AAU Institutional Repository

Rank-Based Directional Test in k-Sample Multivariate Problems

Show simple item record

dc.contributor.advisor Wencheko, Eshetu (Professor)
dc.contributor.advisor Bathke, Arne C. (Professor)
dc.contributor.author Kassahun, Taddesse
dc.date.accessioned 2021-11-23T10:52:23Z
dc.date.available 2021-11-23T10:52:23Z
dc.date.issued 2021-07-01
dc.identifier.uri http://etd.aau.edu.et/handle/123456789/28906
dc.description.abstract Data from several response variables, potentially measured on different scales, occur naturally in various practical settings such as clinical trials. Treatment differences with respect to these response variables are usually analyzed using parametric methods under the assumptions of multivariate normality and covariance homogeneity. In many situations, however, these assumptions are not fulfilled, in particular when the response variables under consideration are ordered categorical. Thus, a rankbased (nonparametric) approach which disregards the above assumptions is desirable. More importantly, an investigator may be interested to test a global hypothesis of no treatment difference versus the alternative that treatment effects are monotonically increasing (decreasing) with respect to all responses. A number of studies have been conducted to address the issue of testing directional alternatives in two or more multivariate samples both in the parametric as well as nonparametric framework. Given that the response variables are measured in a mix of metric and ordered categorical scales, the parametric methods are not suitable. In turn, most of the contributions in the area of nonparametric statistics base their inferences on several pairwise comparisons of treatments in such a way that the ranks are being computed pairwise only, that is, only between those two levels that are compared at each step. This reduces the amount of available information and is well known to potentially lead to paradoxical situations. In order to incorporate more information from multivariate data for testing directional hypotheses which involve variables measured both in metric as well as ordered categorical scales in a unified manner we propose a new rank-based test statistic. The statistic we have derived is a multivariate generalization based on a coordinate-wise approach of a univariate test statistic proposed by Bathke (2009) for alternative patterns within a nonparametric framework. Separate ranking for different variables is employed in order to ensure invariance under monotone transformations of the responses as well as the weights describing alternative patters. Unlike most methods available in the literature, the newly introduced test handles data with ties, in particular, ordered categorical data as the underlying distribution is not required to be continuous. The test statistic introduced in this dissertation is proved to be accurate in detecting pre-specified equi-directional alternative patterns across two or more multivariate samples trough extensive simulation studies. A comparison is also made with that of the rank-sum type test for directional multivariate problems proposed by O’Brien (1984) in which the newly developed test is in par and sometimes better than the test by O’Brien. Applications to several datasets obtained from clinical trials are presented and potential extensions in different directions are discussed. The other more interesting practical issue in directional multivariate problems is to test conjectured alternative patterns in which treatments effects are monotonically increasing for some of the responses and monotonically decreasing for others. So long as treatment effects can be specified on a priori basis, we suggest interchanging the signs of different responses and making the anticipated direction of treatment effects similar. Following this, we employ the newly developed test statistic to test treatment effects in opposite directions in two or more multivariate samples. Furthermore, we employ the closed testing principle in conjunction with the test we have proposed in order to identify on which specific responses or sets of responses the effects are actually observed. An application of this procedure is demonstrated by re-analyzing a dose-response dataset. In summary, the test developed in this dissertation can handle monotone trends based on a complete case multivariate data. Developing a test statistic which can handle umbrella alternatives, and/or incomplete cases is differed to future research. en_US
dc.language.iso en en_US
dc.publisher Addis Ababa University en_US
dc.subject Rank-Based en_US
dc.subject Directional Test en_US
dc.subject k-Sample en_US
dc.subject Multivariate Problems en_US
dc.title Rank-Based Directional Test in k-Sample Multivariate Problems en_US
dc.type Thesis en_US


Files in this item

This item appears in the following Collection(s)

Show simple item record

Search AAU-ETD


Browse

My Account