--- Steve Denham <stevedrd@YAHOO.COM> wrote:

> ----- Original Message ---- > From: Dale McLerran <stringplayer_2@YAHOO.COM> > To: SAS-L@LISTSERV.UGA.EDU > Sent: Friday, January 11, 2008 1:15:54 PM > Subject: Re: Pseudo-AIC & Glimmix > > --- Robin High <robinh@UOREGON.EDU> wrote: > > > Hello Tobias, > > > > My thoughts are that with GLIMMIX if the pseudo values drop by a > > substantial amount with a more complex R-side structure, then > > there is evidence to suggest that it may be more appropriate; if > the > > pseudo values from the two choices are reasonably close, then go > with > > the simpler choice. > > Dale McLerran replied--> > > I have to disagree here. When one changes the error structure, then > one must also change the linearized response variable. When the > response variable differs, you cannot compare the pseudo-AIC values > since the AIC statistic is based on a likelihood computation. One > can only compare likelihood values across models when the response > variable employed for each model is the same. So, my belief is > that the pseudo-AIC is of no value for any model comparisons for a > non-Gaussian response. (For a Gaussian response, the AIC is no > longer a pseudo-AIC. So, one could use the reported AIC values if > the response is normal.) > > And now I ask--> > > Dale, when you say "change the error structure" I assume that you > mean the error distribution, rather than the variance-covariance > structure. That's the only way I can make sense of what you assert. > I would think that for a given distribution, whether it be Gaussian > or non-Gaussian, the pseudo-AIC might be useful for distinguishing > between say, an unstructured covariance matrix and an autoregressive > structure. Help me out on this. >

Steve,

No, I don't mean simply changing the error distribution, but rather any modification of the variance-covariance structure. In GLIMMIX, a response variable linearization step is performed and then a normal mixed model estimation is performed. The linearization step is of the form

Y_lin = f(y - g^-1(eta_hat)) + eta_hat

where

eta_hat = X*beta_hat + Z*gamma_hat

The response Y_lin is used in the next iteration of the procedure and new beta_hat and gamma_hat (and, hence, eta_hat) are estimated for this updated response.

Now, eta_hat depends on the variance-covariance structure through Z*gamma_hat. So, any changes to the covariance structure will result in different response variable Y_lin after the first parameter estimates have been obtained. Once the response variable has been modified due to some modification of the random effect design, then we can no longer compare likelihood values.

Dale

Once more from me--> The writers from the television show "The Simpsons" have this covered with:

HOMER: <annoyed grunt>,

which translates as D'oh.

Thank you, Dale. Once you pointed out the linearization step, I realized my error. Given this, why do you suppose that PROC GLIMMIX continues to report likelihood based fit statistics? I recall that when PROC MIXED was first introduced, all of the tests on the covariance parameters were automatically presented--but when it was pointed out that the tests weren't exactly what they were purported, we soon got a fix. This begs for the same kind of attention.

Steve Denham Associate Director, Biostatistics MPI Research

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