2024 Geisser Lecture

Between and Within: Redux

ABSTRACT

The partitioning of variation into appropriate between and within sources is central to statistical modeling and must be carefully done to avoid obscuring relevant data structure. Multivariate responses complicate this partitioning since the need to visualize data often leads to an initial variable reduction step using principal component analysis (PCA).  Unfortunately, this step in the analysis pipeline can have unintended consequences when the variable reduction does not align with the inferential goals. If the primary interest is to compare treatment groups or to develop a classification rule to distinguish groups, such as species of Arizona rattlesnakes, then the PC scores selected may contain little information to separate these groups. After encountering this data analytic strategy many times over the past 25 years and expecting this practice to become more common as massive data sets become more readily available, I have sought to better inform collaborators about both why and when alternative methods should be preferred. I will discuss some of my research to fill in gaps in the statistical literature about this approach and will contrast and compare this approach with a seemingly related method in which group comparisons are based on factor analytic scores. Examples will be given together with simulation and asymptotic results.

BIO

Edward J. Bedrick is a Professor of Biostatistics and Assistant Director of the Statistics Laboratory at the University of Arizona in Tucson. Previously, Ed was a faculty member at the University of Colorado and the University of New Mexico. He has extensive experience developing statistical methods and in the design and analysis of biomedical studies including cancer clinical trials. His current research and teaching focuses on Bayesian methods and linear models. Two current collaborative projects concern modeling degeneration of the knee and designing a clinical trial for Valley Fever. A native of New York City, Ed received his BA from SUNY at Buffalo and his PhD in 1984 from the University of Minnesota. He is a Fellow of the American Statistical Association and a Past-President of the Western North American Region of the International Biometric Society.