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

[RA Hughes <rachael.hughes@bristol.ac.uk>]

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
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/