chat and fixed parameters

[Eldar]

This is maybe another stupid question but I can't understand how fixing of the parameters affects estimates of c-hat.
As far as I can see from MARK output -2logL(saturated) remains the same in fixed and nonfixed models but I would assume that saturated model changed if I fixed some of the parameters.

I just came to this issue when as I have a lot of the parameters fixed to 0 in mstrata model and it seems that when I estimate "fixed" and "nonfixed" models the estimated (by median chat) overdispersion remains the same (or at least similar).
I would appreciate any explanation.
Eldar

[abreton]

As far as I can see from MARK output -2logL(saturated) remains the same in fixed and nonfixed models but I would assume that saturated model changed if I fixed some of the parameters.

See the 'sidebar' on page 5-2 in the MARK Book, Live Encounter Model (includes mstrata model). Note that fixed parameters are ignored when calculating the -2log(L) of the saturated model.

when I estimate "fixed" and "nonfixed" models the estimated (by median chat) overdispersion remains the same (or at least similar).

I'm assuming the "nonfixed" and "fixed" models you're referring to are identical (same structure) except that in the latter case some parameters have been fixed to 0. I can only speculate here, perhaps the parameters that you fixed to zero are also estimated as (roughly) zero, by MARK, in the nonfixed model. This would explain your comment in parentheses,

(or at least similar)

andre

[Eldar]

Thanks a lot Andre!
All this means that Deviance and dF os saturated model do not depend on parameter fixing..
From this point the next question is arising what will change if we will fix some parameters?
Am I correct that

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(DevS-DevG)/(dfS-dfG)

?

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DevS/dfS =1 => DevS=dfS

Where G is general model and S is saturated model.
DevG is not changing, so the only place to change is dfG
So, the next question is: how mark is estimating dfG?
Eldar

[abreton]

See last paragraph on page 3-16 in the MARK book. Even better, see section 4.6.1 including the sidebar. Pages 5-4 and 5-5, look for, "Now, for the key conceptual step...", may also be helpful. I'm not sure what you're attempting to calculate, hopefully you'll find your answer somewhere on these pages.

andre