For the analysis of square contingency tables with the same row and column ordinal classifications, McCullagh (1978) considered the palindromic symmetry (PS) model, which has a multiplicative form for cumulative probabilities that an observation will fall in row (column) category i or below and column (row) category j (> i) or above. The present paper proposes a modified PS model which indicates that (1) the symmetric odds for cumulative probabilities with distance 1 from main diagonal of the table are constant and (2) there is the structure of quasi-symmetry for them with distance k (≥ 2). Also the present paper gives the decomposition of the symmetry model using the proposed model. Examples are given.
Iki, Kiyotaka; Oda, Takeshi; and Tomizawa, Sadao
"A Modified Palindromic Symmetry Model for Square Contingency Tables with Ordered Categories,"
Journal of Statistics Applications & Probability: Vol. 3
, Article 1.
Available at: https://dc.naturalspublishing.com/jsap/vol3/iss2/1