Jelizarow, Monika (2015): Global tests of association for multivariate ordinal data: Knowledgebased statistical analysis strategies for studies using the international classification of functioning, disability and health (ICF). Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics 

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Abstract
Global tests are in demand whenever it is of interest to draw inferential conclusions about sets of variables as a whole. The present thesis attempts to develop such tests for the case of multivariate ordinal data in possibly highdimensional setups, and has primarily been motivated by research questions that arise from data collected by means of the 'International Classification of Functioning, Disability and Health'. The thesis essentially comprises two parts. In the first part two tests are discussed, each of which addresses one specific problem in the classical twogroup scenario. Since both are permutation tests, their validity relies on the condition that, under the null hypothesis, the joint distribution of the variables in the set to be tested is the same in both groups. Extensive simulation studies on the basis of the tests proposed suggest, however, that violations of this condition, from the purely practical viewpoint, do not automatically lead to invalid tests. Rather, twosample permutation tests' failure appears to depend on numerous parameters, such as the proportion between group sizes, the number of variables in the set of interest and, importantly, the test statistic used. In the second part two further tests are developed which both can be used to test for association, if desired after adjustment for certain covariates, between a set of ordinally scaled covariates and an outcome variable within the range of generalized linear models. The first test rests upon explicit assumptions on the distances between the covariates' categories, and is shown to be a proper generalization of the traditional CochranArmitage test to higher dimensions, covariateadjusted scenarios and generalized linear modelspecific outcomes. The second test in turn parametrizes these distances and thus keeps them flexible. Based on the tests' power properties, practical recommendations are provided on when to favour one or the other, and connections with the permutation tests from the first part of the thesis are pointed out. For illustration of the methods developed, data from two studies based on the 'International Classification of Functioning, Disability and Health' are analyzed. The results promise vast potential of the proposed tests in this data context and beyond.
Item Type:  Thesis (Dissertation, LMU Munich) 

Keywords:  generalized linear model, global test, international classification of functioning, disability and health (ICF), multivariate ordinal data, permutation test 
Subjects:  600 Natural sciences and mathematics 600 Natural sciences and mathematics > 510 Mathematics 
Faculties:  Faculty of Mathematics, Computer Science and Statistics 
Language:  English 
Date Accepted:  17. April 2015 
1. Referee:  Mansmann, Ulrich 
Persistent Identifier (URN):  urn:nbn:de:bvb:19182787 
MD5 Checksum of the PDFfile:  5f4d8a4d1ba8d54e678d1afe091ba8d7 
Signature of the printed copy:  0001/UMC 23129 
ID Code:  18278 
Deposited On:  13. Aug 2015 11:47 
Last Modified:  20. Jul 2016 10:39 