Bayesian approach in model selection for the binary response data

A vast literature in statistics and econometrics is concerned with the analysis of binary response data. The classical approach uses a categorical response model using the maximum likelihood method and inferences about the model parameters are based on asymptotic theory. This approach is often unreliable in small-sample problems and analytically intractable when the associated link function in the regression model is not canonical. A Bayesian approach is more attractive and simpler in this scenario. In this chapter a Bayesian approach in model selection for binary response data is considered. The problem is reduced to the choice of an appropriate link function using the predictive distribution. An adaptive Monte Carlo integration technique known as the Gibbs sampler is proposed as a mechanism for implementing a conceptually and computationally simple solution in such a framework. We illustrate the approach through two examples: in the first example, the objective is to predict presidential election results using six socioeconomic and regional variables; in the second example, the objective is to choose the best model for predicting borrower's choice of mortgage rate.