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Properties of Ideal Point Classification Models for Bivariate Binary Data

Published online by Cambridge University Press:  01 January 2025

Hailemichael M. Worku  and
Mark de Rooij
Hailemichael M. Worku*
Affiliation:
Leiden University
Mark de Rooij
Affiliation:
Leiden University
*
Correspondence should be made to Hailemichael M. Worku, Psychological Institute, Faculty of Social Sciences, Leiden University, PO Box 9555, 2330 RB Leiden, The Netherlands. Email: h.m.worku@fsw.leidenuniv.nl
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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.

Keywords

probabilistic multidimensional unfolding modelideal point classification modelbivariate binary datamarginal modelassociation modelodds ratiobiplot
Type
Original Paper
Information
Psychometrika , Volume 82 , Issue 2 , June 2017 , pp. 308 - 328
Copyright
Copyright © 2017 The Psychometric Society

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Footnotes

Request for reprints can be directed to the first author (Hailemichael M. Worku).

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