Extending ordinal regression with a latent zero-augmented beta distribution

Ecological abundance data are often recorded on an ordinal scale in which the lowest
category represents species absence. One common example is when plant species cover
is visually assessedwithin bounded quadrats and then assigned to pre-defined cover class
categories.We present an ordinal beta hurdle model that directly models ordinal category
probabilitieswith a biologically realistic beta-distributed latent variable.Ahurdle-at-zero
model allows ecologists to explore distribution (absence) and abundance processes in an
integrated framework. This provides an alternative to cumulative link models when data
are inconsistent with the assumption that the odds ofmoving into a higher category are the
same for all categories (proportional odds). Graphical tools and a deviance information
criterion were developed to assess whether a hurdle-at-zero model should be used for
inferences rather than standard ordinal methods. Hurdle-at-zero and non-hurdle ordinal
models fit to vegetation cover class data produced substantially different conclusions.The
ordinal beta hurdle model yielded more precise parameter estimates than cumulative logit
models, although out-of-sample predictions were similar. The ordinal beta hurdle model
provides inferences directly on the latent biological variable of interest, percent cover,
and supports exploration of more realistic ecological patterns and processes through the
hurdle-at-zero or two-part specification.We provide JAGS code as an on-line supplement.
Supplementary materials accompanying this paper appear on-line.