Pooling test statistics across multiply imputed datasets for nonnormal items.

Area of Science:

• Statistics
• Quantitative Psychology
• Econometrics

Background:

• Structural equation modeling (SEM) often requires handling missing data using multiple imputation (MI).
• Evaluating model fit in SEM with MI involves pooling test statistics across imputations.
• Established pooling methods by Li et al. and Meng and Rubin assume data normality.

Purpose of the Study:

• To systematically evaluate the performance of existing pooling approaches for SEM model fit statistics under nonnormality.
• To assess how pooling methods interact with different multiple imputation techniques and robust estimators.
• To identify the most effective pooling strategy when normality assumptions are violated.

Main Methods:

• A simulation study was conducted to examine pooling approaches for likelihood-ratio test statistics.
• The study compared the Li et al. and Meng and Rubin (D3SN) pooling methods.
• Performance was evaluated under conditions of nonnormality, using various imputation methods and robust estimators (MLM, MLMV).

Main Results:

• The naive pooling approach (D3SN), based on Meng and Rubin, demonstrated superior performance.
• Optimal results were achieved when D3SN was combined with normal-theory-based imputation.
• The combination of D3SN, normal-theory imputation, and either the MLM or MLMV estimator yielded the best outcomes.

Conclusions:

• The naive pooling approach (D3SN) is recommended for SEM model fit evaluation with missing data under nonnormality.
• Researchers should utilize normal-theory imputation alongside MLM or MLMV estimators for robust model fit assessment.
• This study provides empirical evidence for selecting appropriate pooling methods in SEM when data deviates from normality.