An Empirical Comparison of Regression Analysis Strategies with Discrete Ordinal Variables

Abstract

The Type I error control and statistical power of three tests of regression models incorporating discrete ordinal variables were compared in a Monte Carlo study. Samples were generated from populations measured on discrete ordinal variables representing 5-point and 7-point response scales. Each sample was analyzed using ordinary least squares regression, ordinal multiple regression and cumulative logit models. Factors examined in the Monte Carlo study were the population effect size, number of regressor variables, level of regressor intercorrelation, population distribution shape and sample size. Results suggest that the logistic regression approach evidenced poor Type I error control with small samples or with large numbers of regressors. In contrast, both the ordinary least squares approach and the ordinal multiple regression approach evidenced good Type I error control across the majority of conditions examined. Further, the power differences between these approaches were negligible.