Bayesian analysis of dichotomous quantal response models

Qualitative response models (QRM's) are analyzed from the Bayesian point of view, using diffuse and informative prior distributions. Exact finite-sample Bayesian and large-sample Bayesian and non-Bayesian estimation results are compared. In addition, the paper provides: (1) plots and discussion of the properties of likelihood functions for QRM's, (2) posterior distributions for logit models' derivatives and elasticities, (3) Bayesian prediction procedures for QRM's, (4) new estimates for the median and other fractiles of the logistic distribution, (5) posterior odds ratios for model selection problems, and (6) comparisons of two alternative Monte Carlo numerical integration procedures. It is concluded that asymptotic approximations are not accurate for small-to moderate-sized samples even when only a single input variable is used, and that operational Bayesian methods are available for providing both exact small-sample and large-sample approximate inferences for DRM's.