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?

On Wed, 2011-10-26 at 21:28 +0200, Riccardo (Jack) Lucchetti wrote: > 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?) Cool ;-) > > 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, Thanks. Very nice tricks. PS: Also c, c_min and c_max were vectors but it doesn't matter. ;-) > > 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

Don't care about my previous email. I have eventually modified the function and it gives me now the series of the residuals. Hence, I can use the following commands: Unconstrained maximum: mle logl = - 0.5*ln(2*pi) - ln(sigma) - 0.5*(e/sigma)^2 series e = pstr_cres(y,X,q,gamma,c,m,Z) params gamma c sigma end mle Constrained maximum: matrix ac = atanh((2*c-c_max-c_min)./(c_max-c_min)) matrix lg = ln(gamma) mle logl = - 0.5*ln(2*pi) - ln(sigma) - 0.5*(e/sigma)^2 series e = pstr_cres(y,X,q,gamma,c,m,Z) matrix gamma = exp(lg) matrix c = c_min + 0.5*(tanh(ac) + 1)*(c_max-c_min) params lg ac sigma end mle Thanks Giuseppe On Thu, 2011-10-27 at 09:57 +0200, Giuseppe Vittucci wrote: > Still on the mle command. > The argument of the mle command in gretl is actually the log-L > contributions and not the Log-L. > Clearly every combination of parameters that maximize the latter also > maximize the former. > So, as far as the point estimates of the parameters are concerned, it > does not really matters which one is used. > > So far I have used mle simply as a maximization BFGS method, and I was > not looking at the covariance or the other ancillary statistics. > > In my case working directly with the log-likelihood is much easier cause > I have a quite complex function that returns the SSR and I use it > directly in the command. > In case of homoscedastic normally distributed residuals, the Log-L is > indeed just: > > Log-L = -n/2*(ln (ssr/n) + 1 + ln 2pi) > > and I can use my function directly in the formula. > On the contrary, working directly with the log-L contributions is not > straightforward in my case. > > I would like to know if I could use the covariance matrix and the other > statistics generated by the program (in particular the information > criteria), if, instead of using the Log-L contributions, I simply divide > the Log-L by n. > > As far as the covariance is concerned, likely I cannot use the matrix > calculated from the outer product of the gradient, but can I use the > Hessian? > > Thanks a lot > Giuseppe