Pooling test statistics across multiply imputed datasets for nonnormal items

In structural equation modeling, when multiple imputation is used for handling missing data, model fit evaluation involves pooling likelihood-ratio test statistics across imputations. Under the normality assumption, the two most popular pooling approaches were proposed by Li et al. (Statistica Sinica, 1(1), 65-92, 1991) and Meng and Rubin (Biometrika, 79(1), 103-111, 1992). When the assumption of normality is violated, it is not clear how well these pooling approaches work with the test statistics generated from various robust estimators and multiple imputation methods. Jorgensen and colleagues (2021) implemented these pooling approaches in their R package semTools; however, no systematical evaluation has been conducted. In this simulation study, we examine the performance of these approaches in working with different imputation methods and robust estimators under nonnormality. We found that the naive pooling approach based on Meng and Rubin (Biometrika, 79(1), 103-111, 1992; D-3SN) worked the best when combining with the normal-theory-based imputation and either MLM or MLMV estimator.