Iteratively reweighted generalized rank-based methods for hierarchical mixed models
Yusuf K. Bilgic
SUNY Geneseo

A rank-based fitting method for handling random, fixed, and scale effects in the general mixed 20 model is developed. A new algorithm, which iteratively obtains robust prediction for both scale and random effects, is used along with an iteratively reweighted generalized rank-based estimate (GR - our method) of the fixed effects. The asymptotic theory for these GR estimates is devel- oped under regularity conditions. The discussion focuses on hierarchical, nested, designs but it can easily be generalized to general mixed models. The results of a Monte Carlo evaluation of 25 the methods, including comparisons with the traditional analysis, are provided. The proposed method is competitive with the traditional method under the ideal normal case (normal errors and random effects) but outperforms it when random errors and/or random effects have contam- inated distributions. The study shows that these procedures are valid over the situations of the study. Further, our study shows that the rank-based estimates of the intra- and inter-class corre- 30 lation estimates remain almost unbiased in the presence of contamination, while the traditional estimates are biased. A real data example illustrates the robustness properties of the proposed rank-based fitting method. With a simple weighting scheme based on robust distances, the these GR procedures can attain 50% breakdown.