The statistical analysis of associations is a central theme in this book. This chapter starts with a description of the properties of the odds ratio, including its maximum likelihood estimation. Because of its variation independence from the marginal distributions, it is argued the odds ratio is the most useful measure of association. The structure of I × J tables, as described by the systems of local or spanning cell odds ratios, which are generalizations of the simple odds ratio defined for 2 × 2 tables, is described and analyzed by association models. The odds ratio is generalized to higher-dimensional tables by introducing a hierarchical structure of conditional odds ratios. Independence may be seen as lack of association, but a related simple structure, conditional independence, is found more often in real data, and properties of the maximum likelihood estimates under conditional independence are studied.
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