Categorical structured additive regression for assessing habitat suitability in the spatial distribution of mussel seed abundance

Abstract

Categorical regression models enable the investigation of regression relationships between a polytomous response and a set of regressor variables. Depending on whether the categories are ordered or nominal, special categorical models such as cumulative and multinomial models have been proposed in the statistical literature. In this paper, we compare various categorical structured additive regression (STAR) models for assessing habitat suitability in the spatial distribution of mussel seed abundance in the Galician coast (northwest Spain). STAR models allow us to include nonlinear effects of continuous covariates on the basis of penalized splines whereas spatial effects can be represented via a Markov random field. Inference is based on a mixed model representation that allows for the simultaneous estimation of regression coefficients and smoothing parameters. Although cumulative models may seem to be the most natural choice in our application because of the ordinal nature of the response, multinomial models provide more detailed information on covariate effects as all effects are allowed to depend on the different categories of mussel seed abundance. The statistical procedures based on STAR models proved very useful in revealing valuable information towards the application of adequate management of this marine resource. Copyright © 2011 John Wiley & Sons, Ltd.