May a less parameterized model have lower deviance?

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May a less parameterized model have lower deviance?

I am wondering if there are cases when a model with a smaller number of estimated parameters may have lower deviance of another with more parameters. This is the specific case I have in mind:
Mod1: {phi(g x IndCov) p(.)} np = 7 Deviance = 580
Mod2: {phi(g + IndCov) p(.)} np = 5 Deviance = 585
Mod3: {phi(g + t) p(.)} np = 9 Deviance = 581

Where IndCov is an individual covariate, g is a group of three levels and t are seven occasions.
This is from a paper I have read and I have been surprised by that because a priori I would have expected that Mod3 cannot have a deviance value higher than that of Mod1.
I wonder if this can be something related to what discussed in the sidebar at page 11-10 of MARK manual about standardization of individual covariates when there is a common intercept and 2 or more slopes.
Or am I missing the point? Any commentary on it would be really appreciated.
simone77

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Joined: Mon Aug 10, 2009 2:52 pm

Re: May a less parameterized model have lower deviance?

Yes a model with fewer parameters can have lower deviance unless the model with fewer parameters is nested within the model with the larger number of parameters. That is not the case in the example you showed.
jlaake

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Location: National Marine Mammal Laboratory, Seattle, WA

Re: May a less parameterized model have lower deviance?

Thank you very much! I did not realize that mod1 is not nested to mod3: quite obvious but could not see....
simone77

Posts: 140
Joined: Mon Aug 10, 2009 2:52 pm

Re: May a less parameterized model have lower deviance?

simone77 wrote:Thank you very much! I did not realize that mod1 is not nested to mod3: quite obvious but could not see....

Actually, whether or not one model is nested in another can be somewhat difficult to determine in some cases (even though in your situation, it is fairly clear). As such, I've had a bunch of text at various places in the MARK book for some time, which goes over this issue of 'nestedness' in a bit more detail -- see for example the -sidebar- beginning on p. 56 of Chapter 4. Might be worth a quick read...

http://www.phidot.org/software/mark/doc ... df#page=56
cooch

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