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

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.     

A new procedure to optimize the selection of groups in a classification tree: Applications for ecological data

Agglomerative cluster analyses encompass many techniques, which have been widely used in various fields of science. In biology, and specifically ecology, datasets are generally highly variable and may contain outliers, which increase the difficulty to identify the number of clusters. Here we present a new criterion to determine statistically the optimal level of partition in a classification tree. The criterion robustness is tested against perturbated data (outliers) using an observation or variable with values randomly generated. The technique, called Random Simulation Test (RST), is tested on (1) the well-known Iris dataset [Fisher, R.A., 1936. The use of multiple measurements in taxonomic problems. Ann. Eugenic. 7, 179–188], (2) simulated data with predetermined numbers of clusters following Milligan and Cooper [Milligan, G.W., Cooper, M.C., 1985. An examination of procedures for determining the number of clusters in a data set. Psychometrika 50, 159–179] and finally (3) is applied on real copepod communities data previously analyzed in Beaugrand et al. [Beaugrand, G., Ibanez, F., Lindley, J.A., Reid, P.C., 2002. Diversity of calanoid copepods in the North Atlantic and adjacent seas: species associations and biogeography. Mar. Ecol. Prog. Ser. 232, 179–195]. The technique is compared to several standard techniques. RST performed generally better than existing algorithms on simulated data and proved to be especially efficient with highly variable datasets.