Fixing gamma's=0 and counting parameters in robust design

[ant]

I'm using the RD. Considering that I have 12 gamma'' and 11 gamma', how should I count the number of parameters when I fix the gamma's=0?

1- fix all the 23 gamma's parameters to zero, then I'll have 21 parameters (plus other parameters on S, p and c), remembering that the last g'' and g' must be constrained...

2- fix the gamma's as in the random model and then set them to zero. So I would have 12 gamma's parameters.

3- make g''(.)=g'(.), and then set it as zero, so I would have only one gamma parameter.

I assume that the second option is not reasonable, but I put it just to illustrate...
Reading the book it says (just cites, don't explicate) that I should stick with the first option, but I'm not convinced, because if all gamma's are equal to zero, then, they're all equals... In the other side, they could be different parameters with the same value.

Thankful as always,
Antonio

[Bill Kendall]

If you plan to set all gamma's to 0, it does not matter what constraints you impose first. In any case, they won't be considered parameters because they are fixed. You will get the same estimates, deviance, and AIC regardless of which approach you take. For simplicity, however, just set them all equal to one another and set that one parameter to 0.