A Comparison of Estimation Methods when an Interaction is Omitted from a Multilevel Model

One of the sources of inaccuracy in parameter estimates of multilevel models is omitted variable bias, caused by the omission of an important predictor. The purpose of this study was to examine the performance of six estimation procedures in estimating the fixed effects when a level-2 interaction term was omitted from a two-level hierarchical linear model. Four alternative estimators (FE, WLS1, WLS2, WLS3) based on the work of Frees (2001) and the Maximum Likelihood (FML, ReML) estimation methods were examined. Findings of the Monte Carlo study revealed that the FML and ReML methods were the least biased methods when a level-2 interaction was omitted from the multilevel model. FML and ReML produced the lowest RMSD values of all six estimation methods regardless of level-2 sample size, ICC, or effect sizes of the level-2 variables. The difference in the performance of the alternative and Maximum Likelihood (ML) procedures diminished as level-2 sample size and ICC increased. The bias in all six estimation methods did not differ much when the effect sizes of the level-2 predictors varied. When the methods were examined using the ECLS data, the results of the Monte Carlo study were confirmed. The ML methods were the least biased of all the methods when a level-2 interaction term was omitted from the model.