The Robustness of the Delta Method and Bootstrap in Calculating Standardized Coefficient in Misspecified SEM Models

AbstractIn practice, models almost always have misfit. The misfit of a structural equation model (SEM) can affect the estimation of model parameters in terms of point estimates, standard errors (SEs), and confidence intervals (CIs). In this article, the performance of different methods are compared including: the delta method, the nonparametric bootstrap (NP-B) method, and the semi-parametric bootstrap (SP-B) method in estimating standardized model parameters under the influence of model misfit. Two methods are used to construct the CI of the bootstrap method, the standard percentile method and the bias-corrected and accelerated (BCa) method. A simulation study is conducted using an SEM model with different amounts of model misfit and various sample sizes. The results show that if the model is correctly specified, all methods give correct point estimates, SE estimates, and CI coverage rates. However, as the amount of model misfit increases, the estimates based on NP-B remain accurate and consistent, whose based on the delta method and SP-B deteriorateKeywords: misspecification, standard error, SEM, standardized parameter