Tuesday 18 December, 2018 at 10:00, The Technical University of Denmark, Richard Petersens Plads, Building 324, room 240
Principal supervisor: Professor and Head of Department, Per Bruun Brockhoff
Co supervisor: Associate Professor Murat Kulahci
Co supervisor: Senior Researcher Kasper Kristensen
Examiners:
Associate Professor Line Harder Clemmensen, DTU Compute, DTU
Professor Claus Thorn Ekstrøm, University of Copenhagen
Director of Research Pascal Schlich, INRA, France
Chairperson at defence:
Associate Professor Anders Stockmarr, DTU Compute
Summary:
Analysis of Variance (ANOVA) is widely used to analyze data in most scientific areas.
However, the standard linear ANOVA models are not always adequate to describe the
structures in a data set sufficiently. This means that an improved insight
and inference might
be obtained by extending the linear ANOVA models.
This thesis studies
multiplicative models
, also named biadditive 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 the multiplicative mixed models, which
is particularly difficult to estimate.
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 power to detect significant effects 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).
READ MORE at orbit.dtu.dk
A copy of the PhD thesis is available for reading at the department
Everyone is welcome.