Ordinal Outcomes: Considerations for a Log Cumulative Probability Model Without a Proportionality Assumption

• Activity Number: 61 - Approaches for Modeling Clustered and Longitudinal Data
• Type: Contributed
• Date/Time: Monday, August 3, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Biometrics Section
• Author(s): Gurbakhshash Singh* and Gordon Hilton Fick
• Companies: Central Connecticut State University and University of Calgary
• Keywords: Cumulative Probability Model; Log Link ; Ordinal Outcomes; Uniqueness; Maximum Likelihood Estimate; Log Binomial Model

Abstract

There are many options available for the analysis of ordinal outcomes. The Proportional Odds Model (POM), based on the logit link, is widely used. Recently, a model comparable to the POM has been developed based on the log link, it is called the Proportional Probability Model (PPM). The PPM provides estimates of the log cumulative probabilities as opposed to the log cumulative odds. In this presentation, we will explore the log cumulative probability model (LCPM) which is again based on the log link but without the proportionality assumption. We present 1) results for the conditions for the uniqueness of the Maximum Likelihood Estimate (MLE), 2) results for some cases where closed form expressions for the MLE are available and 3) our R package, lcpm, which provides a comprehensive analysis of data with the LCPM and the PPM. We will conclude with a discussion of models based on dichotomizing ordinal outcomes. In particular, we compare the MLE from the LCPM with the MLEs from several log binomial models (LBMs). The LBMs are determined by dichotomizing the ordinal outcome at each cut.