Bayesian structural equation modeling: a more flexible representation of substantive theory.

This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed Bayesian approach is particularly beneficial in applications where parameters are added to a conventional model such that a nonidentified model is obtained if maximum-likelihood estimation is applied. This approach is useful for measurement aspects of latent variable modeling, such as with confirmatory factor analysis, and the measurement part of structural equation modeling. Two application areas are studied, cross-loadings and residual correlations in confirmatory factor analysis. An example using a full structural equation model is also presented, showing an efficient way to find model misspecification. The approach encompasses 3 elements: model testing using posterior predictive checking, model estimation, and model modification. Monte Carlo simulations and real data are analyzed using Mplus. The real-data analyses use data from Holzinger and Swineford's (1939) classic mental abilities study, Big Five personality factor data from a British survey, and science achievement data from the National Educational Longitudinal Study of 1988.

[1]  John K. Kruschke,et al.  Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan , 2014 .

[2]  Benjamin Nagengast,et al.  Measurement invariance of big-five factors over the life span: ESEM tests of gender, age, plasticity, maturity, and la dolce vita effects. , 2013, Developmental psychology.

[3]  J. Kruschke Doing Bayesian Data Analysis: A Tutorial with R and BUGS , 2010 .

[4]  Craig K. Enders,et al.  Applied Missing Data Analysis , 2010 .

[5]  Bengt Muthén,et al.  Bayesian Analysis Using Mplus , 2010 .

[6]  Ying Yuan,et al.  Bayesian mediation analysis. , 2009, Psychological methods.

[7]  B. Muthén,et al.  Exploratory Structural Equation Modeling , 2009 .

[8]  Ulrich Trautwein,et al.  Please Scroll down for Article Structural Equation Modeling: a Multidisciplinary Journal Exploratory Structural Equation Modeling, Integrating Cfa and Efa: Application to Students' Evaluations of University Teaching , 2022 .

[9]  Juni Palmgren,et al.  A random change point model for assessing variability in repeated measures of cognitive function , 2008, Statistics in medicine.

[10]  D. Mackinnon Introduction to Statistical Mediation Analysis , 2008 .

[11]  Scott M. Lynch,et al.  Introduction to Applied Bayesian Statistics and Estimation for Social Scientists , 2007 .

[12]  Sik-Yum Lee Structural Equation Modeling: A Bayesian Approach , 2007 .

[13]  George A. Marcoulides,et al.  TEACHER'S CORNER: Examining Identification Issues in Factor Analysis , 2006 .

[14]  N. Hjort,et al.  Post-Processing Posterior Predictive p Values , 2006 .

[15]  R. MacCallum,et al.  Testing differences between nested covariance structure models: Power analysis and null hypotheses. , 2006, Psychological methods.

[16]  Thomas H. Short,et al.  Subjective and Objective Bayesian Statistics: Principles, Models, and Applications , 2005 .

[17]  A. Brix Bayesian Data Analysis, 2nd edn , 2005 .

[18]  William J. Browne,et al.  Bayesian and likelihood-based methods in multilevel modeling 1 A comparison of Bayesian and likelihood-based methods for fitting multilevel models , 2006 .

[19]  D. Dey,et al.  To Bayes or Not to Bayes, From Whether to When: Applications of Bayesian Methodology to Modeling , 2004 .

[20]  David J. Spiegelhalter,et al.  WinBUGS user manual version 1.4 , 2003 .

[21]  S. James Press,et al.  Subjective and objective Bayesian statistics : principles, models, and applications , 2003 .

[22]  J. Gustafsson Measurement From a Hierarchical Point of View , 2002 .

[23]  David E. Wiley,et al.  The role of constructs in psychological and educational measurement , 2001 .

[24]  M. Browne An Overview of Analytic Rotation in Exploratory Factor Analysis , 2001 .

[25]  D. Kaplan Structural Equation Modeling: Foundations and Extensions , 2000 .

[26]  Xiao-Li Meng,et al.  Modeling covariance matrices in terms of standard deviations and correlations, with application to shrinkage , 2000 .

[27]  David E. Booth,et al.  Analysis of Incomplete Multivariate Data , 2000, Technometrics.

[28]  R. Scheines,et al.  Bayesian estimation and testing of structural equation models , 1999 .

[29]  Sylvia Richardson,et al.  Markov Chain Monte Carlo in Practice , 1997 .

[30]  S. Chib,et al.  Bayesian Analysis of Multivariate Probit Models , 1996 .

[31]  Peter Green,et al.  Markov chain Monte Carlo in Practice , 1996 .

[32]  Xiao-Li Meng,et al.  POSTERIOR PREDICTIVE ASSESSMENT OF MODEL FITNESS VIA REALIZED DISCREPANCIES , 1996 .

[33]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[34]  Walter R. Gilks,et al.  MCMC in image analysis , 1995 .

[35]  R. Cudeck,et al.  Applications of standard error estimates in unrestricted factor analysis: significance tests for factor loadings and correlations. , 1994, Psychological bulletin.

[36]  J. S. Long,et al.  Testing Structural Equation Models , 1993 .

[37]  M. Browne,et al.  Alternative Ways of Assessing Model Fit , 1992 .

[38]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[39]  G. Casella,et al.  Explaining the Gibbs Sampler , 1992 .

[40]  R. MacCallum,et al.  Model modifications in covariance structure analysis: the problem of capitalization on chance. , 1992, Psychological bulletin.

[41]  S. E. Hills,et al.  Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling , 1990 .

[42]  J. Oakes,et al.  Indicators for Monitoring Mathematics and Science Education: A Sourcebook , 1995 .

[43]  B. Muthén Latent variable modeling in heterogeneous populations , 1989 .

[44]  H. Harman Modern factor analysis , 1961 .