Regression analysis of forest inventory data with time and space dependencies

In this paper the data of a forest health inventory are analyzed. Since 1983 the degree of defoliation, together with various explanatory variables (covariates) concerning stand, site, soil and weather, are recorded by the second of the two authors, in the forest district of Rothenbuch (Spessart, Bavaria). The focus is on the space and time dependencies of the data. The mutual relationship of space-time functions and the set of covariates is evaluated. For this we use generalized linear models (GLMs) for ordinal response variables and semiparametric estimation approaches. By using goodness-of-fit measures it turns out that (i) the contribution of space-time functions is quantitatively comparable with that of the set of covariates, (ii) the contribution of space-time functions is small compared with the contribution of a set of variables describing the last-year and neighboring response values. By applying appropriate residual methods a detailed analysis of the individual sites in the area can be carried out. This analysis reveals where the predictive power of the covariates fail to explain the observed defoliation.