[Gretl-devel] Re: $test accessor after biprobit

Hm, this will require some more work than I had thought. In fact, I'm not quite sure we're doing the right thing in the current incarnation of biprobit. Let me explain. The number of estimated coefficients is k1 + k2 + 1, where k1 and k2 are the numbers of explanatory variables in the first and second equation respectively, plus there's rho (actually, its hypherbolic arctangent). When we record $vcv into the MODEL struct, we treat the model as if the number of parameters were k1 + k2, although the covariance matrix is 1 element bigger, with the result that (a) the $vcv you now get after biprobit is buggy (it's not symmetric) (b) we don't have in our MODEL struct the estimated variance for atan(rho). Note that we treat $coeff in the same way, that is we don't store rho among the estimated parameters, although its estimate is accessible as $rho or $model.rho. So I'm wondering: while we're at it, should we "correct" this, at the risk of backward incompatibility, by including rho in $coeff and making $vcv a square matrix of dimension (k1 + k2 + 1), or shall we just fix $vcv and maybe provide an accessor for the standard error of rho?

IMO we should change the output of biprobit and make rho a "first class citizen", that is include it in the output just like the other estimated parameters as well as storing it as the last element of $coeff and enlarging $vcv and $stderr as needed, but I'd like to hear your opinion on this before I start working on the code.