On Wed, 27 Nov 2013, Jyotirmoy Bhattacharya wrote:Premise: I'm no big fan of R^2 in any shape or form, so consider my answer as coming from someone who, in applied work, never even looks at the R^2 index.
I was trying to understand how GRETL calculates R^2 for fixed-effects
panel-data models as the value it produces is different from Stata and R's
plm library.
However, it may be argued that a measure of the correlation between your data and the prediction that the model gives you is a desirable descriptive statistic to have. The problem here is: which model and which data.
The fixed-effect model could be conceived in two ways which are, in my mind, equally defensible: (a) a nice, clean way to get rid of the individual effects by using the fact that in the linear model a sufficient stsistic is easy to compute or (b) as a clever way to estimate the "important" parameters of a model in which you want to include (for some reason) individual dummies. If you take perspective (b), then your data is the unmodified y and your model includes the unit dummies as well, and gretl is already doing the "right thing" (especially considering that it could be useful, for instructional purposes, to show the students that FE and a regression with lots of dummies are in practice the same thing); however, if you take stance (a), then your data is really (y-pmean(y)) in hansl parlance, or if you prefer $y_{it} - \bar{y}_i$, and your model just includes the betas, which are the coefficients of the deviations of the x variables from their per-unit means. In this case, the relevant measure of R^2 would be what plm reports and what stata calls the "within" R^2.
After discussing the issue for a bit, Allin and I thought it's probably fair to report both, and simply drop the "adjusted" R^2, which makes little sense in this context, considering that interpretations (a) and (b) lead you to consider a different number of regressors, so you'd have to define two parallel measures of \bar{R}^2 too. We'll commit the change in CVS in a few hours.
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Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti@univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
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