Abstract
The double symmetry model satisfies both the symmetry and point symmetry models simultaneously. To measure the degree of deviation from the double symmetry model, a two-dimensional index that can concurrently measure the degree of deviation from symmetry and point symmetry is considered. This two-dimensional index is constructed by combining two existing indexes. Although the existing indexes are constructed using power divergence, the existing two-dimensional index that can concurrently measure both symmetries is constructed using only Kullback-Leibler information, which is a special case of power divergence. Previous studies note the importance of using several indexes of divergence to compare the degrees of deviation from a model for several square contingency tables. This study, therefore, proposes a two-dimensional index based on power divergence in order to measure deviation from double symmetry for square contingency tables. Numerical examples show the utility of the proposed two-dimensional index using two datasets.
Highlights
Consider an r × r square contingency table that has the same row and column classifications with nominal categories
The point symmetry (PS) model proposed by Wall and Lienert [5] is defined by πij = πi∗ j∗
This study focuses on the index that represents the degree of deviation from the double symmetry (DS) model
Summary
Consider an r × r square contingency table that has the same row and column classifications with nominal categories. Πij = π ji Licensee MDPI, Basel, Switzerland This S model is the most commonly used model for analyzing square contingency tables [2,3,4]. The DS model satisfies both the S and PS models simultaneously, the above index Φ DS cannot concurrently measure the degree of deviation from S and PS To address this gap, Ando et al [10] proposed a two-dimensional index that can concurrently measure those. Previous studies (e.g., [7,8]) pointed out that it is important to use several indexes of divergence to accurately measure the degree of deviation from a model.
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