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Re: st: Why no sum of squared residuals in reg output after robust or cluster?


From   Richard Williams <Richard.A.Williams.5@nd.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Why no sum of squared residuals in reg output after robust or cluster?
Date   Fri, 05 Mar 2004 10:00:47 -0500

At 08:41 PM 3/3/2004 -0600, dbdewalq@uchicago.edu wrote:
This is probably easy, but I have been wondering...
When you add the comand robust or cluster after the regression you don't get in
the regression output the information about the explained sum of squares, the
residual sum of squares and the total sum of squares, information that you
usually get if you perform regress without the robust or the cluster command.
Why is it so?
Is it that the residual sum of square is not reliable when you correct for
heteroscedasticity with the Huber/White/Sandwich estimator, or if you cluster
the standard errors?
But then, how is the R-square (whch is reported, but not the adjusted one)
calculated?
This is a good chance to try out my scanner and optical character recognition software. Here is what the manual says:

From p. 337, Stata 8 Reference Manual N-R (from the documentation for the regress command):

Technical Note

When you specify robust, regress purposefully suppresses displaying the ANOVA table, as it is no longer appropriate in a statistical sense even though, mechanically, the numbers would be unchanged. That is, sums of squares remain unchanged, but the meaning you might be tempted to give those sums is no longer relevant. The F statistic, for instance, is no longer based on sums of squares; it becomes a Wald test based on the robustly estimated variance matrix. Nevertheless, regress continues to report the R^2 and the root MSE even though both numbers are based on sums of squares and are, strictly speaking, irrelevant. In this, the root MSE is more in violation of the spirit of the robust estimator than is R^2. As a goodness-of-fit statistic, R^2 is still fine; just do not use it in formulas to obtain F statistics because those formulas no longer apply. The Root MSE is valid as long as you take its name literally - it is the square root of the mean square error. Root MSE is no longer a prediction of sigma because there is no single sigma; the variance of the residual varies observation by observation.

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