ORDINARY LEAST SQUARES REGRESSION OF ORDERED CATEGORICAL DATA: INFERENTIAL IMPLICATIONS FOR PRACTICE

Abstract

Ordered categorical responses (OCRs) are frequently encountered in many disciplines. Examples of interest in agriculture include quality assessments, such as for soil or food products, and evaluation of lesion severity, such as teat ends status in dairy cattle. OCRs are characterized by multiple categories recorded on a ranked scale that, while apprising relative order, is not informative of absolute magnitude of or proportionality between the categories. A number of statistically sound models for OCRs are available in the statistical literature, such as logistic regression and probit models, but these are commonly underutilized in practice. Instead, the ordinary least squares linear regression (OLSLR) model is often employed despite violation of basic model assumptions. In this study, the inferential implications of OLSLR-based inference on OCRs were investigated using a simulation study that evaluated realized Type I error rate and empirical statistical power. The design of the simulation study was motivated by applications reported in the subject-matter literature. A variety of plausible scenarios were considered for simulation, including various shapes of the frequency distribution and number of categories of the OCR. Using survey data on frequency of antimicrobial use in cattle feedlots, we illustrated the inferential performance of OLSLR on OCRs relative to a probit model.