Visual Partitioning for Multivariate Models: An approach for identifying and visualizing complex multivariate dataset

sers of statistics quite frequently use multivariate models to make conditional inferences (e.g., stress affects depression, after controlling for gender). These inferences are often done without adequately considering (or understanding) the assumptions one makes when claiming these inferences. Of particular concern is when there are unmodeled nonlinear and/or interaction effects. With such unmodeled multiplicative effects, inferences based on a main effects model are not merited. On the other hand, when these effects are properly modeled, complex multivariate analyses can be "partitioned" into distinct components to ease interpretation. In this paper, we highlight when conditional inferences are contaminated by other features of the model and identify the conditions under which effects can be partitioned. We also reveal a strategy for partitioning multivariate effects into uncontaminated blocks using visualizations. This approach simplifies multivariate analyses immensely, without oversimplifying the analysis.