Why do Stata’s xtgee standard errors differ from those reported by SAS’s
Interpreting standard errors produced by Stata’s xtgee and SAS’s proc GENMOD
James Hardin, StataCorp
A user asked
I tried to run the same model using Stata’s
and SAS’s PROC
GENMOD. I get the same coefficient estimates and working correlation
matrix but different standard errors. xtgee seems to be
consistently lower. I’m using a Poisson distribution and exchangeable
The part of the SAS output titled “Analysis of initial
estimates” is the output for a pooled Poisson estimator (which is
almost identical to the GEE output since the extra correlation parameter is
What SAS calls “empirical standard errors” are (almost) equal to
what Stata calls “robust standard errors”. They are not exactly
equal because Stata multiplies clustered robust variance matrices by a
factor equal to C/(C − 1), where C is the number of clusters. Run the
xtpoisson/xtgee with the robust option and you will
see this relationship.
SAS also has an option to the REPEATED statement called MODELSE where you
will get “model standard errors” instead of “empirical
standard errors”. If you use that option you will get Pearson
chi2 scaled standard errors, which are different from what Stata
prints out (without the robust option). To get the same answers as
provided by Stata in its default case, you should also specify the SCALE=1
option on the REPEATED statement in SAS. This applies if the family you
specify is discrete (Poisson or binomial).
Here are the relationships for SAS models again:
- SAS default
Can be duplicated in Stata if you use the robust option.
errors will differ by a scale factor that is equal to sqrt(C/(C − 1)),
which Stata applies to the variance matrix.
- SAS MODELSE option specified
Can be obtained in Stata by default. The standard errors will differ
by a scale factor that is equal to the sqrt(phi coefficient * n/(n − k)).
- SAS MODELSE and SCALE=1 options specified
Can be obtained in Stata using the default options.
There is one difference between SAS 6.12 TS Level 0060 (and Windows version
4.10.1650) and Stata that cannot be explained: The results (beta, working
correlation matrix, and standard errors) of using PROC GENMOD do not match
xtgee when panels are unbalanced.