Statistical Properties of Multivariate Distance Matrix Regression for High-Dimensional Data Analysis

Multivariate distance matrix regression (MDMR) analysis is a statistical technique that allows researchers to relate P variables to an additional M factors collected on N individuals, where P ≫ N. The technique can be applied to a number of research settings involving high-dimensional data types such as DNA sequence data, gene expression microarray data, and imaging data. MDMR analysis involves computing the distance between all pairs of individuals with respect to P variables of interest and constructing an N × N matrix whose elements reflect these distances. Permutation tests can be used to test linear hypotheses that consider whether or not the M additional factors collected on the individuals can explain variation in the observed distances between and among the N individuals as reflected in the matrix. Despite its appeal and utility, properties of the statistics used in MDMR analysis have not been explored in detail. In this paper we consider the level accuracy and power of MDMR analysis assuming different distance measures and analysis settings. We also describe the utility of MDMR analysis in assessing hypotheses about the appropriate number of clusters arising from a cluster analysis.