An Information Analysis on Modeling Interaction Effects in Logistic Regression

TL;DR

This paper introduces a two-step model selection method for logistic regression that directly identifies essential predictors and their interactions, improving model parsimony and interpretability over traditional AIC-based approaches.

Contribution

It proposes a novel two-step selection scheme based on information identity testing to identify key predictors and interactions in logistic regression models.

Findings

The method effectively identifies the most parsimonious logistic model.

It simplifies finding the minimum AIC model near the selected model.

Application to youth worker data demonstrates practical utility.

Abstract

The Akaike information criterion (AIC) is commonly used to select a logistic regression model for optimal prediction of a binary response by a specified family of models. It however lacks a convincing method of prescribing a proper family of models using the desired predictors and their interaction effects. For an alternative approach to model selection, we propose a direct selection scheme which first identifies the indispensable regressors as main-effect predictors, then examines significant interaction effects between the selected predictors such that a logistic model is constructed. The two-step selection scheme is formulated by testing for valid information identity between the response and the predictors, from which the most parsimonious logistic model is derived from the least set of indispensable predictors and interaction effects. As a byproduct, the minimum AIC model is easily found in a neighborhood of the selected model. The scheme is employed to yield the logistic model for predicting the acquisition of professional licenses in a survey of employed youth workers.