Using relative weight analysis with residualization to detect relevant nonlinear interaction effects in ordinary and logistic regressions

TL;DR

This paper introduces a method combining relative weight analysis with residualization to effectively detect relevant nonlinear interaction effects in regression models, including logistic regression, by using restricted cubic splines.

Contribution

It presents a novel approach for analyzing multivariate models to identify key variables and interactions, properly residualized to preserve their true effects.

Findings

Effective detection of nonlinear interactions in simulated data

Proper residualization maintains true interaction effects

Applicable to both ordinary and logistic regressions

Abstract

Relative weight analysis is a classic tool for detecting whether one variable or interaction in a model is relevant. In this study, we focus on the construction of relative weights for non-linear interactions using restricted cubic splines. Our aim is to provide an accessible method to analyze a multivariate model and identify one subset with the most representative set of variables. Furthermore, we developed a procedure for treating control, fixed, free and interaction terms simultaneously in the residual weight analysis. The interactions are residualized properly against their main effects to maintain their true effects in the model. We tested this method using two simulated examples.