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Multilevel models (MLMs) have proven themselves to be very useful in social science research, as data from a variety of sources is sampled such that individuals at level-1 are nested within clusters such as schools, hospitals, counseling centers, and business entities at level-2. MLMs using restricted maximum likelihood estimation (REML) provide researchers with accurate estimates of parameters and standard errors at all levels of the data when the assumption of normality is met, and outliers are not present in the sample. However, if outliers at either levels 1 or 2 occur, the parameter estimates and standard errors produced by REML can both be compromised.
Two estimation approaches for use when outliers are present have been proposed recently in the literature. Although the two methods, one based on ranks and the other on heavy tailed distributions of model errors, show promise, neither has heretofore been studied comprehensively across a wide variety of data conditions, nor have they been compared with one another.
Thus, the purpose of the current study was to compare the rank and heavy tailed based estimation techniques with one another, and with REML, in terms of their ability to estimate level-1 fixed effects, under a variety of data conditions. Results of the study revealed that the rank based and heavy tailed method provide less biased estimates than REML when outliers are present, and that the rank approaches yield smaller standard errors than the heavy tailed approach in the presence of outliers. Implications of these results are discussed.
