# aggDefol ~ ph + depth + watermoisture + alkali + humus + type + Summarises the response variable in a table.Convert the categorical variables to factors.This is converted to a numeric variable for modelling, Aggregates the defoliation data into an ordered categorical variable for low, medium, or high levels of defoliation.Makes a nicer stand label so that we can sort stands numerically even though the id is character,.The data require a little processing to ensure they are correctly coded. Head(forest) # id year defol x y age canopyd gradient alt depth ph watermoisture Springer.įorest <- read.table( "./data/forest-health/beech.raw", header = TRUE, na.strings = ".") The data are extensively analysed in Fahrmeir, Kneib, Lang, and Marx (2013) Regression: Models, Methods and Applications. The aim of the example is to investigate the effect of the measured covariates on the degree of defoliation and to quantify any temporal trend and spatial effect of geographic location in the data set, while adjusting for the effects of the other covariates. humus thickness of the soil humus layer in five categories.alkali - fraction of alkali ions in four categories.watermoisture - soil moisture in three categories.canopyd - canopy density at the location, in %.age - average age of trees at a location.x and y - the x- and y-coordinates of each location.The original classes were 0%, 12.5%, 37.5%, 50%, 62.5%, 75%, 87.5%, 100% and are in variable defol.Īlongside the response variable, a number of continuous and categorical covariates are recorded 50% – 100% defoliation, which is the "high" group.12.5% – 37.5% defoliation, which I refer to as the "med" group, and.0%, healthy trees that I’ll refer to as the "low" defoliation group.For the purposes of this example, several of the nine ordinal classes are merged to form a three class response variable of interest A defoliation value of 0% indicates a healthy beech tree, whilst a value of 100% indicates a tree is dead. Each year the condition of each of 83 trees is categorized into one of nine ordinal classes in terms of the degree (percentage) of defoliation. The project studies five species but here we just consider the beech data. The data come from a project n the forest of Rothenbuch, Germany, which has been ongoing since 1982. We can treat the individual trees as discrete spatial units and fit a spatial term using a special type of spline basis, a Markov random field. In this example, we look at a spatial data set of forest health data from a stand in Germany.
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