The MELODIC family for simultaneous binary logistic regression in a reduced space

TL;DR

The paper introduces the MELODIC family, a novel approach for simultaneous binary logistic regression in a reduced Euclidean space, enhancing interpretability and predictive accuracy for multivariate binary data.

Contribution

It proposes a new modeling framework that reduces dimensionality in multivariate binary logistic regression and provides efficient estimation algorithms.

Findings

Demonstrates the method's effectiveness on personality and health data

Shows improved predictive accuracy over existing approaches

Provides interpretability through logistic coefficients and biplots

Abstract

Logistic regression is a commonly used method for binary classification. Researchers often have more than a single binary response variable and simultaneous analysis is beneficial because it provides insight into the dependencies among response variables as well as between the predictor variables and the responses. Moreover, in such a simultaneous analysis the equations can lend each other strength, which might increase predictive accuracy. In this paper, we propose the MELODIC family for simultaneous binary logistic regression modeling. In this family, the regression models are defined in a Euclidean space of reduced dimension, based on a distance rule. The model may be interpreted in terms of logistic regression coefficients or in terms of a biplot. We discuss a fast iterative majorization (or MM) algorithm for parameter estimation. Two applications are shown in detail: one relating personality characteristics to drug consumption profiles and one relating personality characteristics to depressive and anxiety disorders. We present a thorough comparison of our MELODIC family with alternative approaches for multivariate binary data.