Spatial multinomial regression models for nominal categorical data: a study of land cover in Northern Wisconsin, USA

We develop statistical tools for regression analysis of nominal categorical data on a spatial lattice that are becoming increasingly abundant because of the advances of geographic information systems in environmental science. In a generalized linear mixed model framework, we model the response variable by a multinomial distribution. There are two additive components in the linear predictor: a linear regression on covariates and a spatial random effect such that the spatial dependence in the random effect is induced by a multivariate conditional autoregressive model. Bayesian hierarchical modeling is used for statistical inference, and Markov chain Monte Carlo algorithms are devised to obtain posterior samples. The methodology is applied to analyze a northern Wisconsin land cover data set in a study that assesses the relationship between forest landscape structure and past social conditions, expanding the analytical tools available in landscape ecology and environmental history.