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Some properties of measures of disagreement and disorder in paired ordinal data
Örebro University, Swedish Business School at Örebro University.
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The measures studied in this thesis were a measure of disorder, D, and a measure of the individual part of the disagreement, the measure of relative rank variance, RV, proposed by Svensson in 1993. The measure of disorder is a useful measure of order consistency in paired assessments of scales with a different number of possible values. The measure of relative rank variance is a useful measure in evaluating reliability and for evaluating change in qualitative outcome variables.

In Paper I an overview of methods used in the analysis of dependent ordinal data and a comparison of the methods regarding the assumptions, specifications, applicability, and implications for use were made. In Paper II an application, and a comparison of the results of some standard models, tests, and measures to two different research problems were made. The sampling distribution of the measure of disorder was studied both analytically and by a simulation experiment in Paper III. The asymptotic normal distribution was shown by the theory of U-statistics and the simulation experiments for finite sample sizes and various amount of disorder showed that the sampling distribution was approximately normal for sample sizes of about 40 to 60 for moderate sizes of D and for smaller sample sizes for substantial sizes of D. The sampling distribution of the relative rank variance was studied in a simulation experiment in Paper IV. The simulation experiment showed that the sampling distribution was approximately normal for sample sizes of 60-100 for moderate size of RV, and for smaller sample sizes for substantial size of RV. In Paper V a procedure for inference regarding relative rank variances from two or more samples was proposed. Pair-wise comparison by jackknife technique for variance estimation and the use of normal distribution as approximation in inference for parameters in independent samples based on the results in Paper IV were demonstrated. Moreover, an application of Kruskal-Wallis test for independent samples and Friedman’s test for dependent samples were conducted.

Place, publisher, year, edition, pages
Örebro: Örebro university , 2010. , 38 p.
Series
Örebro Studies in Statistics, ISSN 1651-8608 ; 4
Keyword [en]
agreement, augmented ranks, categorical data, disorder, jackknife, paired ordinal data, rating scales, sample size, sampling distribution, simulation, U-statistics, variance
National Category
Social Sciences Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:oru:diva-12350ISBN: 978-91-7668-769-7 (print)OAI: oai:DiVA.org:oru-12350DiVA: diva2:359506
Public defence
2010-12-17, Örebro universitet, Hörsal M, Fakultetsgatan 1, Örebro, 13:15 (Swedish)
Opponent
Supervisors
Projects
Statistical methods for ordinal data
Available from: 2010-10-28 Created: 2010-10-28 Last updated: 2011-04-21Bibliographically approved
List of papers
1. An overview of methods in the analysis of dependent ordered categorical data: assumptions and implications
Open this publication in new window or tab >>An overview of methods in the analysis of dependent ordered categorical data: assumptions and implications
2008 (English)Report (Other academic)
Abstract [en]

Subjective assessments of pain, quality of life, ability etc. measured by rating scales and questionnaires are common in clinical research. The resulting responses are categorical with an ordered structure and the statistical methods must take account of this type of data structure. In this paper we give an overview of methods for analysis of dependent ordered categorical data and a comparison of standard models and measures with nonparametric augmented rank measures proposed by Svensson. We focus on assumptions and issues behind model specifications and data as well as implications of the methods. First we summarise some fundamental models for categorical data and two main approaches for repeated ordinal data; marginal and cluster-specific models. We then describe models and measures for application in agreement studies and finally give a summary of the approach of Svensson. The paper concludes with a summary of important aspects.

Place, publisher, year, edition, pages
Örebro: Örebro universitet, 2008. 33 p.
Series
Working paper series, Swedish business school at Örebro, ISSN 1403-0586 ; 7
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:oru:diva-12664 (URN)
Available from: 2010-12-06 Created: 2010-12-06 Last updated: 2015-01-19Bibliographically approved
2. Comparison of methods in the analysis of dependent ordered catagorical data
Open this publication in new window or tab >>Comparison of methods in the analysis of dependent ordered catagorical data
2008 (English)Report (Other academic)
Abstract [en]

Rating scales for outcome variables produce categorical data which are often ordered and measurements from rating scales are not standardized. The purpose of this study is to apply commonly used and novel methods for paired ordered categorical data to two data sets with different properties and to compare the results and the conditions for use of these models.

The two applications consist of a data set of inter-rater reliability and a data set from a follow-up evaluation of patients. Standard measures of agreement and measures of association are used. Various loglinear models for paired categorical data using properties of quasi-independence and quasi-symmetry as well as logit models with a marginal modelling approach are used. A nonparametric method for ranking and analyzing paired ordered categorical data is also used.

We show that a deeper insight when it comes to disagreement and change patterns may be reached using the nonparametric method and illustrate some problems with standard measures as well as parametric loglinear and logit models. In addition, the merits of the nonparametric method are illustrated.

Place, publisher, year, edition, pages
Örebro: Örebro university, 2008. 19 p.
Series
Working paper series, Swedish business school at Örebro, ISSN 1403-0586 ; 6
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:oru:diva-12665 (URN)
Available from: 2010-12-06 Created: 2010-12-06 Last updated: 2015-01-19Bibliographically approved
3. Statistical properties of a nonparametric measure of discordance in paired ordinal data
Open this publication in new window or tab >>Statistical properties of a nonparametric measure of discordance in paired ordinal data
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:oru:diva-12666 (URN)
Available from: 2010-12-06 Created: 2010-12-06 Last updated: 2016-11-21Bibliographically approved
4. Rank-based methods for analysis of individual variations in paired ordinal data
Open this publication in new window or tab >>Rank-based methods for analysis of individual variations in paired ordinal data
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:oru:diva-12667 (URN)
Available from: 2010-12-06 Created: 2010-12-06 Last updated: 2016-11-21Bibliographically approved
5. Statistical aspects on multiple comparisons of relative rank variance in paired ordinal data
Open this publication in new window or tab >>Statistical aspects on multiple comparisons of relative rank variance in paired ordinal data
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:oru:diva-12668 (URN)
Available from: 2010-12-06 Created: 2010-12-06 Last updated: 2016-11-21Bibliographically approved

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