Mixtures of Probit Regression Models with Overlapping Clusters

Studies with binary outcomes on a heterogeneous population are quite common. Typically, the heterogeneity is modelled through varying effect coefficients within some regression setting combined clustering procedure. Most of existing methods assign statistical units to distinct and non-overlapping clusters. However, there scenarios where exhibit more complex organization clusters can be thought as partially overlapping. In this case, standard approach does not work. paper, we define mixture models that allows overlapping This involves an overlap function maps coefficients, either at unit or response level, parent into multiple allocation order deal intrinsic heterogeneity, analyses have stratified for different groups observations We present computationally efficient Monte Carlo Markov Chain (MCMC) scheme case probit regressions. A simulation study shows overall performance method. conclude two illustrative examples modelling voting behavior, involving United States (US) Supreme Court justices over number topics members Kingdom (UK) parliament divisions related Brexit. These applications provide insights usefulness method in real applications. The described extended generic multivariate generalized linear under