Effect of correlation boundaries on collinearity and bias in ordinary least square regression

Authors

• Yumo Xue, University of Alabama at Birmingham

Advisor(s)

Jeff Szychowski

Committee Member(s)

Ashley Battarbee
Dustin Long
Hemant Tiwari
Mark Beasley

School

School of Public Health

Document Type

Dissertation

Department (new version)

Biostatistics

Date of Award

9-9-2024

Abstract

Linear regression (LM) stands as one of the prevailing methods used to assess the association between a dependent variable and independent variables, typically estimated using ordinary least squares. However, this approach frequently faces obstacles when applied to biomedical data, due to the issue of correlated independent variables (collinearity). Collinearity is a potential issue in observational studies, where researchers might omit less significant correlated variables from their model. This is often guided by the rule of thumb that a Variance Inflation Factor (VIF) of 10 indicates severe collinearity. Our hypothesis is that relying on this rule of thumb is arbitrary, and determining the significance of collinearity requires more considerations beyond a single threshold value. To examine the issue, we demonstrate that correlation boundaries exist to restrict the range of correlations, distinguishing it from the conventional interval of [-1, 1], thereby questioning the traditional guidance on using a general VIF to identify collinearity. We calculate the bias estimate in the presence of collinearity to determine the effect on regression parameters and carry out a simulation study. Our results indicate that the widely accepted VIF threshold of 10 is not a universally applicable criterion. Depending on the variables' correlations with the outcome and the sample size, the appropriate threshold should vary. We also evaluate the performance of various models designed to manage collinearity and confirm that ridge regression typically outperforms the others.

ProQuest ID

https://proquest.com/docview/3101841770