Maximum likelihood estimation and multiple imputation: A Monte Carlo comparison of modern missing data techniques for multilevel data

Date of Completion

January 2008


Statistics|Education, Educational Psychology




This Monte Carlo study examined the relative performance of four missing data treatment (MDT) approaches applied to incomplete cross-sectional hierarchical data: maximum likelihood (ML) estimation, multiple imputation under a normal model (MI/NM), multiple imputation under a linear mixed model (MI/LMM), and listwise deletion (LD). One thousand replications of each of three missing data (MD) conditions were simulated; data missing on the outcome variable at rates of 10%, 30%, and 50%. The data sets, each containing 1,000 cases nested within 20 level-2 units, were analyzed as two-level data in M plus Version 5 using each of the four MDTs, for a 4 x 3 design. Parameter estimation accuracy, efficiency and bias as well as parameter coverage and model convergence were compared within and across MDTs and rates of missing data. Results showed that MDTs performed similarly in the estimation of fixed effects with only 10% missing data, however estimates of σ2 and τ00 under the MI/NM condition were substantially more biased than with other MDTs. This MDT performed the least well overall, underestimating the level-2 intercept variance and overestimating the error variance at level 1. ML and LD performed remarkably similarly on most indices, and provided accurate, efficient, and unbiased estimates of most parameters. However, MI/LMM outperformed other MDTs in the estimation of parameters measured on substantially smaller scales than other parameters in the model, and performed similarly well in terms of estimation accuracy and efficiency for all other parameters. ML and LD provided the least biased estimates overall whereas the MI conditions had the fewest convergence failures. ML provided the best parameter coverage, with MI/LMM performing similarly well on that measure. LD tended to underestimate standard errors of estimates, resulting in the poor parameter coverage. The implications of results are summarized and suggestions are proposed for the selection of appropriate MDTs under specific conditions. Limitations of the study are discussed and areas for future research are recommended. ^