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@PHDTHESIS{Espendiller:688951,
author = {Espendiller, Michael},
othercontributors = {Kateri, Maria and Kamps, Udo},
title = {{A}ssociation in contingency tables : an
informationtheoretic approach},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
reportid = {RWTH-2017-04133},
pages = {1 Online-Ressource (iv, 221 Seiten) : Illustrationen},
year = {2017},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University; Dissertation, RWTH Aachen University, 2017},
abstract = {This Ph.D. thesis deals with one of the fundamental
problems of categorical data analysis, namely that of
measuring the association between categorical variables,
cross-classified in a two-way table. Such tables occur in
many scientific fields such as economics, social and
biomedical sciences. Although a sensitive and more
informative analysis is provided through adequate models,
which constitute a basic and flexible tool, their
implementation and interpretation often require advanced
model fitting procedures and statistical software skills
that can be too complex for practitioners. Association
measures provide a convenient alternative offering a compact
identification and overall quantification of underlying
association. They are easy to understand and interpret. This
thesis develops new association measures for 2 x 2 tables
based on the phi-divergence by generalising the most
fundamental measure of association, the odds ratio. The
adopted approach is motivated by an extensive study on
continuity corrections and confidence interval construction
techniques, which are approaches for dealing with the
problems caused by sampling zeros, i.e. cells with observed
zero frequencies. Sampling zeros may lead to infinite
estimates of the log-odds ratio and prohibit the use of
asymptotic inferential methods due to infinite asymptotic
variance estimates. The newly introduced measure, the
phiscaled odds ratio, aims at solving these deficiencies by
using a phi-divergence induced scale change. A scale change
can improve the compatibility with sampling zeros and can --
in some set-ups -- lead to better Wald confidence intervals
for the phi-scaled odds ratios with respect to their
coverage probability and average relative length. A scalar
measure can often be misleading in I x J tables when the
association structure is more complex and cannot be
described by a single parameter. The classical generalised
odds ratios are naturally linked to parameters of
association models. This close connection is used to
construct new non-scalar measures of association. These
measures are more informative since they inherit the
increased sensibility of models and offer more options to
cover association structures without losing the easy
interpretability. Closed-form estimators for these
model-based measures are introduced which are close to the
maximum likelihood estimators, which have to be computed
iteratively. A scale change can lead to more adequate
measures. Therefore, this model-based approach is extended
using the phi-divergence by providing and studying new
generalised phi-scaled odds ratios for I x J tables. They
are linked to a new phi-scaled association model, the
generalised phi-linear model, and thus provide a phi-scaled
extension of the modelbased measures for which closed-form
estimators are also developed. I x I square tables with
commensurable classification variables are of special
interest, e.g. in social mobility studies to value the
permeability of economical systems. Such tables can be
analysed with symmetry models. The already existing
phi-scaled symmetry models form the basis to develop a
phiscaled asymmetry measure. Thus, a new family of directed
asymmetry measures is introduced along with new phi-scaled
versions of the standard symmetry tests of McNemar and
Bowker. The main contribution of this work is the
exploration and signalisation of the great flexibility of
phi-divergence based categorical data measures, thus paving
the way for further research, among others, on small-sized
multi-way tables, which are naturally confronted with the
presence of sampling zeros.},
cin = {116510 / 110000},
ddc = {510},
cid = {$I:(DE-82)116510_20140620$ / $I:(DE-82)110000_20140620$},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2017-04133},
url = {https://publications.rwth-aachen.de/record/688951},
}
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