Ordinary Least Squares Regression of Ordered Categorical Data: Inferential Implications for Practice
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Ordered categorical variables are frequently encountered as response variables in many disciplines. Agricultural examples include quality assessments of soil or food products, and evaluation of lesion severity, such as teat ends status in dairy cattle. Ordered categorical responses (OCR) are characterized by multiple levels recorded on a ranked scale, whereby levels appraise order but may not be informative of relative magnitude or proportionality between levels. A number of statistically sound methods are available in the standard toolbox to deal with OCR, such as constrained cumulative logit and probit models; however, these are commonly underutilized in practice. Instead, ordinary least squares linear regression (OLSLR) is often employed to infer upon OCR, despite violation of basic model assumptions. In this study, we investigate the inferential implications of OLSLR-based inference on OCR using simulated data to explore realized Type I error rate and realized statistical power under a variety of scenarios. The design of the simulation study was motivated by a data application, thus considering increasing number of levels and various frequency distributions of the OCR. We then illustrate inferential performance of OLSLR relative to a probit regression model fitted to an OCR using a survey dataset of veterinarian antimicrobial use in cattle feedlots. This article has supplementary material online.
Key WordsType I error Statistical power Violation of assumptions
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