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A Bayesian multivariate probit for ordinal data with semiparametric random-effects

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  • Kim, Jung Seek
  • Ratchford, Brian T.

Abstract

A heterogeneous thresholds probit for ordered ratings is developed to remove conditional independence among responses and incorporate respondent traits. We propose a semiparametric approach to relaxing normality of random-effects in the probit model that account for differences in response style. Simulation studies provide evidence of the ability for the proposed semiparametric model to better recover an underlying distribution of respondent effects than the parametric one with a normal hierarchical prior. The application to ratings on the value of information sources for automobiles demonstrates significant correlations among responses and irregularity in the shape of unobserved heterogeneity.

Suggested Citation

  • Kim, Jung Seek & Ratchford, Brian T., 2013. "A Bayesian multivariate probit for ordinal data with semiparametric random-effects," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 192-208.
    • Handle: RePEc:eee:csdana:v:64:y:2013:i:c:p:192-208
    DOI: 10.1016/j.csda.2013.03.004
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    References listed on IDEAS

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    1. Rossi P. E & Gilula Z. & Allenby G. M, 2001. "Overcoming Scale Usage Heterogeneity: A Bayesian Hierarchical Approach," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 20-31, March.
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    4. Forrest Young, 1981. "Quantitative analysis of qualitative data," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 357-388, December.
    5. Keisuke Hirano, 2002. "Semiparametric Bayesian Inference in Autoregressive Panel Data Models," Econometrica, Econometric Society, vol. 70(2), pages 781-799, March.
    6. Hajivassiliou, Vassilis & McFadden, Daniel & Ruud, Paul, 1996. "Simulation of multivariate normal rectangle probabilities and their derivatives theoretical and computational results," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 85-134.
    7. Timothy Johnson, 2003. "On the use of heterogeneous thresholds ordinal regression models to account for individual differences in response style," Psychometrika, Springer;The Psychometric Society, vol. 68(4), pages 563-583, December.
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    Cited by:

    1. Ryo Kato & Takahiro Hoshino, 2018. "Semiparametric Bayes Multiple Imputation for Regression Models with Missing Mixed Continuous-Discrete Covariates," Discussion Paper Series DP2018-15, Research Institute for Economics & Business Administration, Kobe University.
    2. Ryo Kato & Takahiro Hoshino, 2020. "Semiparametric Bayesian multiple imputation for regression models with missing mixed continuous–discrete covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 803-825, June.
    3. Rainer Hirk & Kurt Hornik & Laura Vana, 2019. "Multivariate ordinal regression models: an analysis of corporate credit ratings," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 507-539, September.

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