Rlme: An R Package for Rank-Based Estimation and Prediction in Random Effects Nested Models

Abstract

There is a lack of robust statistical analyses for random effects linear models. In practice, statistical analyses, including estimation, prediction and inference, are not reliable when data are unbalanced, of small size, contain outliers, or not normally distributed. It is fortunate that rank-based regression analysis is a robust nonparametric alternative to likelihood and least squares analysis. We propose an R package that calculates rank-based statistical analyses for two- and three-level random effects nested designs. In this package, a new algorithm which recursively obtains robust predictions for both scale and random effects is used, along with three rank-based fitting methods. Rank-based procedures retain distribution-free estimation and testing properties. These procedures are much less sensitive to outliers than the traditional analyses when random errors are not normally distributed. Alternative robust score functions can be accommodated with the rank-based methods to protect analyses from influential observations in factor and response spaces. Also, the choice of these score functions could depend on the prior knowledge on error distributions. The Wilcoxon score function is fairly efficient for moderate to heavy-tailed error distributions. For example, rank-based procedures with Wilcoxon scores achieve up to 95% efficiency relative to least squares methods when the data are normal and are much more efficient than least squares methods for heavy tailed error distributions. These properties make the rank-based methods appealing. However, to our knowledge, statistical analyses for random effects models using the rank-based methodology have not yet been considered in any statistical package. This article proposes an R package with three rank-based fitting methods that estimate fixed effects and predict random effects in two- and three-level random effects nested models. The rank-based norm, analogous to the least squares norm, is briefly defined as