A Constructive Procedure for Modeling Categorical Variables: Log-Linear and Logit Models

TL;DR

This paper introduces a geometric decomposition approach for constructing concise log-linear and logit models for categorical data, improving model selection and interpretability.

Contribution

It develops a new constructive scheme based on information identities and geometric decompositions to identify key predictors and interactions in categorical modeling.

Findings

Effective identification of indispensable predictors and interactions

Facilitates search for minimum AIC models

Applied successfully to stroke risk factors data

Abstract

Association between categorical variables in contingency tables is analyzed using the information identities based on multivariate multinomial distributions. A scheme of geometric decompositions of the information identities is developed to identify indispensable predictors and interaction effects in the construction of concise log-linear and logit models; it suggests a new approach for selecting parsimonious log-linear and logit models which would facilitate the search for the minimum AIC models as a byproduct. The proposed constructive schemes are illustrated along with the analysis of a contingency data table collected in a study on the risk factors of ischemic cerebral stroke.