Assessing the fit of structural equation models with multiply imputed data

Multiple imputation has enjoyed widespread use in social science applications, yet the application of imputation-based inference to structural equation modeling has received virtually no attention in the literature. Thus, this study has 2 overarching goals: evaluate the application of Meng and Rubin's (1992) pooling procedure for likelihood ratio statistic to the SEM test of model fit, and explore the possibility of using this test statistic to define imputation-based versions of common fit indices such as the TLI, CFI, and RMSEA. Computer simulation results suggested that, when applied to a correctly specified model, the pooled likelihood ratio statistic performed well as a global test of model fit and was closely calibrated to the corresponding full information maximum likelihood (FIML) test statistic. However, when applied to misspecified models with high rates of missingness (30%-40%), the imputation-based test statistic generally exhibited lower power than that of FIML. Using the pooled test statistic to construct imputation-based versions of the TLI, CFI, and RMSEA worked well and produced indices that were well-calibrated with those of full information maximum likelihood estimation. This article gives Mplus and R code to implement the pooled test statistic, and it offers a number of recommendations for future research.