ASA Connect

Statistical modeling relies on correctly partitioning variation into between-group and within-group sources. But what happens when principal component analysis (PCA)—often used for dimensionality reduction—does not align with the actual inferential goals?

In this talk, we explore a common analytical pitfall: using PCA before group comparisons or classification, where selected principal components may contain little information for distinguishing groups.

Read the abstract below for more insight to the talk.

Date and Time: March 18th @ 6pm CST

Zoom link: https://stevens.zoom.us/j/92356532680

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 that are 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.

The talk title alludes to Terry Speed's column in the 2006 IMS Bulletin written by Terry Speed titled "Between and Within" in which he discusses his experiences working with researchers who use this approach to "post-variable reduction inference".