Extending a Distance-Based Approach to Multivariate Multiple Regression

This dissertation concerns the development of a person-centered extension to the linear model that can be used to test the association of multivariate outcome data and a set of covariates. While the focus of the standard linear model test statistic is the sum of squares of the outcome variable(s), the focus of the Multivariate Distance Matrix Regression (MDMR) test statistic is the sum of squared distances between response profiles. The freedom to choose any distance metric to quantify the dissimilarity between these response profiles can result in the relaxation of several assumptions that are commonly required to conduct multivariate association tests. This renders MDMR a flexible, powerful alternative to standard approaches to multivariate multiple regression. MDMR, however, is not commonly used in the social sciences, and this is partially due to three key issues that are addressed in this dissertation: (1) the null distribution of the MDMR test statistic is unknown, so the computation of p-values is currently contingent upon permutation tests that can be computationally infeasible, (2) the MDMR framework does not provide a useful measure of effect size for specific outcome variables, and (3) the MDMR framework relies on the assumption of independent observations.