Modeling and Measuring Association for Ordinal Data
Date
2012-07
Authors
Gong, Huihan
Journal Title
Journal ISSN
Volume Title
Publisher
Faculty of Graduate Studies and Research, University of Regina
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.
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.