evolved to a level of sophistication that can allow for heterogeneity in the threshold parameters, in the explanatory variables (through random parameters), and in the decomposition of the residual variance. This book brings together contributions in ordered choice modeling from a number of disciplines, synthesizing developments over the last fifty years, and suggests useful extensions to account for the wide range of sources of influence on choice.

Author Biography

William H. Greene is Professor of Economics and Toyota Motor Corp Professor at the Stern School of Business, New York University. David A. Hensher is Professor of Management and Director of the Institute of Transport and Logistics at the University of Sydney.

Table of Contents

List of tables	p. ix
List of figures	p. xi
Preface	p. xiii
Introduction: random utility and ordered choice models	p. 1
Modeling binary choices	p. 9
Random utility formulation of a model for binary choice	p. 10
Probability models for binary choices	p. 11
Estimation and inference	p. 16
Covariance matrix estimation	p. 26
Application of the binary choice model to health satisfaction	p. 28
Partial effects in a binary choice model	p. 30
Hypothesis testing	p. 39
Goodness of fit measures	p. 44
Heteroscedasticity	p. 54
Panel data	p. 57
Parameter heterogeneity	p. 75
Endogeneity of a right-hand-side variable	p. 80
Bivariate binary choice models	p. 83
The multivariate probit and panel probit models	p. 93
Endogenous sampling and case control studies	p. 96
A model for ordered choices	p. 99
A latent regression model for a continuous measure	p. 99
Ordered choice as an outcome of utility maximization	p. 103
An observed discrete outcome	p. 105
Probabilities and the log likelihood	p. 108
Log likelihood function	p. 108
Analysis of data on ordered choices	p. 109
Antecedents and contemporary counterparts	p. 111
The origin of probit analysis: Bliss (1934a), Finney (1947a)	p. 111
Social science data and regression analysis for binary outcomes	p. 116
Analysis of binary choice	p. 117
Ordered outcomes: Aitchison, Silvey (1957), Snell (1964)	p. 117
Minimum chi squared estimation of an ordered response model: Gurland et al. (1960)	p. 123
Individual data and polychotomous outcomes: Walker and Duncan (1967)	p. 125
McKelvey and Zavoina (1975)	p. 127
Cumulative odds model	p. 127
Continuation ratio model	p. 130
The ordered regression model	p. 130
Other related models	p. 132
The latent continuous variable	p. 134
Estimation, inference and analysis using the ordered choice model	p. 136
Application of the ordered choice model to self-assessed health status	p. 136
Distributional assumptions	p. 138
The estimated ordered probit (logit) model	p. 138
The estimated threshold parameters	p. 140
Interpretation of the model - partial effects and scaled coefficients	p. 142
Inference	p. 150
Prediction - computing probabilities	p. 157
Measuring fit	p. 160
Estimation issues	p. 167
Specification issues and generalized models	p. 181
Functional form issues and the generalized ordered choice model (1)	p. 181
Model implications for partial effects	p. 193
Methodological issues	p. 198
Specification tests for ordered choice models	p. 198
Accommodating individual heterogeneity	p. 208
Threshold models - the generalized ordered probit model (2)	p. 209
Nonlinear specifications - a hierarchical ordered probit (HOPIT) model	p. 214
Thresholds and heterogeneity - anchoring vignettes	p. 219
Heterogeneous scaling (heteroscedasticity) of random utility	p. 232
Individually heterogeneous marginal utilities	p. 237
Appendix: Equivalence of the vignette and HOPIT models	p. 237
Parameter variation and a generalized model	p. 239
Random-parameters models	p. 239
Latent class and finite mixture modeling	p. 247
Generalized ordered choice model with random thresholds (3)	p. 262
Ordered choice modeling with panel and time series data	p. 268
Ordered choice models with fixed effects	p. 268
Ordered choice models with random effects	p. 275
Testing for random or fixed effects: a variable addition test	p. 278
Extending parameter heterogeneity models to ordered choices	p. 281
Dynamic models	p. 285
Spatial autocorrelation	p. 289
Bivariate and multivariate ordered choice models	p. 290
Multiple equations	p. 290
Bivariate ordered probit models	p. 291
Polychoric correlation	p. 294
Semi-ordered bivariate probit model	p. 295
Applications of the bivariate ordered probit model	p. 295
A panel data version of the bivariate ordered probit model	p. 297
Trivariate and multivariate ordered probit models	p. 299
Two-part and sample selection models	p. 302
Inflation models	p. 302
Sample selection models	p. 306
An ordered probit model with endogenous treatment effects	p. 319
Semiparametric and nonparametric estimators and analyses	p. 320
Heteroscedasticity	p. 321
A distribution free estimator with unknown heteroscedasticity	p. 323
A semi-nonparametric approach	p. 324
A partially linear model	p. 327
Semiparametric analysis	p. 327
A nonparametric duration model	p. 329
References	p. 337
Index	p. 361
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