Alternative Multiple Imputation Inference for Mean and Covariance Structure Modeling

Model-based multiple imputation has become an indispensable method in the educational and behavioral sciences. Mean and covariance structure models are often fitted to multiply imputed data sets. However, the presence of multiple random imputations complicates model fit testing, which is an important aspect of mean and covariance structure modeling. Extending the logic developed by Yuan and Bentler, Cai, and Cai and Lee, we propose an alternative method for conducting multiple imputation–based inference for mean and covariance structure modeling. In addition to computational simplicity, our method naturally leads to an asymptotically chi-square model fit test statistic. Using simulations, we show that our new method is well calibrated, and we illustrate it with analyses of three real data sets. A SAS macro implementing this method is also provided.