Journal
PSYCHOMETRIKA
Volume 75, Issue 4, Pages 675-693Publisher
SPRINGER
DOI: 10.1007/s11336-010-9174-4
Keywords
Dirichlet process; factor analysis; latent class; latent trait; mixture model; nonparametric Bayes; parameter expansion
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Funding
- National Institute of Environmental Health Sciences (NIEHS) of the National Institutes of Health (NIH) [R01 ES017240-01]
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Structural equation models (SEMs) with latent variables are widely useful for sparse covariance structure modeling and for inferring relationships among latent variables. Bayesian SEMs are appealing in allowing for the incorporation of prior information and in providing exact posterior distributions of unknowns, including the latent variables. In this article, we propose a broad class of semiparametric Bayesian SEMs, which allow mixed categorical and continuous manifest variables while also allowing the latent variables to have unknown distributions. In order to include typical identifiability restrictions on the latent variable distributions, we rely on centered Dirichlet process (CDP) and CDP mixture (CDPM) models. The CDP will induce a latent class model with an unknown number of classes, while the CDPM will induce a latent trait model with unknown densities for the latent traits. A simple and efficient Markov chain Monte Carlo algorithm is developed for posterior computation, and the methods are illustrated using simulated examples, and several applications.
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