Abstract
The -divergence association models for two-way contingency tables is a family of models that includes the association and correlation models as special cases. We present this family of models, discussing its features and demonstrating the role of -divergence in building this family. The most parsimonious member of this family, the model of -scaled uniform local association, is considered in detail. It is implemented and representative examples are commented on.
Highlights
Contingency tables and their analysis are of special importance for various diverse fields, like medical sciences, psychology, education, demography and social sciences
It is of practical interest to have estimators of this common local association, alternative to the maximum likelihood estimators (MLEs), that are provided in explicit forms
Observe that the closed form estimates for the λ-scaled local associations are close to the corresponding maximum likelihood estimates in case the assumed model is of adequate fit while they diverge for models of bad fit
Summary
Contingency tables and their analysis are of special importance for various diverse fields, like medical sciences, psychology, education, demography and social sciences. We aim at highlighting a different structural role of φ-divergence in contingency tables modelling, namely that of linking phenomenological different models, forming a family of models and providing a basis for their comparison, understanding and unified treatment Through this approach, new insight is gained for the standard association and correlation models (see [4,5]) while further alternatives are considered.
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