Loss of Power in Logistic, Ordinal Logistic, and Probit Regression When an Outcome Variable Is Coarsely Categorized

Abstract

Variables that have been coarsely categorized into a small number of ordered categories are often modeled as outcome variables in psychological research. The authors employ a Monte Carlo study to investigate the effects of this coarse categorization of dependent variables on power to detect true effects using three classes of regression models: ordinary least squares (OLS) regression, ordinal logistic regression, and ordinal probit regression. Both the loss of power and the increase in required sample size to regain the lost power are estimated. The loss of power and required sample size increase were substantial under conditions in which the coarsely categorized variable is highly skewed, has few categories (e.g., 2, 3), or both. Ordinal logistic and ordinal probit regression protect marginally better against power loss than does OLS regression.