A comparison of methods for estimating the random effects distribution of a linear mixed model

This article reviews various recently suggested approaches to estimate the random effects distribution in a linear mixed model, i.e. (1) the smoothing by roughening approach of Shen and Louis,1 (2) the semi-non-parametric approach of Zhang and Davidian,2 (3) the heterogeneity model of Verbeke and Lesaffre 3 and (4) a flexible approach of Ghidey et al. 4 These four approaches are compared via an extensive simulation study. We conclude that for the considered cases, the approach of Ghidey et al. 4 often shows to have the smallest integrated mean squared error for estimating the random effects distribution. An analysis of a longitudinal dental data set illustrates the performance of the methods in a practical example.