Skip to main content

Bayesian Inference for Semiparametric Quantal Response Equilibrium Models

Building on work of McKPal 95, McKPal 96, McKPal 98 and Sig 99 on quantal response equilibrium models and NewCzaCha 96, IshZar 00, IshJam 01and IshZar 02, on semiparametric Bayesian methods, we develop Bayesian inference for a particular class of semiparametric strategic choice models. Unlike previous approaches that have assumed the disturbances entering into actors' random utility functions follow a particular, known distribution such as a Gaussian distribution or a type I extreme value distribution, we instead assume only that the differenced disturbances have a right-continuous distribution function with fixed median and interquartile range. We model such a random distribution function using an approximation to the centrally standardized Dirichlet process prior of NewCzaCha 96. Model fitting is accomplished via Markov chain Monte Carlo. We present results from Monte Carlo experiments and a simulated data example. Our Monte Carlo results show that incorrectly specifying the distribution of the actors' utility disturbances within a parametric model can dramatrically bias quantities of interest such as the conditional expectation function and fitted probabilities. Our simulated data example demonstrates that our semiparametric approach works well on a difficult example in which the underlying true distribution function of the differenced disturbances is highly skewed.

This work is joint with Anton Westveld, Department of Statistics, University of Washington