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Modeling Associations Among Multivariate Longitudinal Categorical Variables in Survey Data: A Semiparametric Bayesian Approach

Published online by Cambridge University Press:  01 January 2025

Sylvie Tchumtchoua  and
Dipak K. Dey
Sylvie Tchumtchoua*
Affiliation:
Statistical and Applied Mathematical Sciences Institute
Dipak K. Dey
Affiliation:
Department of Statistics, University of Connecticut
*
Requests for reprints should be sent to Sylvie Tchumtchoua, Statistical and Applied Mathematical Sciences Institute, 19 T. W. Alexander Drive, Research Triangle Park, P.O. Box 14006, Durham, NC 27709, USA. E-mail: sylvie.tchumtchoua@gmail.com
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Abstract

This paper proposes a semiparametric Bayesian framework for the analysis of associations among multivariate longitudinal categorical variables in high-dimensional data settings. This type of data is frequent, especially in the social and behavioral sciences. A semiparametric hierarchical factor analysis model is developed in which the distributions of the factors are modeled nonparametrically through a dynamic hierarchical Dirichlet process prior. A Markov chain Monte Carlo algorithm is developed for fitting the model, and the methodology is exemplified through a study of the dynamics of public attitudes toward science and technology in the United States over the period 1992–2001.

Keywords

dynamic hierarchical Dirichlet processfactor analysishierarchical factor analysishigh-dimensional datalongitudinal categorical variables
Type
Original Paper
Information
Psychometrika , Volume 77 , Issue 4 , October 2012 , pp. 670 - 692
Copyright
Copyright © 2012 The Psychometric Society

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References

Albert, J.H., & Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association, 88(422), 669–679.CrossRefGoogle Scholar
Bak, H.J. (2001). Education and public attitudes toward science: implications for the deficit model of education and support for science and technology. Social Science Quarterly, 82(4), 779–795.CrossRefGoogle Scholar
Bhattacharya, A., & Dunson, D.B. (2011). Sparse Bayesian infinite factor models. Biometrika, 98(2), 291–306.CrossRefGoogle ScholarPubMed
Caron, F., Davy, M., & Doucet, A. (2007). Generalized poly urn for time-varying Dirichlet process mixtures. In Proceedings of the twenty-third annual conference on uncertainty in artificial intelligence (pp. 33–40). Corvallis: AUAI Press.Google Scholar
Dunson, D.B. (2006). Bayesian dynamic modeling of latent trait distributions. Biostatistics, 7(4), 551–568.CrossRefGoogle ScholarPubMed
Escofier, B., & Pages, J. (1988). Analyses factorielles simples et multiples; objectifs, méthodes et interprétations. Paris: Dunod.Google Scholar
Everitt, B.S. (1992). The analysis of contingency tables. (2 ed.). London: Chapman & Hall.CrossRefGoogle Scholar
Fokoue, E., & Titterington, D.M. (2003). Mixtures of factor analysers: Bayesian estimation and inference by stochastic simulation. Machine Learning, 50, 73–94.CrossRefGoogle Scholar
Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to calculating posterior moments. In Bernardo, J.M., Berger, J.O., Dawid, A.P., & Smith, A.F.M. (Eds.), Bayesian statistics (pp. 169–193). Oxford: Clarendon Press.Google Scholar
Ghosh, J., & Dunson, D.B. (2009). Default priors and efficient posterior computation in Bayesian factor analysis. Journal of Computational and Graphical Statistics, 18, 306–320.CrossRefGoogle ScholarPubMed
Goodman, L.A. (1974). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61, 215–231.CrossRefGoogle Scholar
Goodman, L.E. (1986). Some useful extensions of the usual correspondence analysis approach and the usual log-linear models approach in the analysis of contingency tables (with discussion). International Statistical Review, 54, 243–270.CrossRefGoogle Scholar
Goodman, L.A., & Hout, M. (1998). Statistical methods and graphical displays for analyzing how the association between two qualitative variables differs among countries, among groups, or over time: a modified regression-type approach. Sociological Methodology, 28, 175–230.CrossRefGoogle Scholar
Greenacre, M.J. (2007). Correspondence analysis in practice. (2 ed.). Boca Raton: Chapman & Hall.CrossRefGoogle Scholar
Ishwaran, H., & James, L.F. (2001). Gibbs sampling methods for stick-breaking priors. Journal of the American Statistical Association, 96, 161–173.CrossRefGoogle Scholar
Lazarsfeld, P.F., & Henry, N.W. (1968). Latent structure analysis. Boston: Houghton Mifflin.Google Scholar
Lee, S.Y., & Song, X.Y. (2002). Bayesian selection on the number of factors in a factor analysis model. Behaviormetrika, 29, 23–40.CrossRefGoogle Scholar
Lopes, H.F., & West, M. (2004). Bayesian model assessment in factor analysis. Statistica Sinica, 14, 41–67.Google Scholar
MacEachern, S.N. (1999). Dependent nonparametric processes. In Proceedings of Bayesian statistical science section (pp. 50–55). Alexandria: Am. Statist. Assoc..Google Scholar
MacEachern, S.N., (2000). Dependent Dirichlet processes. Unpublished manuscript, Department of Statistics, The Ohio State University. .Google Scholar
MacEachern, S.N. (2001). Decision theoretic aspects of dependent nonparametric processes. In George, E., & Nanopoulos, P. Bayesian methods with applications to science, policy and official statistics (pp. 551–560). Crete: International Society for Bayesian Analysis.Google Scholar
McLachlan, G.J., Peel, D., & Bean, R.W. (2003). Modelling high-dimensional data by mixtures of factor analyzers. Computational Statistics & Data Analysis, 41, 379–388.CrossRefGoogle Scholar
Mislevy, R.J. (1986). Recent developments in the factor analysis of categorical variables. Journal of Educational Statistics, 11(1), 3–31.CrossRefGoogle Scholar
Ng, S., & Moench, E. (2011). A hierarchical factor analysis of US housing market dynamics. Econometrics Journal, 14(1), 1–24.Google Scholar
Ren, L., Dunson, D.B., & Carin, L. (2008). The dynamic hierarchical Dirichlet process. In Proceedings of the international conference on machine learning (pp. 824–831). Helsinki: ACM.CrossRefGoogle Scholar
Sasaki, M., & Suzuki, T. (1991). Dimensions of public acceptance of science and technology among five industrialized nations. Behaviormetrika, 29, 73–82.CrossRefGoogle Scholar
Teh, Y.W., Jordan, M.I., Beal, M.J., & Blei, D.M. (2006). Hierarchical Dirichlet processes. Journal of the American Statistical Association, 101, 1566–1581.CrossRefGoogle Scholar
Thurstone, L.L. (1947). Multiple factor analysis. Chicago: University of Chicago Press.Google Scholar
Yang, M., & Dunson, D.B. (2010). Bayesian semiparametric structural equation models with latent variables. Psychometrika, 75(4), 675–693.CrossRefGoogle Scholar