Evaluating local model misspecification with modification indices in Bayesian structural equation modeling

Model evaluation is a crucial step in SEM, consisting of two broad areas: global and local fit, where local fit indices are used to modify the original model. In the modification process, the modification index (MI) and the standardized expected parameter change (SEPC) are used to select the parameters that can be added to improve the fit. The purpose of this study is to extend the application of MI and SEPC to Bayesian SEM. We present how researchers can estimate posterior distributions of MI and SEPC using a posterior predictive model check (PPMC). We evaluated the effectiveness of these PPMCs with a simulation and found that MI can be used to detect the most relevant added parameters and that SEPC can be used as an effect size. Similar to maximum-likelihood estimation, the SEPC can overestimate the population value. Lastly, we present an example application of these indices.