A Bayesian Approach to Model-Based Clustering for Binary Panel Probit Models

Considering latent heterogeneity is of special importance in non-linear models in order to

gauge correctly the effect of explanatory variables on the dependent variable. A stratified modelbased clustering approach is adapted for modeling latent heterogeneity in binary panel probit

models. Within a Bayesian framework an estimation algorithm dealing with the inherent label

switching problem is provided. Determination of the number of clusters is based on the marginal

likelihood and a cross-validation approach. A simulation study is conducted to assess the ability

of both approaches to determine on the correct number of clusters indicating high accuracy for

the marginal likelihood criterion, with the cross validation approach performing similarly well

in most circumstances. Different concepts of marginal effects incorporating latent heterogeneity

at different degrees arise within the considered model setup and are directly at hand within

Bayesian estimation via MCMC methodology. An empirical illustration of the methodology

developed indicates that consideration of latent heterogeneity via latent clusters provides the

preferred model specification over a pooled and a random coefficient specification.