Model selection in Structural Equation Models
Selecting between competing structural equation models is a common problem. Often selection is based on the chi-square test statistic or other fit indices. In other areas of statistical research Bayesian information criteria are commonly used, but they are less frequently used with structural equation models compared to other fit indices. This article examines several new and old information criteria (IC) that approximate Bayes factors. We compare these IC measures to common fit indices in a simulation that includes the true and false models. In moderate to large samples, the IC measures outperform the fit indices. In a second simulation we only consider the IC measures and do not include the true model. In moderate to large samples the IC measures favor approximate models that only differ from the true model by having extra parameters. Overall, SPBIC, a new IC measure, performs well relative to the other IC measures.
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Abstract
We present a new approach to model selection and Bayes factor determination, based on Laplace expansions (as in BIC), which we call Prior-based Bayes Information Criterion (PBIC). In this approach, the Laplace expansion is only done with the likelihood function, and then a suitable prior distribution is chosen to allow exact computation of the (approximate) marginal likelihood arising from the Laplace approximation and the prior. The result is a closed-form expression similar to BIC, but now involves a term arising from the prior distribution (which BIC ignores) and also incorporates the idea that different parameters can have different effective sample sizes (whereas BIC only allows one overall sample size n). We also consider a modification of PBIC which is more favourable to complex models. 2019, East China Normal University 2019.
Abstract
Selecting between competing structural equation models is a common problem. Often selection is based on the chi-square test statistic or other fit indices. In other areas of statistical research Bayesian information criteria are commonly used, but they are less frequently used with structural equation models compared to other fit indices. This article examines several new and old information criteria (IC) that approximate Bayes factors. We compare these IC measures to common fit indices in a simulation that includes the true and false models. In moderate to large samples, the IC measures outperform the fit indices. In a second simulation we only consider the IC measures and do not include the true model. In moderate to large samples the IC measures favor approximate models that only differ from the true model by having extra parameters. Overall, SPBIC, a new IC measure, performs well relative to the other IC measures. 2014 Copyright Taylor and Francis Group, LLC.
Abstract
Bayes factors (BFs) play an important role in comparing the fit of statistical models. However, computational limitations or lack of an appropriate prior sometimes prevent researchers from using exact BFs. Instead, it is approximated, often using the Bayesian Information Criterion (BIC) or a variant of BIC. The authors provide a comparison of several BF approximations, including two new approximations, the Scaled Unit Information Prior Bayesian Information Criterion (SPBIC) and Information matrix-based Bayesian Information Criterion (IBIC). The SPBIC uses a scaled unit information prior that is more general than the BIC's unit information prior, and the IBIC utilizes more terms of approximation than the BIC. Through simulation, the authors show that several measures perform well in large samples, that performance declines in smaller samples, and that SPBIC and IBIC provide improvement to existing measures under some conditions, including small sample sizes. The authors illustrate the use of the fit measures with the crime data of Ehrlich and then conclude with recommendations for researchers. The Author(s) 2012.