Generalization of Conditional Logit Choice Model Using Gaussian Copula

• Activity Number: 129
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Marketing
• Author(s): Arjun Poddar* and N. Rao Chaganty
• Companies: Old Dominion University and Old Dominion University
• Keywords: Discrete Choice ; Multivariate Conditional Logit Model ; Gaussian Copula ; Choice Models ; Conjoint Analysis ; Gumbel Distribution

Abstract

A popular tool for analyzing product choices of consumers is the well-known conditional logit discrete choice model. Originally publicized by McFadden (1974), this model assumes that the random components of the underlying utility functions of the consumers follow independent Gumbel distributions. However, in practice the independence assumption may be violated and a more reasonable model should account for the dependence. In this research we use the Gaussian copula with compound symmetric correlation matrix to construct a general multivariate model for the joint distribution of the utilities. The induced dependence on the utilities and the choice probabilities are studied using analytic expressions and simulations. For regression with consumer and product specific covariates, we derive expressions for the likelihood function, score functions and the Fisher information. We use numerical methods and computer code to obtain the maximum likelihood estimates and standard errors. Comparison of our model with other competing methods and practical applicability is illustrated using real world consumer preference data.