TY - JOUR

T1 - Adapting Fit Indices for Bayesian Structural Equation Modeling

T2 - Comparison to Maximum Likelihood

AU - Garnier-Villarreal, Mauricio

AU - Jorgensen, Terrence D.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In a frequentist framework, the exact fit of a structural equation model (SEM) is typically evaluated with the chi-square test and at least one index of approximate fit. Current Bayesian SEM (BSEM) software provides one measure of overall fit: the posterior predictive p value (PPP±2). Because of the noted limitations of PPPχ2, common practice for evaluating Bayesian model fit instead focuses on model comparison, using information criteria or Bayes factors. Fit indices developed under maximumlikelihood estimation have not been incorporated into software for BSEM. We propose adapting 7 chi-square-based approximate fit indices for BSEM, using a Bayesian analog of the chi-square model-fit statistic. Simulation results show that the sampling distributions of the posterior means of these fit indices are similar to their frequentist counterparts across sample sizes, model types, and levels of misspecification when BSEMs are estimated with noninformative priors. The proposed fit indices therefore allow overall model-fit evaluation using familiar metrics of the original indices, with an accompanying interval to quantify their uncertainty. Illustrative examples with real data raise some important issues about the proposed fit indices' application to models specified with informative priors, when Bayesian and frequentist estimation methods might not yield similar results.

AB - In a frequentist framework, the exact fit of a structural equation model (SEM) is typically evaluated with the chi-square test and at least one index of approximate fit. Current Bayesian SEM (BSEM) software provides one measure of overall fit: the posterior predictive p value (PPP±2). Because of the noted limitations of PPPχ2, common practice for evaluating Bayesian model fit instead focuses on model comparison, using information criteria or Bayes factors. Fit indices developed under maximumlikelihood estimation have not been incorporated into software for BSEM. We propose adapting 7 chi-square-based approximate fit indices for BSEM, using a Bayesian analog of the chi-square model-fit statistic. Simulation results show that the sampling distributions of the posterior means of these fit indices are similar to their frequentist counterparts across sample sizes, model types, and levels of misspecification when BSEMs are estimated with noninformative priors. The proposed fit indices therefore allow overall model-fit evaluation using familiar metrics of the original indices, with an accompanying interval to quantify their uncertainty. Illustrative examples with real data raise some important issues about the proposed fit indices' application to models specified with informative priors, when Bayesian and frequentist estimation methods might not yield similar results.

KW - Bayesian

KW - BSEM

KW - Fit indices

KW - Model fit

KW - Structural equation modeling

UR - http://www.scopus.com/inward/record.url?scp=85066974609&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066974609&partnerID=8YFLogxK

U2 - 10.1037/met0000224

DO - 10.1037/met0000224

M3 - Article

C2 - 31180693

AN - SCOPUS:85066974609

JO - Psychological Methods

JF - Psychological Methods

SN - 1082-989X

ER -