  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.
