A Model and Diagnostic Tool for Evaluating Correlated Predictors

• Activity Number: 212
• Type: Contributed
• Date/Time: Tuesday, August 13, 2002 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section*
• Author(s): David Weitzenkamp*+
• Affiliation(s): Craig Hospital
• Keywords: collinearity ; correlation matrix ; correlated predictors ; variance inflation

Abstract

In regression analysis, correlation among the predictors inflates the confidence intervals of parameter estimates. By converting one or more of the continuous predictors into categorical predictors, using a series of dummy variables, it may be possible to alleviate some inflation of confidence intervals. One diagnostic for assessing collinearity, the determinant of the predictor correlation matrix, can be decomposed into three portions associated with: 1.) the unchanged predictors; 2.) the soon-to-be-changed predictors; and 3.) the relationships between the predictors in #1 and #2. As a diagnostic tool, it is proposed that quantity #3, rescaled to account for the differing number of parameters, is compared before and after the recategorization. The new model, if successful, reduces #3 without unduly increasing #2. This model and the new diagnostic are illustrated on a dataset with the correlated predictors of age and years post-spinal cord injury. Using this dataset, the new parameterization improves the collinearity and reduces the variance inflation in the unchanged predictor. The diagnostic tool proves useful in measuring this impact.