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Semiparametric Thurstonian Models for Recurrent Choices: A Bayesian Analysis

Published online by Cambridge University Press:  01 January 2025

Asim Ansari  and
Raghuram Iyengar
Asim Ansari*
Affiliation:
Columbia Business School, Columbia University
Raghuram Iyengar
Affiliation:
The Wharton School, University of Pennsylvania
*
Requests for reprints should be sent to Asim Ansari, Columbia Business School, Columbia University, 517 Uris Hall, 3022 Broadway, New York, NY 10027, USA. E-mail: maa48@columbia.edu;
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Abstract

We develop semiparametric Bayesian Thurstonian models for analyzing repeated choice decisions involving multinomial, multivariate binary or multivariate ordinal data. Our modeling framework has multiple components that together yield considerable flexibility in modeling preference utilities, cross-sectional heterogeneity and parameter-driven dynamics. Each component of our model is specified semiparametrically using Dirichlet process (DP) priors. The utility (latent variable) component of our model allows the alternative-specific utility errors to semiparametrically deviate from a normal distribution. This generates a robust alternative to popular Thurstonian specifications that are based on underlying normally distributed latent variables. Our second component focuses on flexibly modeling cross-sectional heterogeneity. The semiparametric specification allows the heterogeneity distribution to mimic either a finite mixture distribution or a continuous distribution such as the normal, whichever is supported by the data. Thus, special features such as multimodality can be readily incorporated without the need to overtly search for the best heterogeneity specification across a series of models. Finally, we allow for parameter-driven dynamics using a semiparametric state-space approach. This specification adds to the literature on robust Kalman filters. The resulting framework is very general and integrates divergent strands of the literatures on flexible choice models, Bayesian nonparametrics and robust time series specifications. Given this generality, we show how several existing Thurstonian models can be obtained as special forms of our model. We describe Markov chain Monte Carlo methods for the inference of model parameters, report results from two simulation studies and apply the model to consumer choice data from a frequently purchased product category. The results from our simulations and application highlight the benefits of using our semiparametric approach.

Keywords

semiparametric modelsDirichlet process priorschoice models
Type
Original Paper
Information
Psychometrika , Volume 71 , Issue 4 , December 2006 , pp. 631 - 657
Copyright
Copyright © 2007 The Psychometric Society

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