Biadditive Mixed Models - Advancing Computational Methods and Applications

This thesis studies multiplicative models, also named biadditi ve models, which arise when one or more multiplicative terms are added to a linear ANOVA model. These models are especially popular within agriculture to analyze genotype- by-environment data, but they are also used in e.g. sensometrics to analyse sensory profile data or in medicine to analyse data from method comparison studies. In general, these models are relevant whenever an interaction between two factors is not completely unstructured, but can be described either fully or partly by a linear regression, where one of the variables in the multiplicative term can be interpreted as the regressor and the other variable as the slope.

The main focus in this thesis is on a specific version of t he multiplicative mixed models, which is particularly difficult to e stimate. One main goal of this work was to develop a user - friendly open- source software tool to fit this kind of models. For this purpose, R - package mumm was created, which is now available on CRAN. The thesis demonstrates how to use the package, which was found to be faster than the commercial alternative. Another aim of this thesis was to investigate the advantages obtained by using the multiplicative mixed model, instead of a simple linear mixed ANOVA model. By simulation studies, it was demonstrated that the pow er to detect significant effect s in the data increases by using a multiplicative mixed model instead of a two- way mixed ANOVA model, when the ''multiplicative effect'' is present in the data. The performance of the multiplicative mixed model was also compared to the performance of a linear approximation of the model.

Further, the thesis gives an overview of the different biadditive (mixed) model versions, including a literature review and a description of their applications. Finally, it was demo nstrated how these models can be estimated by the R - package TMB (Template Model Builder).