Treatment of missing data at the second level of hierarchical linear models

This research was a Monte Carlo investigation of the performance of five missing data treatments applied to data having a hierarchical structure. Data were generated to simulate the 1982 High School and Beyond data set. The number of level-2 variables, level-2 sample size, level-1 intercept-slope correlation, and the percent of missing data were included as study conditions. The five missing data treatments evaluated were listwise deletion, overall mean substitution, group mean substitution, the EM algorithm, and multiple imputation. Data were randomly deleted from one level-2 variable under each condition. The estimates of regression weight for the fixed effects and the estimates for the random effects produced after the application of each missing data treatment were compared to the estimates obtained from the complete data set.;The results indicate that listwise deletion, group mean substitution, and the EM algorithm perform equally well in the context of estimating the regression weight for the variable having missing values. The application of overall mean substitution and multiple imputation yielded an underestimated regression weight for this variable. For the variables having no missing data, the application of listwise deletion and the EM algorithm resulted in estimates of regression weight that were not statistically different than the complete data estimates. The application of overall mean substitution and multiple imputation resulted in estimates of regression weights for these variables that were both statistically different from the complete data estimates and of practical importance. The results for group mean substitution were inconsistent. For some conditions the application of group mean substitution resulted in regression weight estimates that were consistent with the complete data estimates. For other conditions, the missing data treatment yielded estimates that were statistically different from the estimates produced with complete data.;All of the imputation procedures (overall mean substitution, group mean substitution, the EM algorithm, and multiple imputation) produced distorted estimates for the random effects. Listwise deletion performed well in estimating the random effects except when the level-2 sample size was 30 and 40% of the data were missing.