A Correlated Binomial Regression Model

A Corporation is a company that owns other companies outstanding stock. In business matters, a Corporation is a defaul company if, at least, one of its subsidiary is on default. The statistical interest is, in a specific period of time, to determine the Default probability for the Corporation given that the subsidiaries of this Corporation are correlated. Therefore, the model must address the issue of covariation between the companies inside the Corporation. In this paper a correlated binomial regression model CBR(ni, pi = f(β xi), ρi), is proposed. The developed methodology permits the covariance structure to be incorporated into the model and the behaviour of the response variable is modelled as a function of exogenous variables available for the Corporations and the revenues for each company inside the Corporation. The data augmentation scheme is used in order to overcome the complexity of the mixture likelihood. MCMC methods are applied to estimate the posterior marginal for the regression coefficients, consequentely for the probabilities of success pi, and for the correlation coefficients ρi. The article is motivated by a study of Financial default in Corporations.