1. ## Defining Contrast Matrix

In the book Applied Longitudinal Analysis, 2nd Edition there is an example in the chapter "Marginal Models: Generalized Estimating Equations (GEE)" in "Muscatine Coronary Risk Factor Study" sub-section. I am illustrating it below :

Let if the child is classified as obese at the occasion, and otherwise.

The marginal probability of obesity at each occasion follows the logistic model

If one construct the hypothesis that changes in the log odds of obesity are the same for boys and girls, then $H_0:\beta_5=\beta_6=0$.

To test the hypothesis

where and is the contrast matrix.

But I can't write the contrast matrix for the .

Because if the were (notice that there ISN'T equal to at the most right ), then I can construct the contrast matrix easily as :
so that

But When the is (notice that there IS equal to at the most right ), then
so that

but necessarily the contrast matrix is NOT correct as the row sum of a contrast matrix is equal to . How can I define the contrast matrix?

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