MEASURES OF DEPARTURE FROM ORDINAL QUASI-SYMMETRY MODELS FOR SQUARE CONTINGENCY TABLES

For square contingency tables with ordered categories, Agresti (2002) considered the ordinal quasi-symmetry (OQS) model and Iki, Tahata and Tomizawa (2009) considered the ridit score type quasi-symmetry (RQS) model. The present paper proposes measures which represent the degree of departure from each of the OQS and RQS models. The proposed measures are expressed by using the Cressie-Read power-divergence or Patil-Taillie diversity index. These measures would be useful for comparing the degrees of departure from OQS and RQS in several tables. The measures are applied to the data of individual’s education and father’s or mother’s education in Japan.