A Versatile Model for Clustered and Highly Correlated Multivariate Data

Abstract

For the analysis of multivariate data with an approximately one-dimensional latent structure, it is suggested to model this latent variable by a random effect, allowing for the use of mixed model methodology for dimension reduction purposes. We implement this idea through the mixture-based approach for the estimation of random effect models, hence conveniently enabling clustering of observations along the latent linear subspace, and derive the estimators required for the ensuing EM algorithm under several error variance parameterizations. A simulation study is conducted, and several important inferential problems, including clustering, projection, ranking, regression on covariates, and regression of an external response on the predicted latent variable, are considered and illustrated by real data examples.