Re: [Gretl-users] Constrained maximization in gretl

On Wed, 26 Oct 2011, Giuseppe Vittucci wrote: > The following code (adapted from the manual): > > mle logl = check ? - ln(pstr_cssr(y,X,q,gamma,c,m,Z) : NA > scalar check = (gamma > zeros(r,1)) && (c >= c_min) && (c <=c_max) > params gamma c > end mle > > simply checks that the unconstrained maximum is in the parameter space > and returns an error if it is not so. > But is there a way to find such a constrained maximum in gretl? > > If there is not, what is the best way to circumvent the problem? There isn't. The idea is to check whether the parameters are admissible when the loglik is computed, just like you're doing. A couple of tips: 1) I suppose gamma is a vector; you can achieve the same result as what I think you're tryng to do by writing (gamma > 0) (cool, huh?)

2) if you have constrained parameters, you're probably much better off if you use some 1-to-1 transformation to some unbounded parameter. In your example, assuming you really mean to use <= and >= rather than strict inequalities, you may use mle logl = ln(pstr_cssr(y,X,q,gamma,c,m,Z) matrix gamma = exp(lg) scalar c = c_min + 0.5*(sin(ac) + 1)*c_max params lg ac end mle and then retrieve the $vcv for your original parametrisation by the delta method. Otherwise, if what you mean is really c_min < c < cmax (more customary in ml problems), then a nicer alternative is scalar c = c_min + 0.5*(tanh(ac) + 1)*c_max or perhaps scalar c = c_min + cnorm(ac)*c_max HTH,

Riccardo (Jack) Lucchetti Dipartimento di Economia Università Politecnica delle Marche r.lucchetti(a)univpm.it http://www.econ.univpm.it/lucchetti _______________________________________________ Gretl-users mailing list Gretl-users(a)lists.wfu.edu http://lists.wfu.edu/mailman/listinfo/gretl-users