Modeling and Measuring Association for Ordinal Data

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dc.contributor.advisor Deng, Dianliang
dc.contributor.author Gong, Huihan
dc.date.accessioned 2012-11-13T20:31:14Z
dc.date.available 2012-11-13T20:31:14Z
dc.date.issued 2012-07
dc.identifier.uri http://hdl.handle.net/10294/3626
dc.description A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Statistics, University of Regina. ix, 73 l. en_US
dc.description.abstract We propose the modified Pearson goodness-of-fit statistic and consider it in the cumulative contingency tables. For the non-cumulative tables, we provide the scoring systems and the variance minimization correction term to Pearson goodness-of-fit statistic. We also put forward the average of individual odds ratios as the common odds ratio and modify the Mantel-Haenszel estimator of common odds ratio in a K x K ordinal contingency table where the category numbers of the variables are the same. The M[superscript2] statistic with scoring systems is also introduced. From the simulation results, we figure out that the chi-square statistics do not work except for those without the ordinal information. However, the M[superscript2] statistic accurately detects the association between ordinal variables in a contingency table no matter if it is sparse or not. The scoring systems can be considered together with the M[superscript2] statistic. The estimators of common odds ratio are appropriate as well. However, the estimators of common odds ratio are more appropriate for the lightly sparse tables because the test errors are relatively larger for the extremely sparse tables. The Mantel-Haenszel estimator of common odds ratio works better than the average of individual odds ratios in the extremely sparse tables. en_US
dc.language.iso en en_US
dc.publisher Faculty of Graduate Studies and Research, University of Regina en_US
dc.subject.lcsh Goodness-of-fit tests
dc.subject.lcsh Contingency tables
dc.subject.lcsh Multivariate analysis
dc.title Modeling and Measuring Association for Ordinal Data en_US
dc.type Thesis en
dc.description.authorstatus Student en
dc.description.peerreview yes en
thesis.degree.name Master of Science (MSc) en_US
thesis.degree.level Master's en
thesis.degree.discipline Statistics en_US
thesis.degree.grantor University of Regina en
thesis.degree.department Department of Mathematics and Statistics en_US
dc.contributor.committeemember Volodin, Andrei
dc.contributor.committeemember Zhao, Yang Y.
dc.contributor.externalexaminer Fan, Lisa


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