Properties of Ideal Point Classification Models for Bivariate Binary Data

作     者：Worku, Hailemichael M. de Rooij, Mark 

作者机构：Leiden Univ Leiden Netherlands 

出 版 物：《PSYCHOMETRIKA》 (心理测量学)

年 卷 期：2017年第82卷第2期

页      面：308-328页

核心收录：

学科分类：0402[教育学-心理学(可授教育学、理学学位）] 04[教育学] 0701[理学-数学] 

基　　金：Netherlands Organization for Scientific Research [400-09-384  452-06-002] 

主　　题：probabilistic multidimensional unfolding model ideal point classification model bivariate binary data marginal model association model odds ratio biplot 

摘      要：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.