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Properties of Ideal Point Classification Models for Bivariate Binary Data

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  • Hailemichael M. Worku

    (Leiden University)

  • Mark De Rooij

    (Leiden University)

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.

Suggested Citation

  • Hailemichael M. Worku & Mark De Rooij, 2017. "Properties of Ideal Point Classification Models for Bivariate Binary Data," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 308-328, June.
    • Handle: RePEc:spr:psycho:v:82:y:2017:i:2:d:10.1007_s11336-017-9565-x
    DOI: 10.1007/s11336-017-9565-x
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    References listed on IDEAS

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    1. Yoshio Takane, 1987. "Analysis of contingency tables by ideal point discriminant analysis," Psychometrika, Springer;The Psychometric Society, vol. 52(4), pages 493-513, December.
    2. Mark Rooij, 2009. "Ideal Point Discriminant Analysis Revisited with a Special Emphasis on Visualization," Psychometrika, Springer;The Psychometric Society, vol. 74(2), pages 317-330, June.
    3. Bartolucci F. & Forcina A. & Dardanoni V., 2001. "Positive Quadrant Dependence and Marginal Modeling in Two-Way Tables With Ordered Margins," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1497-1505, December.
    4. D. R. Cox, 1972. "The Analysis of Multivariate Binary Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 21(2), pages 113-120, June.
    5. Mark Rooij & Willem Heiser, 2005. "Graphical representations and odds ratios in a distance-association model for the analysis of cross-classified data," Psychometrika, Springer;The Psychometric Society, vol. 70(1), pages 99-122, March.
    6. Yoshio Takane & Hamparsum Bozdogan & Tadashi Shibayama, 1987. "Ideal point discriminant analysis," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 371-392, September.
    7. Jeroen K. Vermunt & Marã A Florencia Rodrigo & Manuel Ato-Garcia, 2001. "Modeling Joint and Marginal Distributions in the Analysis of Categorical Panel Data," Sociological Methods & Research, , vol. 30(2), pages 170-196, November.
    8. Yee, Thomas W., 2010. "The VGAM Package for Categorical Data Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i10).
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