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.
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