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

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Summary

Introduction

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.

Preliminaries
Association Models
Correlation Models
Uniform Local Association
Illustrations
Conclusions

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