Abstract
For square contingency tables with ordered categories, this article proposes new models which indicate that in addition to the structure of asymmetry of the probabilities with respect to the main diagonal of the table, the expected frequency has an exponential form along every subdiagonal of the table. Also it gives the new three kinds of decompositions using the proposed model and proves the orthogonality of the test statistics.
Highlights
Consider an R × R square contingency table with the same row and column classifications
Yamamoto & Tomizawa (2014) considered the quasi-diagonal exponent symmetry (QDES) model defined by pi j =
The present paper proposes two new models and gives the new three kinds of decompositions of the DES model
Summary
Consider an R × R square contingency table with the same row and column classifications. Tomizawa (1992) considered the diagonal exponent symmetry (DES) model defined by. Iki, Yamamoto & Tomizawa (2014) considered the quasi-diagonal exponent symmetry (QDES) model defined by αiβ jd| j−i| (i j), ψii (i = j). The QDES model states that in addition to the structure of the QS model (instead of the S model), the expected frequency has an exponential form along every subdiagonal of the table. Iki et al (2014) gave the theorem that the DES model holds if and only if both the QDES and ME models hold. We are interested in considering new models which indicate that in addition to the structure of the CS model (instead of the S model), the expected frequency has an exponential form along every subdiagonal of the table. The present paper proposes two new models and gives the new three kinds of decompositions of the DES model
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