A Comparison of Full Information Maximum Likelihood and Multiple Imputation in Structural Equation Modeling With Missing Data

Abstract

This article compares two missing data procedures, full information maximum likelihood (FIML) and multiple imputation (MI), to investigate their relative performances in relation to the results from analyses of the original complete data or the hypothetical data available before missingness occurred. By expressing the FIML estimator as a special MI estimator, we predicted the expected patterns of discrepancy between the two estimators. Via Monte Carlo simulation studies where we have access to the original complete data, we compare the performance of FIML and MI estimators to that of the complete data maximum likelihood (ML) estimator under a wide range of conditions, including differences in sample size, percent of missingness, and degrees of model misfit. Our study confirmed well-known knowledge that the two estimators tend to yield essentially equivalent results to each other and to those from analysis of complete data when the postulated model is correctly specified. However, some noteworthy patterns of discrepancies were found between the FIML and MI estimators when the hypothesized model does not hold exactly in the population: MI-based parameter estimates, comparative fit index (CFI), and the Tucker Lewis index (TLI) tend to be closer to the counterparts of the complete data ML estimates, whereas FIML-based chi-squares and root mean square error of approximation (RMSEA) tend to be closer to the counterparts of the complete data ML estimates. We explained the observed patterns of discrepancy between the two estimators as a function of the interplay between the parsimony and accuracy of the imputation model. We concluded by discussing practical and methodological implications and issues for further research. Translational Abstract In this article, two classes of modern missing data procedures, maximum likelihood (ML) and multiple imputation (MI), are systematically compared. Although it has been argued that the two classes of missing data procedures are essentially equivalent, we showed that they may not produce equivalent results as practiced empirically under realistic conditions where researchers work with imperfect models. Following a review of relevant estimation theory, we have made specific a priori predictions on the expected patterns of the discrepancy between FIML and MI estimators, with respect to parameter estimates, their associated sampling variabilities, and the goodness of fit indices. Via Monte Carlo simulation studies where we have access to the original complete data, we showed that the two classes of procedures exhibit subtle but important differences in their performance in relation to the results from complete data analysis. Based on our theoretical predictions and the observed patterns, we provided a few practical recommendations and directions for future research.