## Colloquium: September 22, Lloyd Edwards, UAB

- Details
- Category: 2017-2018

Lloyd J. Edwards, PhD, Charles R. Katholi, PhD, Byron C. Jaeger, PhD

UAB Department of Biostatistics

Title: Properties of $R^2_\beta$ and Tests of Hypotheses for Fixed Effects in the Linear Mixed Model

Abstract:

Properties of the $R^2$ statistic used in linear regression with least squares estimation are well developed. Additionally, the $R^2$ statistic used in linear regression has a corresponding test of hypoyhesis associated with it. Similar properties are developed for $R^2_\beta$, an $R^2$ statistic for fixed effects in the linear mixed model. The central and non-central Beta distributions are used to approximate the distribution of $R^2_\beta$ under corresponding null and alternative test hypotheses. The asymptotic expectation and variance of $R^2_\beta$ are derived. Simulations are used to demonstrate the performance of the Beta approximation. Test statistics are proposed that are based on estimators of the derived expectation and variance. Simulations are used to compare the test statistics to the overall $F$ test for fixed affects in the linear mixed model. Using simulations, the Type I error rate of the proposed $R^2_\beta$ test statistics is shown to be equivalent to the Type I error rate for the overall $F$ test.

## News 2017

- Details
- Category: News

- Fast-track student
**Garrett Higginbotham**won an Alabama Space Grant Scholarship Award for FY2017-18. Congratulations! - Fast-track student
**Kenneth Davis**won a*Benjamin A. Gilman International Scholarship*sponsored by the US State Department and a*Freeman-ASIA Scholarship*sponsored by the Freeman Foundation. Kenneth will use these to study in Japan. Congratulations! - On March 24
**Ivan Mann**successfully defended his Ph.D. thesis*A Metrically Defined Uniformization Map of Planar Domains*. His studies were directed by Dr. L. Oversteegen. - Former Fast-track student
**Rachel Ejem**(now**Anthonia Carter**) has been selected for a Fulbright award to the United Kingdom. She will study Multidisciplinary Innovation in Newcastle upon Tyne. Congratulations. **Elizabeth Scribner**won one of three College of Arts and Sciences’ 2017 Dean's Awards on the Graduate level. Congratulations.