Re: [Gretl-users] Quadratic form in log-likelihood (CONT'D)

Thanks for this. I waited until I run various cases before providing feedback. Both approaches work fine in general... but not in a specific model I work with now. And I cannot understand why, because even in the simple bivariate normal example, the qqq construct includes parameters under estimation in any case. So I would really appreciate any idea why the following does not work (it gives immediately a numerical derivative value of exactly zero for the rho correlation parameter irrespective of starting value, which is suspicious, and stays there for ever, and after some iterations it aborts with a message "matrix is not positive-definite") . I am not saying that it necessarily has to do with the code, it may be the model's problem. But the thing is,  if I write out explicitly the likelihood (since this is the bivariate case), without using the qqq construct, the code does provide results, this is why I am at a loss here. <hansl> [data...] [starting values for the parameters...] matrix R2 = {1,rho; rho,1} mle logl = check ? -0.5*ldet(R2) -0.5*qqq  + 0.5*((invcdf(N,CDF))^2)  +  log(B1+B2) :NA    series resCor = Depv - Regrs*kVec     series B1 = (resCor/vu)+ ...     series B2 = (resCor/vu) +... series CDF = cnorm(resCor/vu) + mix*B1 - (1-mix)*B2      matrix q = {W, invcdf(N,CDF)}     matrix qq = q*inv(R2)     series qqq = sumr(q.*qq) scalar check = (vu>0)   && (mix>0) && (mix < 1)   && (abs(rho)<1) params kVec vu mix rho end mle </hansl> Alecos Papadopoulos PhD Candidate Athens University of Economics and Business, Greece School of Economic Sciences Department of Economics https://alecospapadopoulos.wordpress.com/ On 16/2/2018 09:22, gretl-users-request(a)lists.wfu.edu wrote: Having said this, though, there's a more general point, on the check for positive definiteness of S. If you reparametrise the problem, you can make S pd by construction simply optimising over the elements of the Cholesky factor of S rather than S itself. This is a very nice trick, which saves you lots of intermediate computation, works quite well in practice and is trivial to generalise to any number of columns of q. For example: <hansl> nulldata 128 series N1 = normal() series N2 = normal() scalar s1 = 1 scalar s2 = 1 scalar c12 = 0.5 matrix q = {N1, N2} matrix S = I(2) matrix theta = vech(S) mle logl = -0.5 * (qqq + ldet(S)) matrix K = lower(unvech(theta)) matrix S = K*K' matrix qq = q * invpd(S) series qqq = sumr(q.*qq) params theta end mle # check Shat = q'q ./ $nobs eval cholesky(Shat) </hansl> Hope this helps. ------------------------------------------------------- Riccardo (Jack) Lucchetti Dipartimento di Scienze Economiche e Sociali (DiSES) Universit? Politecnica delle Marche (formerly known as Universit? di Ancona) r.lucchetti(a)univpm.it http://www2.econ.univpm.it/servizi/hpp/lucchetti