Properties of Ideal Point Classification Models for Bivariate Binary Data

Abstract

The ideal point classification (IPC) model was originally proposed for analysing multinomial data in the presence of predictors. In this paper, we studied properties of the IPC model for analysing bivariate binary data with a specific focus on three quantities: (1) the marginal probabilities; (2) the association structure between the two binary responses; and (3) the joint probabilities. We found that the IPC model with a specific class point configuration represents either the marginal probabilities or the association structure. However, the IPC model is not able to represent both quantities at the same time. We then derived a new parametrization of the model, the bivariate IPC (BIPC) model, which is able to represent both the marginal probabilities and the association structure. Like the standard IPC model, the results of the BIPC model can be displayed in a biplot, from which the effects of predictors on the binary responses and on their association can be read. We will illustrate our findings with a psychological example relating personality traits to depression and anxiety disorders.

A Multivariate Logistic Distance Model for the Analysis of Multiple Binary Responses

“…De Rooij (2009) also showed that a simple logistic regression for binary response variable can be written as a unidimensional IPC model. Worku and De Rooij (2016) extended the IPC model to the analysis of two binary response variables, i.e., the bivariate, binary data setting, and showed that a new parameterization of the IPC model recovered both the marginal probabilities and the association structure of bivariate binary data well. However, this parameterization cannot be easily extended to handling multivariate binary data because all the possible pairwise and higher order association terms must be specified in the likelihood function, which makes the model complex and therefore hard to estimate.…”