"A New Residual for Ordinal Outcomes and a New Test of Association for Ordinal Predictors "
April 12, 2011 @ 3:30 - 4:30 pm
Bryan E. Shepherd, Ph.D., Vanderbilt University School of Medicine
Location: Room 701 Blockley Hall
TITLE: A New Residual for Ordinal Outcomes and a New Test of
Association for Ordinal Predictors
ABSTRACT: Standard regression models treat ordered categorical predictors as either continuous or categorical. The former approach requires assigning arbitrary numbers to ordinal categories; the latter ignores order information. We propose a new method for testing the association between ordinal predictors (X) and continuous, binary, or ordered categorical outcomes (Y), adjusting for covariates (Z). Our method tests the correlation between residuals of the regression of Y on Z and residuals of the regression of X on Z, using a new residual for ordinal variables. Under the null of independence between X and Y conditional on Z, our test statistics are asymptotically normal with mean 0 and estimable variance. Through simulations we show that our test statistics outperform standard regression approaches. We also show some of the nice properties of our new residual for ordinal variables and demonstrate its use in model diagnostics. We apply our methods to data from HIV-infected women in Zambia.