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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