"A New Residual for Ordinal Outcomes and a New Test of Association for Ordinal Predictors "
Bryan E. Shepherd, Ph.D., Vanderbilt University School of Medicine
April 12, 2011 @ 3:30 - 4:30 pm
Location: Room 701 Blockley Hall
Biostatistics
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.
