Psychological Institute, Faculty of Social Sciences, Leiden University, PO Box 9555, 2330 RB, Leiden, The Netherlands.
Psychometrika. 2017 Jun;82(2):308-328. doi: 10.1007/s11336-017-9565-x. Epub 2017 Jun 13.
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.
理想点分类 (IPC) 模型最初是为了在存在预测变量的情况下分析多项数据而提出的。在本文中，我们研究了 IPC 模型分析具有特定焦点的二元二值数据的性质，重点研究了三个数量：(1)边缘概率；(2)两个二元响应之间的关联结构；以及(3)联合概率。我们发现，具有特定类点配置的 IPC 模型表示边缘概率或关联结构。然而，IPC 模型不能同时表示这两个数量。然后，我们推导出了该模型的新参数化，即二元 IPC (BIPC) 模型，它能够同时表示边缘概率和关联结构。与标准 IPC 模型一样，BIPC 模型的结果可以显示在双标图中，从中可以读取预测变量对二元响应及其关联的影响。我们将通过一个与人格特质与抑郁和焦虑障碍相关的心理学示例来说明我们的发现。
