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Regression models for multivariate ordered responses via the Plackett distribution

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  • Forcina, A.
  • Dardanoni, V.

Abstract

We investigate the properties of a class of discrete multivariate distributions whose univariate marginals have ordered categories, all the bivariate marginals, like in the Plackett distribution, have log-odds ratios which do not depend on cut points and all higher-order interactions are constrained to 0. We show that this class of distributions may be interpreted as a discretized version of a multivariate continuous distribution having univariate logistic marginals. Convenient features of this class relative to the class of ordered probit models (the discretized version of the multivariate normal) are highlighted. Relevant properties of this distribution like quadratic log-linear expansion, invariance to collapsing of adjacent categories, properties related to positive dependence, marginalization and conditioning are discussed briefly. When continuous explanatory variables are available, regression models may be fitted to relate the univariate logits (as in a proportional odds model) and the log-odds ratios to covariates.

Suggested Citation

  • Forcina, A. & Dardanoni, V., 2008. "Regression models for multivariate ordered responses via the Plackett distribution," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2472-2478, November.
  • Handle: RePEc:eee:jmvana:v:99:y:2008:i:10:p:2472-2478
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    References listed on IDEAS

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    1. Bahjat F. Qaqish & Anastasia Ivanova, 2006. "Multivariate logistic models," Biometrika, Biometrika Trust, vol. 93(4), pages 1011-1017, December.
    2. D. R. Cox, 2002. "On some models for multivariate binary variables parallel in complexity with the multivariate Gaussian distribution," Biometrika, Biometrika Trust, vol. 89(2), pages 462-469, June.
    3. Bartolucci, Francesco & Forcina, Antonio, 2006. "A Class of Latent Marginal Models for CaptureRecapture Data With Continuous Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 786-794, June.
    4. 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.
    5. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    6. Debashis Ghosh, 2006. "Semiparametric Global Cross‐ratio Models for Bivariate Censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 609-619, December.
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    Cited by:

    1. Domenico Piccolo & Rosaria Simone, 2019. "The class of cub models: statistical foundations, inferential issues and empirical evidence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 389-435, September.
    2. Sam Hakim & Simon Neaime, 2011. "An Analysis of the Mobile Telephone Sector in MENA: Potential for Deregulation and Privatization," Working Papers 649, Economic Research Forum, revised 12 Jan 2011.

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