Harnessing a Latent Beta Distribution for Ordinal Regression with Application to Plant Cover Data

• Activity Number: 140
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Kathryn Irvine*+ and Ilai Keren and Thomas Rodhouse
• Companies: U.S. Geological Survey and Washington Department of Fish and Wildlife and National Park Service
• Keywords: Ordinal ; latent variable ; Beta distribution ; proportional odds model

Abstract

We develop an alternative model to the cumulative logit model with a dispersion parameter for analyzing discretized continuous data. The cumulative logit model can be motivated by relating the observed ordinal categories to a partition of a logistic random variable into adjacent non-overlapping intervals. In vegetation surveys, it is common to visually assess species cover within plots and record integer values representing cover classes. The continuous percent cover scale is a priori discretized into categories, i.e., Daubenmire cover classes. If continuous percent cover values were actually recorded, Beta regression could be used to analyze these data. However, plots are assigned an integer value; we argue that an ordinal model with a latent Beta distribution is more biologically meaningful for these data. Further this approach accommodates non-constant variance typical with ecological scenarios. We implement our model using JAGS with the rjags package in R which allows for Gibbs sampling from the latent variable's Beta distribution. We compare our model to more common ordinal models used in Ecology through simulation and a real data application.