Effects of Modeling the Heterogeneity on Inferences Drawn from Multilevel Designs

This article uses Monte Carlo techniques to examine the effect of heterogeneity of variance in multilevel analyses in terms of relative bias, coverage probability, and root mean square error (RMSE). For all simulated data sets, the parameters were estimated using the restricted maximum-likelihood (REML) method both assuming homogeneity and incorporating heterogeneity into multilevel models. We find that (a) the estimates for the fixed parameters are unbiased, but the associated standard errors are frequently biased when heterogeneity is ignored; by contrast, the standard errors of the fixed effects are almost always accurate when heterogeneity is considered; (b) the estimates for the random parameters are slightly overestimated; (c) both the homogeneous and heterogeneous models produce standard errors of the variance component estimates that are underestimated; however, taking heterogeneity into account, the REML-estimations give correct estimates of the standard errors at the lowest level and lead to less underestimated standard errors at the highest level; and (d) from the RMSE point of view, REML accounting for heterogeneity outperforms REML assuming homogeneity; a considerable improvement has been particularly detected for the fixed parameters. Based on this, we conclude that the solution presented can be uniformly adopted. We illustrate the process using a real dataset.