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What are the divisors used in xtgee?

Title   The divisor choice in xtgee
Author David M. Drukker, StataCorp
Date July 2011

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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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