In Pursuit of Higher Power Through Integrated Multivariate Regression

Abstract

. Univariate regression models are commonly used in statistics and machine learning to examine the relationship between an outcome variable and a set of explanatory variables, and possibly use this relationship to predict the unknown values of the outcome variable. However, when dealing with multiple outcome variables that are interrelated, multivariate regression models are preferred. These models simultaneously capture the dependencies between outcome variables and their collective relationships with explanatory variables. While multivariate regression models provide a rigorous and comprehensive understanding of factors associated with outcomes of interest, they have several limitations including: increased model complexity, larger sample size requirements, and lack of interpretability. To address these issues, we propose an alternative approach, called Integrated Multivariate Regression (IMR) that reduces the dimensionality of the outcome variables by transforming them into one or more derived outcome variables that retain important information. Using simulated and real data, we demonstrate that IMR simplifies the analysis and increases statistical power by reducing the number of parameters, while simultaneously maintaining interpretability and accounting for interdependencies among the outcome variables.