Journal ArticleDOI
Semiparametric Bayesian analysis of structural equation models with fixed covariates
Sik-Yum Lee,Bin Lu,Xinyuan Song +2 more
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TLDR
A general Bayesian framework is provided in which a semiparametric hierarchical modeling with an approximate truncation Dirichlet process prior distribution is specified for the latent variables in SEMs with covariates.Abstract:
Latent variables play the most important role in structural equation modeling. In almost all existing structural equation models (SEMs), it is assumed that the distribution of the latent variables is normal. As this assumption is likely to be violated in many biomedical researches, a semiparametric Bayesian approach for relaxing it is developed in this paper. In the context of SEMs with covariates, we provide a general Bayesian framework in which a semiparametric hierarchical modeling with an approximate truncation Dirichlet process prior distribution is specified for the latent variables. The stick-breaking prior and the blocked Gibbs sampler are used for efficient simulation in the posterior analysis. The developed methodology is applied to a study of kidney disease in diabetes patients. A simulation study is conducted to reveal the empirical performance of the proposed approach. Supplementary electronic material for this paper is available in Wiley InterScience at http://www.mrw.interscience.wiley.com/suppmat/1097-0258/suppmat/.read more
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Basic and Advanced Bayesian Structural Equation Modeling: With Applications in the Medical and Behavioral Sciences
Xinyuan Song,Sik-Yum Lee +1 more
TL;DR: Basic and Advanced Bayesian Structural Equation Modeling introduces basic and advanced SEMs for analyzing various kinds of complex data, such as ordered and unordered categorical data, multilevel data, mixture data, longitudinal data, highly non-normal data, as well as some of their combinations.
Journal ArticleDOI
Bayesian Semiparametric Structural Equation Models with Latent Variables
Mingan Yang,David B. Dunson +1 more
TL;DR: 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 is proposed, based on centered Dirichlet process and CDP mixture models.
Journal ArticleDOI
A Nonlinear Structural Equation Mixture Modeling Approach for Nonnormally Distributed Latent Predictor Variables
TL;DR: In this article, a nonlinear structural equation mixture approach is proposed for testing nonlinear hypotheses in the social sciences, which integrates the strength of parametric approaches (specification of the nonlinear functional relationship) and the flexibility of semiparametric structural equation mixtures approaches for approximating the nonnormality of latent predictor variables.
Journal ArticleDOI
Bayesian estimation of semiparametric nonlinear dynamic factor analysis models using the Dirichlet process prior.
TL;DR: In this article, the truncated Dirichlet process (DP) is used as a nonparametric prior for dynamic parameters in a novel nonlinear Bayesian dynamic factor analysis model, which is equivalent to specifying the prior distribution to be a mixture distribution composed of an unknown number of discrete point masses.
Journal ArticleDOI
The time has come:Toward Bayesian SEM estimation in tourism research
TL;DR: This paper provides first some foundations of Bayesian estimation and inference, and presents an illustration of the method using a tourism application, and conducts a Monte Carlo simulation to illustrate the performance of the Bayesian approach in small samples.
References
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Lisrel 8: Structural Equation Modeling With the Simplis Command Language
Karl G. Jöreskog,Dag Sörbom +1 more
TL;DR: The SIMPLIS language shifts the focus away from the technical question "How to do it", so that researchers can concentrate on the question, "What does it all mean?"
Journal ArticleDOI
A Bayesian Analysis of Some Nonparametric Problems
TL;DR: In this article, a class of prior distributions, called Dirichlet process priors, is proposed for nonparametric problems, for which treatment of many non-parametric statistical problems may be carried out, yielding results that are comparable to the classical theory.
Journal ArticleDOI
Bayesian Density Estimation and Inference Using Mixtures
Michael Escobar,Mike West +1 more
TL;DR: In this article, the authors describe and illustrate Bayesian inference in models for density estimation using mixtures of Dirichlet processes and show convergence results for a general class of normal mixture models.
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