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

Studies on forest damage can generally not be carried out by common
regression models, mainly for two 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 neighborhood 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 GEE1 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 analyzing the
influence of covariates, that characterize the stand, on the damage
state of spruce.