6.4. Consider a cross-classification of two ordinal variables with fixed row and column scores.

(a) Describe the association pattern represented by the model log ßij = ë + ë* + ë] + ß\UiVj + ß2U2 iVj.

For a 3xc table, explain why this model is equivalent to the row effects model. [More generally, Haberman (1974) expressed the general association term \f? by an expansion using orthogonal polynomials.]

(b) For the model log/i,;; =a+ X\Ui + X2uj + y\Vj + Y2Vj + ßUiVj, show that the likelihood equations equate the sample marginal means, marginal standard deviations, and correlation with their fitted values.