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Doctoral Dissertation Announcement
Candidate: Gabriel A. Okyere
Doctor of Philosophy
Title: Robust Adaptive Scheme for Linear Mixed Models
Dr. Joseph McKean, Chair
Dr. Joshua Naranjo
Dr. Thomas Vidmar
Date: Thursday, May 19, 2011 1:00 p.m. to 3:00 p.m.
6625 Everett Tower
If the underlying distribution of a statistical model is known, then a procedure that maximizes power and efficiency can be selected. For example, if the distribution of errors is known to be normal in a linear model then inference based on least squares maximizes power and efficiency. More generally, if this distribution is known then a ranked-based inference based on the appropriate rank score function has maximum efficiency. In practice, this distribution is not known. Adaptive schemes are procedures that hopefully select appropriate methods to optimize the analysis.
Hogg (1974) presented an adaptive rank-based scheme for testing in the simple two-sample location model. It consists of a family of distribution free tests, each associated with a rank score function, and a selection procedure which chooses a test from this family. For continuous error distributions, Hogg’s scheme is valid for testing; it retains the level. This is not true for estimation and fitting. Little has been done to extend Hogg's scheme beyond simple location problems. In this research we extend Hogg’s adaptive scheme for testing to mixed models consisting of m clusters of observations.
This is an important practical family of models, including, for example, repeated measure designs, multi-center clinical designs, and randomized block designs. Under the assumption of exchangeable errors, we establish that our testing scheme is valid. In practice, for these models, fitting is crucial. Based on the fitting of a model a residual analysis can be performed to check quality of fit and to determine outliers. Further, standard errors of the estimates can then be obtained so that confidence intervals for contrasts of interests can readily be formed. With this in mind, the researcher has also developed several adaptive fitting schemes for these models. These are based on several types of rank-based estimation procedures, including joint ranking and multiple ranking types of fitting.
The schemes are robust and highly efficient. A large Monte Carlo study over error distributions ranging from heavy-tailed to light-tailed distributions and from symmetric distributions to skewed distributions gives empirical credence to our adaptive procedures. The research illustrates the procedures with several real clinical examples.