A Monte Carlo study of REML and robust rank-based analyses for the random intercept mixed model

ABSTRACT

Restricted maximum likelihood (REML) methods are traditionally used for analyzing mixed models. Based on a multivariate normal likelihood, these analyses are sensitive to outliers. Recently developed robust rank-based procedures offer a complete analysis of mixed model: estimation of fixed effects, standard errors, and estimation of variance components. The results of a large Monte Carlo study are presented, comparing these two analyses for many situations over multivariate normal and contaminated normal distributions. The rank-based analyses are much more powerful and efficient than the REML analyses over all non-normal situations, while losing little power for normal errors.

Keywords:

• Cluster correlated data
• Nonparametrics
• Wilcoxon procedures

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62G35
• Secondary 62j05

Acknowledgment

The authors would like to thank an anonymous referee for comments which clarified parts of this article.