Latent factor regression models for grouped outcomes

We consider regression models for multiple correlated outcomes, where the outcomes are nested in domains. We show that random effect models for this nested situation fit into a standard factor model framework, which leads us to view the modeling options as a spectrum between parsimonious random effect multiple outcomes models and more general continuous latent factor models. We introduce a set of identifiable models along this spectrum that extend an existing random effect model for multiple outcomes nested in domains. We characterize the tradeoffs between parsimony and flexibility in this set of models, applying them to both simulated data and data relating sexually dimorphic traits in male infants to explanatory variables.