Abstract
For square contingency tables with ordered categories, the present paper gives several theorems that the symmetry model holds if and only if the generalized linear diagonals-parameter symmetry model for cell probabilities and for cumulative probabilities and the mean nonequality model of row and column variables hold. It also shows the orthogonality of statistic for testing goodness-of-fit of the symmetry model. An example is given.
Highlights
This model describes the structure of symmetry with respect to the cell probabilities pij
Assuming that the linear diagonals-parameter symmetry (LDPS)(K) and mean equality (ME) models hold and we shall show that the S model holds
Theorem 4 that the poor fit of the S model is caused by the influence of the lack of structure of the ME model rather than the cumulative linear diagonals-parameter symmetry (CLDPS)(K) model K 1, 2,5
Summary
This model describes the structure of symmetry with respect to the cell probabilities pij. As a model which indicates the structure of asymmetry for pij , Agresti [2] considered the linear diagonals-parameter symmetry (LDPS) model defined by pij j i i j. Yamamoto and Tomizawa [3] considered the generalized linear diagonals-parameter symmetry (LDPS(K)) model as follows; for a fixed. The S model has the structure of symmetry with respect to the cumulative probabilities Gij , i j. Miyamoto et al [4] considered the cumulative linear diagonals-parameter symmetry (CLDPS) model defined by. Yamamoto and Tomizawa [3] considered the generalized cumulative linear diagonals-parameter symmetry (CLDPS(K)) model as follows; for a fixed. The CLDPS(0) model is equivalent to the CLDPS model.
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