Statistics and Its Interface

Volume 1 (2008)

Number 1

Auto-multicategorical regression model for the distribution of vegetation

Pages: 63 – 70



Fangliang He (Department of Renewable Resources, University of Alberta, Edmonton, Alberta, Canada)

Julie Zhou (Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., Canada)

Hongtu Zhu (Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, N.C., U.S.A.)


Modeling the contagious distribution of species has long been a challenging issue in ecology. Autologistic regression modeling has been a primary approach used to describe the spatially correlated distribution of single species on landscapes. Here we introduce a generalized auto multicategorical regression method to model the simultaneous distribution of multiple species. The auto multicategorical regression model includes the autologistic model as a special case. We develop a stochastic approximation algorithm for calculating the maximum likelihood estimates of parameters in the auto-multicategorical model. Based on the pseudo-likelihood likelihood function, we propose three model selection criteria for the selection of a ‘good’ model. A simulation study is carried out to examine the performance of the maximum likelihood estimation method and the three model selection criteria. An application of the model is provided through the analysis of the distribution of vegetation types in terms of climate variables in British Columbia, Canada.


auto-multicategorical regression, maximum likelihood, model selection, pseudolikelihood, stochastic approximation, vegetation

2010 Mathematics Subject Classification


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