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# st: Question about GEE error term

 From "Bryan W. Griffin" To statalist@hsphsun2.harvard.edu Subject st: Question about GEE error term Date Wed, 16 Mar 2005 13:47:33 -0500

Hi all --

I have a question about GEE estimates. First, let me specify a model from a generalized linear mixed model perspective, more specifically a logistic regression model with random effects with one within and one between predictor. The within-cluster (or subject-specific) model is:

logit(y) = b0 + b1(X1)

and the between-cluster (or between subject) models are:

b0 = g00 + g01(Z1) + u0j

b1 = g10 + g11(Z1) + u1j

combined these produce:

logit(y) = g00 + g01(Z1) + g10(X1) + g11 (X1 * Z1) + u0j + u1j(X1)

In this model there are two random effects, u0j and u1j(X1).

In GEE framework, I understand there are difference in parameter estimates (population-averaged vs. cluster-specific) and that the error terms are handled differently. Within GEE, I know that u0j represents the within-cluster (or subject-specific) correlated error and is modeled via the working correlation matrix with specifications appropriate for the given model such as exchangeable, auto-regressive, etc.

Now my question. What about the second error term, u1j(X1); is this error simply ignored in the GEE framework or is it somehow modeled within the working correlation matrix?

Along similar lines, suppose one has a three level logistic model with many possible error terms if using generalized linear mixed model (cluster-specific). How are these additional error terms addressed with GEE estimation?
___________________________________________________________________
Bryan W. Griffin
Curriculum, Foundations, & Reading
P.O. Box 8144
Georgia Southern University
Statesboro, GA 30460-8144

Phone: 912-681-0488
E-Mail: bwgriffin@GeorgiaSouthern.edu
WWW: http://coe.georgiasouthern.edu/foundations/bwgriffin/

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