Re: [Gretl-users] Heckit goodness of fit
On Sat, 11 Apr 2009, Riccardo (Jack) Lucchetti wrote:
On Thu, 9 Apr 2009, Allin Cottrell wrote:
> There's no "correct" R-squared value for this sort of regression,
> and it's not ML so the likelihood is not strictly relevant. I
> suppose you could calculate the square of the correlation between
> the the actual and fitted values of the dependent variable.
Hmm. That would be an ingenious way to get "something like an
R^2", but I doubt it'd be of much use for models, like heckit,
where you have some form of censoring/truncation etc. On the
other hand, a similar line of criticism involving R^2 in the
context of IV models is well known, so it may be worthwhile to
think this R2 thing out once and for all.
That would be nice!
Maybe a nice way to generalise R2, that we could use for every model
we
have, is to define
R2 = W/(W + $T)
where W is a Wald-type test for zeroing all explanatory variables
(constant excluded). That is: suppose we have a model with the intercept
as first explanatory variable,
<foo> y const x1 x2 x3 < possibly more stuff... >
where <foo> can be two-step heckit or whatever you like. Then
matrix b= $coeff[2:]
matrix V = $vcv[2:,2:]
W = qform(b', invpd(V))
R2 = W / ( W + $T )
The variant
R2 = W / ( W + ($T - $ncoeff))
would give the regular R^2 for OLS estimates.
This would have several advantages...
Yes, I like it. But note that at present it produces a horrid
mess for two-step heckit since the covariance matrix is stuffed
with NAs/nans. I guess we should be able to fix that up without
too much difficulty.
Allin.