xtreg and areg R^2

[Andrea Lupi]

I do not understand how the adjusted R^2 are calculated in these two commands.

Here I follow what has been done in the xtreg documentation

webuse nlswork, clear
xtset idcode

xtreg ln_w grade age c.age#c.age ttl_exp c.ttl_exp#c.ttl_exp tenure c.tenure#c.tenure 2.race not_smsa south, fe

Running

 ereturn list

and looking at e(r2_a) = .00626099 I found the R^2 adjusted.

However, if I run the following regression

areg ln_w grade age c.age#c.age ttl_exp c.ttl_exp#c.ttl_exp tenure c.tenure#c.tenure 2.race not_smsa south, absorb(idcode)

everything is the same except for the adjusted R^2 that is very different: Adj R-squared = 0.6299

I do not understand why. Thanks for your answers

[Andrew Musau]

areg's adjusted R-Squared is the OLS R-Squared (Model Sum of Squares/ Total Sum of Squares) adjusted for the number of regressors in the model. For xtreg,fe, the adjusted R-Squared is the R-Squared from the mean-deviated regression (or within R-squared) adjusted for both the number of regressors in that regression plus the additional fixed effects. In #9 of the link below, I argue that the additional adjustment renders this statistic meaningless and provide a formula for an alternative computation. The link also illustrates the calculation of the latter.


https://www.statalist.org/forums/for...ted-as-missing

[Andrea Lupi]

Thanks, Andrew. Your link was very helpful! In your opinion what is the best R^2 in order to evaluate the goodness of fit of a model?

[Andrew Musau]

For the linear fixed effects model, I would guess that the LSDV R-squared (reported by areg) is more intuitive. My experience (from the Economics literature) indicates that a lot of authors report this statistic. However, as long as your readers understand what these statistics are, reporting either is fine.