Regression analysis of forest damage by marginal models for correlated ordinal responses

Abstract

Studies on forest damage generally cannot be carried out by common regression models, for two main reasons: Firstly, the response variable, damage state of trees, is usually observed in ordered categories. Secondly, responses are often correlated, either serially, as in a longitudinal study, or spatially, as in the application of this paper, where neighbourhood interactions exist between damage states of spruces determined from aerial pictures. Thus so-called marginal regression models for ordinal responses, taking into account dependence among observations, are appropriate for correct inference. To this end we extend the binary models of Liang and Zeger (1986) and develop an ordinal GEEI model, based on parametrizing association by global cross-ratios. The methods are applied to data from a survey conducted in Southern Germany. Due to the survey design, responses must be assumed to be spatially correlated. The results show that the proposed ordinal marginal regression models provide appropriate tools for analysing the influence of covariates, that characterize the stand, on the damage state of spruce.