Asymptotics of AIC, BIC, and RMSEA for Model Selection in Structural Equation Modeling

Model selection is a popular strategy in structural equation modeling (SEM). To select an “optimal” model, many selection criteria have been proposed. In this study, we derive the asymptotics of several popular selection procedures in SEM, including AIC, BIC, the RMSEA, and a two-stage rule for the...

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Bibliographic Details
Published inPsychometrika Vol. 82; no. 2; pp. 407 - 426
Main Author Huang, Po-Hsien
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2017
Springer Nature B.V
Subjects
Assessment
Bayes Theorem
Behavioral Science and Psychology
Estimating techniques
Humanities
Humans
Law
Likelihood Functions
Models, Genetic
Models, Statistical
Psychology
Psychometrics
Selection Criteria
Statistical Theory and Methods
Statistics for Social Sciences
Structural equation modeling
Structural Equation Models
Testing and Evaluation
model selection
root-mean-square error of approximation
Akaike information criterion
Bayesian information criterion
structural equation modeling
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Summary:Model selection is a popular strategy in structural equation modeling (SEM). To select an “optimal” model, many selection criteria have been proposed. In this study, we derive the asymptotics of several popular selection procedures in SEM, including AIC, BIC, the RMSEA, and a two-stage rule for the RMSEA (RMSEA-2S). All of the results are derived under weak distributional assumptions and can be applied to a wide class of discrepancy functions. The results show that both AIC and BIC asymptotically select a model with the smallest population minimum discrepancy function (MDF) value regardless of nested or non-nested selection, but only BIC could consistently choose the most parsimonious one under nested model selection. When there are many non-nested models attaining the smallest MDF value, the consistency of BIC for the most parsimonious one fails. On the other hand, the RMSEA asymptotically selects a model that attains the smallest population RMSEA value, and the RESEA-2S chooses the most parsimonious model from all models with the population RMSEA smaller than the pre-specified cutoff. The empirical behavior of the considered criteria is also illustrated via four numerical examples.
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ISSN:0033-3123
1860-0980
DOI:10.1007/s11336-017-9572-y