Bivariate beta regression models: a Bayesian approach applied to educational data

Abstract

In this paper we propose a bivariate beta regression model, de¯ning the beta distribution derived from Farlie-Gumbel-Morgenstern (FGM) copulas. This model could be a good alternative to analyze pairs of proportions, when they are not independent. To ¯t the proposed models we apply standard existing MCMC (Markov Chain Monte Carlo) methods to simulate samples for the joint posterior of interest, using the Bayesian methodology proposed by Cepeda and Gamerman (2001) and Cepeda and Gamerman (2005). Two examples are introduced to illustrate the proposed methodology: an example with simulated bivariate data and an example with a real data set.