Hi!
I need help with this question:

Consider the general two-way loglinear model between x and Y at a fixed level k of Z,
\log m_{ijk} = \mu(k)+\lambda_{i}^{x}(k)+\lambda_{j}^{y}(k)+\lamb  da_{ij}^{xy}(k), 1 \leq i \leq I, 1 \leq j \leq J.

Using zero-sum constraints, show that parameters in the general three-way loglinear model satisfy
(a) \mu=[\sum \mu(k)]/K

(b) \lambda_{i}^{x}=[\sum \lambda_{i}^{x}(k)]/K

(c) \lambda_{ij}^{xy}=[\sum \lambda_{ij}^{xy}(k)]/K

(d) \lambda_{k}^{z}=\mu(k)-\mu

(e) \lambda_{ik}^{xz}=\lambda_{i}^{x}(k)-\lambda_{i}^{x}

(f) \lambda_{ijk}^{xyz}=\lambda_{ij}^{xy}(k)-\lambda_{ij}^{xy}


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I think that the zero-sum constraints in the two-way loglinear model are (but I'm not sure):
 \sum_{i} \lambda_{i}^{x}(k)=\sum_{j} \lambda_{j}^{y}(k)=\sum_{i} \lambda_{ij}^{xy}(k)=\sum_{j} \lambda_{ij}^{xy}(k)=0
And the zero-sum constraints in the three-way loglinear model are:
\sum_{i} \lambda_{i}^{x}=\sum_{j} \lambda_{j}^{y}=\sum_{k} \lambda_{k}^{z}=\sum_{i} \lambda_{ij}^{xy}=\sum_{j} \lambda_{ij}^{xy}=...=\sum_{k} \lambda_{ijk}^{xyz}=0
However, I do not see how I can use these constraints to prove the parts (a)-(f).
For example, in part (b) I get
\lambda_{i}^{x}=[\sum_{k} \lambda_{i}^{x}(k)]/K
\sum_{k} \lambda_{i}^{x}=\sum_{k} \lambda_{i}^{x}(k)
How can I use the constraints to show that the equation above is true?
Please help me.