Re: [Gretl-users] Heckit goodness of fit

On Thu, 9 Apr 2009, Allin Cottrell wrote: 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. The way I personally see it is, people like R2 because it's easy to read, although its "real" meaning is not particularly clear. Yes, for OLS models it _happens_ to be equal to the squared correlation coefficient beween y and yhat, but for me it's just a number that tells me if a particular model contains any explanatory variables worth keeping, apart from the constant; the closer to 1, the better. 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 ) This would have several advantages: 1) It'd be defined for every model you can reasonably speak of "explanatory variables" and perform hypothesis tests on their coefficients (so that includes tsls, probit, logit, heckit, arma, etcetera) 2) The estimation method you use (ml, cml, gmm, least squares etcetera) wouldn't matter, as long as you can make tests. 3) It lies between 0 and 1 by construction, since a Wald-type test is a pd quadratic form. 4) It would coincide with the usual R2 for OLS. Do you guys like the idea? Riccardo (Jack) Lucchetti Dipartimento di Economia Università Politecnica delle Marche r.lucchetti(a)univpm.it http://www.econ.univpm.it/lucchetti