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Bayesian latent variable model for mixed continuous and ordinal responses with possibility of missing responses

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  • E. Bahrami Samani
  • M. Ganjali

Abstract

A general framework is proposed for joint modelling of mixed correlated ordinal and continuous responses with missing values for responses, where the missing mechanism for both kinds of responses is also considered. Considering the posterior distribution of unknowns given all available information, a Markov Chain Monte Carlo sampling algorithm via winBUGS is used for estimating the posterior distribution of the parameters. For sensitivity analysis to investigate the perturbation from missing at random to not missing at random, it is shown how one can use some elements of covariance structure. These elements associate responses and their missing mechanisms. Influence of small perturbation of these elements on posterior displacement and posterior estimates is also studied. The model is illustrated using data from a foreign language achievement study.

Suggested Citation

  • E. Bahrami Samani & M. Ganjali, 2011. "Bayesian latent variable model for mixed continuous and ordinal responses with possibility of missing responses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(6), pages 1103-1116, March.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:6:p:1103-1116
    DOI: 10.1080/02664763.2010.484485
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    References listed on IDEAS

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    1. Wai-Yin Poon & Sik-Yum Lee, 1987. "Maximum likelihood estimation of multivariate polyserial and polychoric correlation coefficients," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 409-430, September.
    2. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-959, July.
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    1. M. Teimourian & T. Baghfalaki & M. Ganjali & D. Berridge, 2015. "Joint modeling of mixed skewed continuous and ordinal longitudinal responses: a Bayesian approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(10), pages 2233-2256, October.

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