BAYESIAN ANALYSIS AND TESTING FOR STUDENT T-DICHOTOMOUS QUANTAL RESPONSE MODELS

This paper is concerned with statistical inference in Student t-Dichotomous Quantal Response Models. We analyze discrete choice models from Bayesian point of view. Bayesian methods for modeling binary data are applied because of a nonstandard property of maximum likelihood function in the case of the Student -t model. Details of the construction of the prior are presented. We observed than only a proper prior density guarantees existence of the posterior density of parameters. Bayesian inference in this model is feasible using a Markov chain Monte Carlo posterior Simulator i.e. Metropolis- Hastings algorithm. We took advantage of the fact that, approximately, one can view the logistic distribution as a member of the 't' family. Thus, there is possibility testing probit and logit models within the confines of t-model. Then we illustrate probit and logit models extensions for retail loan data. Thus, the first generalization relies on it, that the errors are Student-t distributed with unknown degrees of freedom. Secondly, we assume that a latent variable (represent a utility associated with loans repayment) is a second-order polynomial of the explanatory variables. An important concern of this paper is the question of comparing the fit of alternative models. We show that the posterior model probabilities and the Bayes factors framework are quite useful for this purpose. The data give very strong evidence that Student-t model with second-order approximation compared to the other models. The Student-t model with unknown parameter, degrees of freedom, is equivalent the Bayesian model averaging which involves keeping all models (i.e. probit and logit models), but presenting results averaged over these models