Date of Award

6-2012

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Joseph W. McKean

Second Advisor

Jeffrey Terpstra

Third Advisor

Jung C. Wang

Fourth Advisor

Jon Davis

Abstract

Hierarchical designs frequently occur in many research 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. Traditional analyses are quite sensitive to outliers and lose considerable power to detect the fixed effects of interest.

This work proposes three rank-based fitting methods for handling random, fixed and scale effects in k-level nested designs for estimation and inference. An algorithm, which iteratively obtains robust prediction for both scale and random effects, is used along with the proposed fitting methods including Joint Ranking (JR), Iteratively Reweighted Generalized Rank Estimate (GR), and Rank-based General Estimating Equation (GEER). For simplicity, a 3-level nested design that deals with students nested within sections in schools is handled. 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, outperform it when random errors are contaminated, and inherit better efficiency properties of the estimates when outlier exists. The performance of the rank-based estimators of fixed parameters is more efficient than the REML. When random errors are contaminated, the intra-class correlation estimates in the proposed algorithm are unbiased, while the REML estimates are biased. Also, real data examples of applications are presented.

Access Setting

Dissertation-Open Access

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