Iteratively Reweighted Generalized Rank-Based Method in Mixed Models

• Activity Number: 352
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yusuf Bilgic*+ and Joseph McKean
• Companies: SUNY-Geneseo and Western Michigan University
• Keywords: Mixed-models ; Rank-based ; Hierarchical models ; Nested-Random-Effects ; Generalized ; Robust

Abstract

This work proposes a rank-based fitting method for handling random, fixed and scale effects in the general mixed models. A new algorithm, which iteratively obtains robust prediction for both scale and random effects, is used along with an iteratively re-weighted generalized rank-based estimate (GR) of the fixed effects. For simplicity, a two- and three-level hierarchical model (nested designs) is discussed but this can easily be generalized for any degree of nesting. The asymptotic derivations for the proposed estimators are discussed. The results of a Monte Carlo evaluation of the methods, including comparisons with the traditional analysis are provided. The proposed methods compete with the traditional method under normal case and outperform it when random errors and/or random effects have contaminated distributions. Our study shows that the rank-based estimates of the intra- and inter-class correlation estimates remain almost unbiased in the presence of contamination, while the REML estimates are biased. Also, a real data example illustrates these robustness properties of the proposed estimators and algorithm.