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st: Query regarding formula for calculating the conventional variance for the xtgee command


From   RA Hughes <rachael.hughes@bristol.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   st: Query regarding formula for calculating the conventional variance for the xtgee command
Date   Mon, 19 Mar 2012 14:21:53 +0000

Dear Statalist

I have a query regarding the formula for the calculation of the conventional variance when the model is the generalized estimating equations logistic regression model with an exchange working correlation matrix, i.e. Stata command

xtgee outcome covariates, family(binomial) link(logit) corr(exchangeable) vce(conventional) nmp

In keeping with Liang and Zeger's 1986 Biometrika paper I am using Stata's vce option nmp.

Dropping the cluster subscripts, the Stata documentation for the xtgee command states that the conventional variance is calculated as {sum(D'V^{-1}D)}^-1, where V = A^{1/2}R(alpha)A^{1/2}. Using this formula I obtain the same result as Stata.

My query is that in Liang and Zeger's 1986 paper
V = A^{1/2}R(alpha)A^{1/2}/phi.

Note that the estimate of phi (the scale parameter) is close to 1 but not exactly 1. I have confirmed that my estimate for phi is the same as Stata's by confirming I get the same answer for the parameter estimate alpha, which is dependent upon phi. (alpha is the parameter of the exchangeable working correlation matrix).

Could you please confirm if I am correct that Stata's xtgee command calculates V different to the formula stated in the Liang and Zeger 1986 paper?

Many thanks
Rach

References
Liang and Zeger, Longitudinal data analysis using generalized linear models, Biometrika, 1986, 73,13-22.


----------------------
RA Hughes
rachael.hughes@bristol.ac.uk
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