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

• Abstract

  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.

• Keywords

  Bayesian Estimation, MCMC Methods, Panel Probit Model, Mixture Modelling

• JEL classification

  C11, C23, C25

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