For the analysis of two-way contingency tables, this paper presents a note on a useful decomposition of the likelihood ratio (LR) statistic for the point-symmetry (PS) model. The PS is decomposed into the row (column) conditional PS and the row (column) marginal PS. This decomposition is orthogonal with respect to the LR statistic; namely, the statistic for PS is exactly equal to the sum of those for the decomposed models.
- Conditional point-symmetry
- likelihood ratio statistic
- row (column) marginal point-symmetry