A New Residual for Ordinal Outcomes

• Activity Number: 667
• Type: Contributed
• Date/Time: Thursday, August 5, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Chun Li*+ and Bryan E. Shepherd
• Companies: Vanderbilt University and Vanderbilt University
• Keywords: Residuals ; Ordinal variable ; ordinal regression model diagnostics ; association between ordinal variables

Abstract

Ordinal categorical variables are common in medical and social research. Ordinal regression models allow us to study the effect of covariates on ordinal outcomes. We propose a new residual for ordinal outcomes. It is individual based, and each individual has a single residual irrespective of the number of categories of the outcome. We study its properties and describe its connections with other residuals. The new residual can be used in constructing test statistics and performing model diagnostics. When testing for association between two ordinal variables Y and X while adjusting for covariates Z, we can fit separate regression models of Y on Z and X on Z and construct test statistics using their residuals. We describe some properties of these statistics and their connections with tau, gamma, and rank correlation. We also demonstrate the use of the residual for model diagnostics.