Improve the Bayesian generalized latent variable models with non-linear variable and covariate of dichotomous data
Published on Apr 1, 2019
· DOI :10.1063/1.5097806
Abstract
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Model comparison of Bayesian structural equation models with mixed ordered categorical and dichotomous data
The purpose of this paper is to describe the mixed variables (ordered categorical and dichotomous) in Bayesian structural equation models. Markov chain Monte Carlo simulation (MCMC) via Gibbs sampling method is applied for estimation the parameters. Statistical analyses, which include parameters estimation, standard error, higest posterior density and Devience information creterion for testing the prposed models, are discussed. Hidden continuous normal distribution with censoring is used to hand...
In this article, dichotomous variables are used to compare between linear and nonlinear Bayesian structural equation models. Gibbs sampling method is applied for estimation and model comparison. Statistical inferences that involve estimation of parameters and their standard deviations and residuals analysis for testing the selected model are discussed. Hidden continuous normal distribution (censored normal distribution) is used to solve the problem of dichotomous variables. The proposed procedur...
Bayesian Analysis of Linear and Nonlinear Latent Variable Models with Fixed Covariate and Ordered Categorical Data
In this paper, ordered categorical variables are used to compare between linear and nonlinear interactions of fixed covariate and latent variables Bayesian structural equation models. Gibbs sampling method is applied for estimation and model comparison. Hidden continuous normal distribution (censored normal distribution) is used to handle the problem of ordered categorical data. Statistical inferences, which involve estimation of parameters and their standard deviations, and residuals analyses f...
A reference guide for applications of SEM using MplusStructural Equation Modeling: Applications Using Mplus is intended as both a teaching resource and a reference guide. Written in non-mathematical terms, this book focuses on the conceptual and practical aspects of Structural Equation Modeling (SEM). Basic concepts and examples of various SEM models are demonstrated along with recently developed advanced methods, such as mixture modeling and model-based power analysis and sample size estimate f...
Abstract In this paper, we provide a tutorial exposition on the Bayesian approach in analyzing structural equation models (SEMs). SEMs, which can be regarded as regression models with observed and latent variables, have been widely applied to substantive research. However, the classical methods and most commercial software in this area are based on the covariance structure approach, which would encounter serious difficulties when dealing with complicated models and/or data structures. In contras...
A Bayesian Approach for Nonlinear Structural Equation Models With Dichotomous Variables Using Logit and Probit Links
Analysis of ordered binary and unordered binary data has received considerable attention in social and psychological research. This article introduces a Bayesian approach, which has several nice features in practical applications, for analyzing nonlinear structural equation models with dichotomous data. We demonstrate how to use the software WinBUGS and R2WinBUGS to obtain Bayesian estimates of the unknown parameters, estimates of latent variables, and the Deviance Information Criterion for mode...
This document is intended for computer scientists who would like to try out a Markov Chain Monte Carlo (MCMC) technique, particularly in order to do inference with Bayesian models on problems related to text processing. We try to keep theory to the absolute minimum needed, though we work through the details much more explicitly than you usually see even in \introductory" explanations. That means we’ve attempted to be ridiculously explicit in our exposition and notation. After providing the reaso...
In this article, we formulate a nonlinear structural equation model (SEM) that can accommodate covariates in the measurement equation and nonlinear terms of covariates and exogenous latent variables in the structural equation. The covariates can come from continuous or discrete distributions. A Bayesian approach is developed to analyze the proposed model. Markov chain Monte Carlo methods for obtaining Bayesian estimates and their standard error estimates, highest posterior density intervals, and...
The main purpose of this article is to develop a Bayesian approach for a general multigroup nonlinear factor analysis model. Joint Bayesian estimates of the factor scores and the structural parameters subjected to some constraints across different groups are obtained simultaneously. A hybrid algorithm that combines the Metropolis-Hastings algorithm and the Gibbs sampler is implemented to produce these joint Bayesian estimates. It is shown that this algorithm is computationally efficient. The Bay...
Summary. We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. Using an information theoretic argument we derive a measure pD for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest. In general pD approximately corresponds to the trace of the product of Fisher's information and the posterior covariance, w...
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