| Bayesian Models for Ordered Categorical Spatial Data and Categorical Habitat Data
Megan Dailey Higgs
Ph.D. Candidate, Department of Statistics
Colorado State University
Thursday, September 28, 2006
The collection of ecological and environmental data often results in categorical response variables that are correlated across space and/or time. While many models and methods exist for incorporating such spatial and/or temporal dependence into models for continuous responses, such models are sparser for point-referenced categorical data, and especially for ordered categorical data. We propose a spatial model for ordered categorical data, and estimate parameters within a Bayesian framework using Markov chain Monte Carlo (MCMC) methods. The ordinal categorical portion of the model relies on a latent continuous variable, along with a vector of cut points, as proposed by Albert and Chib (1993). The spatial dependence is introduced through a latent mean zero stationary Gaussian process, as described by Diggle, Tawn, and Moyeed (1998). We apply the model to simulated data and to EPA collected data for stream substrate size. In many cases, spatial data sets can be large, resulting in computational challenges due to matrix inversion and rounding errors. Thus, we explore other computational methods such as importance sampling and spectral parameterization of the spatial process. We also present a model for use with data collected in animal habitat selection studies using radio telemetry. Such categorical data consist of a sequence of observed habitat types. We extend a model proposed by Ramsey and Usner (2003) to further relax the assumption of independent animal relocations across time. We use a Bayesian approach that allows for the habitat selection probabilities, a persistence parameter, or both, to change with season. These extensions are particularly important when movement patterns are expected to differ seasonally and/or when availabilities of habitats change throughout the study period. We implement this model using radio telemetry data for westslope cutthroat trout.