Bayesian analysis of ordinal survey data using the Dirichlet process ...

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6 DISCUSSIONWe have developed a Bayesian latent variable model to analyze ordinal response surveydata. We have also facilitated a clustering mechanism based on personalities. Mostimportantly, clustering takes place as a consequence of Dirichlet process modelling ofthe personality parameters. In a WinBUGS programming environment, the model issuccinctly formulated, and is not complicated by latent variables and missing data.Our model identifies areas where performance has been poor or exceptional in a ordinalsurvey data by investigating standardized parameters. It also allows us to check whethersome questions in a survey are redundant. A goodness-of-fit procedure is advocated thatis based on comparing prior-predictive output versus observed data. The approach isintuitive and is flexible in the sense that one can investigate features which are relevant tothe particular model. Future enhancements may be considered such as including subjectcovariates and handling longitudinal data structures.One of the assumptions in our model concerns the use of fixed cut-points in transformingthe underlying continuous latent responses Y ij to the observed discrete responsesX ij . Although it may have been preferable to allow variable cut-points, we were unableto implement the generalization. Issues of non-identifiablility and model complexity leadto Markov chains which did not achieve practical convergence.7 REFERENCESAgresti, A. (2010). Analysis of Ordinal Categorical Data, Second Edition, Wiley: New York.Bernardo, J.M. and Smith, A.F.M. (1994). Bayesian Theory, Wiley: New York.Box, G. E. (1980). “Sampling and Bayes’ inference in scientific modelling and robustness”(with discussion), Journal of the Royal Statistical Society, Series A, 143, 383–430.22
Brooks, S. P. and Gelman, A. (1997). “Alternative methods for monitoring convergence ofiterative simulations”, Computational and Graphical Statistics, 7, 434–455.Cowen, L., Manion, L. and Morrison, K. (2007). Research Methods in Education, Sixth Edition,Routledge: New York.Dawes, J. (2008). “Do data characteristics change according to the number of scale pointsused? An experiment using 5-point, 7-point and 10-point scales”, International Journalof Market Research, 50, 61-77.Dolnicar, S. and Grun, B. (2007). “Cross-cultural differences in survey response patterns”,International Marketing Review, 24, 127-143.Dunson, D.B. and Gelfand, A.E. (2009). “Bayesian nonparametric functional data analysisthrough density estimation”, Biometrika, 96, 149-162.Emons, W.H.M. (2008). “Nonparametric person-fit analysis of polytomous item scores”, AppliedPsychologial Measurement, 32, 224-247.Evans, M. (2007). Comment on “Bayesian checking of the second levels of hierarchical models”by Bayarri and Castellanos, Statistical Science, 22, 344-348.Fanning, E. (2005). “Formatting a paper-based survey questionnaire: best practices”, PracticalAssessment Research & Evaluation, online: http://pareonline.net/pdf/v10n12.pdf.Ferguson, T.S. (1973). “A Bayesian analysis of some nonparametric problems”, Annals ofStatistics, 1, 209-230.Forrest, M. and Andersen, B. (1986). “Ordinal scale and statistics in medical research”, BritishMedical Journal, 292, 537-538.Gelfand, A. E., Dey, D. K. and Chang, H. (1992). “Model determination using predictive distributionswith implementation via sampling-based methods” (with discussion), In BayesianStatistics 4 (J. M. Bernardo, J. O. Berger, A. P. Dawid & A. F. M. Smith, editors),Oxford: Oxford University Press, 147–167.Gelman, A., Meng, X. L. and Stern, H. S. (1996). “Posterior predictive assessment of modelfitness via realized discrepancies”, Statistica Sinica, 6, 733–807.Gill, J. and Casella, G. (2009). “Nonparametric priors for ordinal Bayesian social sciencemodels: specification and estimation”, Journal of the American Statistical Association,104, 453-464.23
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Page 5 and 6: validity of the model. The proposed
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