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Bayesian Inferences of Latent Class Models with an Unknown Number of Classes

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  • Jia-Chiun Pan
  • Guan-Hua Huang

Abstract

This paper focuses on analyzing data collected in situations where investigators use multiple discrete indicators as surrogates, for example, a set of questionnaires. A very flexible latent class model is used for analysis. We propose a Bayesian framework to perform the joint estimation of the number of latent classes and model parameters. The proposed approach applies the reversible jump Markov chain Monte Carlo to analyze finite mixtures of multivariate multinomial distributions. In the paper, we also develop a procedure for the unique labeling of the classes. We have carried out a detailed sensitivity analysis for various hyperparameter specifications, which leads us to make standard default recommendations for the choice of priors. The usefulness of the proposed method is demonstrated through computer simulations and a study on subtypes of schizophrenia using the Positive and Negative Syndrome Scale (PANSS). Copyright The Psychometric Society 2014

Suggested Citation

  • Jia-Chiun Pan & Guan-Hua Huang, 2014. "Bayesian Inferences of Latent Class Models with an Unknown Number of Classes," Psychometrika, Springer;The Psychometric Society, vol. 79(4), pages 621-646, October.
    • Handle: RePEc:spr:psycho:v:79:y:2014:i:4:p:621-646
    DOI: 10.1007/s11336-013-9368-7
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    References listed on IDEAS

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    1. Guan-Hua Huang & Karen Bandeen-Roche, 2004. "Building an identifiable latent class model with covariate effects on underlying and measured variables," Psychometrika, Springer;The Psychometric Society, vol. 69(1), pages 5-32, March.
    2. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    3. Bert Green, 1951. "A general solution for the latent class model of latent structure analysis," Psychometrika, Springer;The Psychometric Society, vol. 16(2), pages 151-166, June.
    4. Elizabeth S. Garrett & Scott L. Zeger, 2000. "Latent Class Model Diagnosis," Biometrics, The International Biometric Society, vol. 56(4), pages 1055-1067, December.
    5. Guan-Hua Huang, 2005. "Selecting the number of classes under latent class regression: a factor analytic analogue," Psychometrika, Springer;The Psychometric Society, vol. 70(2), pages 325-345, June.
    6. Hirotugu Akaike, 1987. "Factor analysis and AIC," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 317-332, September.
    7. Yao, Weixin & Lindsay, Bruce G., 2009. "Bayesian Mixture Labeling by Highest Posterior Density," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 758-767.
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    Cited by:

    1. Jing Ouyang & Gongjun Xu, 2022. "Identifiability of Latent Class Models with Covariates," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1343-1360, December.
    2. Yinghan Chen & Steven Andrew Culpepper & Yuguo Chen, 2023. "Bayesian Inference for an Unknown Number of Attributes in Restricted Latent Class Models," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 613-635, June.
    3. Lee, Jung Wun & Chung, Hwan & Jeon, Saebom, 2021. "Bayesian multivariate latent class profile analysis: Exploring the developmental progression of youth depression and substance use," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    4. Kazem Nasserinejad & Joost van Rosmalen & Wim de Kort & Emmanuel Lesaffre, 2017. "Comparison of Criteria for Choosing the Number of Classes in Bayesian Finite Mixture Models," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-23, January.
    5. Francesco Bartolucci & Alessio Farcomeni & Luisa Scaccia, 2017. "A Nonparametric Multidimensional Latent Class IRT Model in a Bayesian Framework," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 952-978, December.

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