The MELODIC family for simultaneous binary logistic regression in a reduced space
This work addresses the need for efficient simultaneous analysis of multivariate binary data in fields like psychology and medicine, though it appears incremental as it builds on existing logistic regression and dimension reduction techniques.
The authors tackled the problem of analyzing multiple binary response variables simultaneously by proposing the MELODIC family for logistic regression in a reduced-dimensional space, which allows for insights into dependencies and improved predictive accuracy, as demonstrated through applications to drug consumption and mental health data.
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.