Bayesian evaluation of a semi-parametric binary response model

In this paper, we develop a Bayesian analysis of a semi-parametric binary choice model. The prior specification of the functional parameter, namely the distribution function of a latent variable, is of the Dirichlet process type and the prior specification of the Euclidean parameter, namely the coefficients of a linear combination of exogenous variables, is left arbitrary. The model identification is ensured by fixing the prior expectation of the functional parameter (see Mouchart et al. (1997)). Approximations for the posterior predictive distributions are obtained from two different sampling methods. Several questions are studied through an exploratory numerical analysis, such as the numerical convergence of the algorithms and of the methods and the general problem of contrasting semi-parametric and purely parametric specification