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Using Binary Logistic Regression Models for Ordinal Data with Non-proportional Odds

  • Ralf Bender
    Correspondence
    Address for correspondence: Ralf Bender, Ph.D., Department of Metabolic Diseases and Nutrition, Heinrich-Heine-University of Düsseldorf, P.O. Box 101007, D-40001, Düsseldorf, Germany
    Affiliations
    Department of Metabolic Diseases and Nutrition, Heinrich-Heine-University of Düsseldorf, Düsseldorf, Germany
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  • Ulrich Grouven
    Affiliations
    Department of Anesthesiology, Research Group Informatics and Biometry, Hannover Medical School, Hospital Oststadt, Hannover, Germany
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      Abstract

      The proportional odds model (POM) is the most popular logistic regression model for analyzing ordinal response variables. However, violation of the main model assumption can lead to invalid results. This is demonstrated by application of this method to data of a study investigating the effect of smoking on diabetic retinopathy. Since the proportional odds assumption is not fulfilled, separate binary logistic regression models are used for dichotomized response variables based upon cumulative probabilities. This approach is compared with polytomous logistic regression and the partial proportional odds model. The separate binary logistic regression approach is slightly less efficient than a joint model for the ordinal response. However, model building, investigating goodness-of-fit, and interpretation of the results is much easier for binary responses. The careful application of separate binary logistic regressions represents a simple and adequate tool to analyze ordinal data with non-proportional odds.

      Keywords

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