What are the divisors used in xtgee?
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Title
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The divisor choice in xtgee
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Author
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David M. Drukker, StataCorp
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Date
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July 2011
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Technical Note: This is a technical FAQ. Technical FAQs
address specific issues or computational aspects of estimators or other
commands. They are typically written for someone who already knows and
fully understands the statistics of the command—an expert in the area.
All of the materials in the Stata manual, including the Methods and Formulas
and sometimes the references, are assumed to be understood.
These FAQs often deal with issues that are not considered or adequately
addressed in the literature, and as such we welcome insights from readers or
related citations that we may have missed.
Divisors in xtgee
The default divisor for computing correlations and standard errors in
xtgee is N, the
number of observations in the dataset. With this divisor, the estimates are
invariant to the scale of the dataset. Scale invariance is an important
property. No weights are equivalent to frequency weights of one. If you
multiply these weights by a scale factor, you would not want your estimates
to change.
In some other packages and in some previous versions of xtgee, the
divisor is N − p, where p is the number of covariates in the model.
This divisor is used to obtain unbiased estimates. This divisor, however,
causes the estimates not to be scale invariant. As N goes to infinity, the
difference between the two divisors goes to zero.
In xtgee, if you specify the option nmp, the divisor N −
p will be used instead of the default divisor N.
The scaling issue also affects the normalization factor for the robust VCE
when family(gaussian) is specified. Historically, xtgee used
{(npanels)/(npanels − 1)}{(N − 1)/(N − p)}, where npanels
is the number of panels in the dataset and N and p are defined as above.
This normalization factor would prevent the VCE from being invariant to the
scale of the weights. For this reason, the default normalization factor is
now (npanels)/(npanels − 1) instead of {(npanels)/(npanels − 1)}
{(N − 1)/(N − p)}. One can use the previous normalization
factor by specifying the option rgf.
The divisor used in computing the unstructured and nonstationary correlation
matrices for each element in the correlation matrix has changed to the
number of panels that have valid observations for the ti and
tj defined by that element.
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