Rank-Based Approach for Mixed Effects Hierarchical Models in Nested Designs

• Activity Number: 525
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yusuf K. Bilgic*+ and Joseph McKean
• Companies: Western Michigan University and Western Michigan University
• Keywords: Rank-based analysis ; Mixed Hierarchical Model ; Nested Design ; Educational Research

Abstract

Hierarchical designs frequently occur in many areas. The experimental design of interest is expressed in terms of fixed effects but, for these designs, nested factors are a natural part of the experiment. These nested effects are generally considered random and must be taken into account in the statistical analysis. In many of the applications that we have considered outliers frequently occur. Traditional analyses are quite sensitive to these outliers and lose considerable power to detect the fixed effects of interest. We offer two new rank-based algorithms, Rank Prediction Procedure (RPP) and Iterative Generalized Rank Estimation Procedure (IGREP), which iteratively obtain robust estimation for both the fixed and random effects. We present the results of a small sample investigation of these analyses, including a comparison with traditional analyses.