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,

Using zero-sum constraints, show that parameters in the general three-way loglinear model satisfy

(a)

(b)

(c)

(d)

(e)

(f)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I think that the zero-sum constraints in the two-way loglinear model are (but I'm not sure):

And the zero-sum constraints in the three-way loglinear model are:

However, I do not see how I can use these constraints to prove the parts (a)-(f).

For example, in part (b) I get

How can I use the constraints to show that the equation above is true?

Please help me.