To obtain the log-linear models for association homogeneity, we need the following two key facts: (a) Prove

Question:

To obtain the log-linear models for association homogeneity, we need the following two key facts:

(a) Prove (7.25).

(b) Prove that \(\lambda_{i^{\prime} j k}^{x y z}+\lambda_{i j^{\prime} k}^{x y z}=\lambda_{i j k}^{x y z}+\lambda_{i^{\prime} j^{\prime} k}^{x y z}\) for all \(i, i^{\prime}, j, j^{\prime}\), and \(k\) implies \(\lambda_{i j k}^{x y z}=0\) for all \(i, j, k\), i.e., no three-way interaction.

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