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E. Mair:
"Generalized linear models with compositional data";
Supervisor: P. Filzmoser; E105 Institut für Stochastik und Wirtschaftsmathematik, 2015; final examination: 2015-11-23.

In this diploma thesis generalized linear models are adapted to compositional data.
Compositional data describe the parts of some whole and carry only relative information.
They should not be used directly with generalized linear models as the interpretation of
the model can become misleading. The data need to be appropriately transformed. We
use the isometric logratio (ilr) transformation proposed by Hron et al. (2010, 2012). In
application of this special ilr transformation a meaningful interpretation of the unknown
parameters and the inference statistics is possible.
We implemented generalized linear models with compositional data sets in the statistical
software R. A model for binary data and a model for count data were adapted. We used a
compositional data set resulting from the GEMAS (Geochemical mapping of agricultural
and grazing land soils) project to investigate the difference in soil composition in northern
and southern Europe. Furthermore we used another compositional data set from the
project "Biogeochemical exploration of forests as a base for the long-term landscape
exploitation in the Czech Republic" to find a relation between traffic volume and chemical
composition of moss and thus model traffic induced pollution in Czech Republic.

compositional data isometric logratio transformation