Descriptive and Inferential Aspects of Ordinal Multiple Regression

Abstract

This paper discusses the ordinal multiple regression (OMR) method of Cliff (1994, 1996) and the development of a confidence interval (CI) for population regression weights. First, the OMR methodology is presented along with a discussion of the differences between OMR and least squares multiple regression (LSMR). Next, it is shown how a confidence interval (CI) for a population predictor weight can be derived. The OMR CI is based on an estimated standard deviation of a weight derived from a fixed effects model. Finally, the sampling properties of the OMR CI are discussed. It is pointed out that the OMR CI is more robust than the LSMR CI to predictor correlations and violations of assumptions. The OMR CI is recommended when a researcher wants to consider only ordinal information in multivariate prediction, and/or when predictor correlations are moderate to high, and/or when the assumptions of fixed effects LSMR are violated.