Factorization and latent variable models for joint analysis of binary and continuous outcomes

Many studies, particularly in the health sciences, involve measurements of multiple outcomes on each subject. When the outcomes are of the same type and measured on the same scale, such as continuous variables, classical tools of multivariate statistics can be used. However, multivariate methods to analyze outcomes measured on different scales or measuring different underlying variables, i.e., non-commensurate outcomes, are less common and rarely used in applied research.