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From |
Sun Yutao <yutao.sun.statalist@outlook.com> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: inaccurate hessian from mata: deriv() |

Date |
Fri, 26 Oct 2012 15:33:36 +0200 |

Thanks Maarten, But I would consider a case where I do not know the loglikelihood when I'm writing the code....and later yesterday I found that it was because of the h-value (or delta or e depending on how you want to call it), it looks like the default 1e-6 was way too small for this kind of functions and derivatives. Other values such as 0.01 give a very similar result as -ml-. I will find some book on that issue... By the way I see your point in the log likelihood function, it was from a script from my professor and probably he made a mistake or something...the weirdest thing is it was working (seemingly)...let me see what will happen if I change it to normal() Best regards, Sun Yutao -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Maarten Buis Sent: Thursday, October 25, 2012 8:42 PM To: statalist@hsphsun2.harvard.edu Subject: Re: st: inaccurate hessian from mata: deriv() The solution is simple, use -ml- if you want to use Stata or -moptimze()- if you want to use Mate. Alternatively, you can work out the analytical solution, which is not that hard for a -probit-. The easiest solution is just not to program what is already implemented in Stata, and just use -probit-. Regardless of which solution you choose, your log likelihood function is wrong: you should use -normal()- instead of -normprob()- as the latter is obsolete. More importantly, you never want to code -(1-normal(`xb'))- if you can avoid it. Instead you should use -normal(-`xb')-. Mathematically, the two are equivalent, but for computers the latter computation is much more precise than the former. See: William Gould (2006) "Mata Matters: Precision" The Stata Journal, 6(4): 550-560. <http://www.stata-journal.com/article.html?article=pr0025> Hope this helps, Maarten On Thu, Oct 25, 2012 at 7:24 PM, Sun Yutao <yutao.sun.statalist@outlook.com> wrote: > Hello users, > > I¡¯m having a problem on the function derive(), it looks like it¡¯s > giving a very inaccurate hessian. Here the problem goes: > > I wrote a Stata probit log-like function and enveloped it with a Mata > function, which does no more than compute and sum the log-likelihood > contributions from the Stata program. > ---------------------------------------------------------- > function MleLikeMata(input_param,struct mPML_model scalar model,|LogLik) { > if (cols(input_param)!=1) { > param=input_param' > } else { > param=input_param > } > > for(i=1;i<=rows(model.equation);i++) { > data_range=strtoreal(tokens(model.equation[i,7])) > param_range=model.location[i,1]::model.location[i,2] > if (model.equation[i,4]=="1") { > > model.data[.,model.offset+i]=(model.data[.,data_range],J(rows(model.data),1,1))*param[param_range,.] > } else { > model.data[.,model.offset+i]=model.data[.,data_range]*param[param_range,.] > > } > } > stata(model.StataLike+" "+model.XB) > LogLik=sum(model.data[.,model.offset]) > //LogLik=model.data[.,model.offset] > if (args()==2) { > return(LogLik) > } > } > ---------------------------------------------------------- > Where model is just an extra argument I need > > > Then I use this code to compute the gradients and hessian: > ---------------------------------------------------------- > D=deriv_init() > deriv_init_evaluator(D,&MleLikeMata()) > //deriv_init_evaluatortype(D,"v") > deriv_init_search(D, "off")deriv_init_params(D, > param') > deriv_init_argument(D, 1, model) > grad=deriv(D, 1)' > hess=deriv(D, 2) > ---------------------------------------------------------- > > It looks like it's giving a more or less OK gradient but a VERY > inaccurate hessian (I'm comparing this with stata ml command with the > same data and same parameter vector, but -ml- works well!) , i.e. I'm > 100% sure the Stata probit log-likelihood function is concave and > hence the hessian should be negative-definite. > however, it gives some hessian like this. > > +----------------------------------------------------------------------------+ > 1 | 238418.5803 > 2 | -119209.2902 476837.1606 > 3 | -178813.9352 -327825.5479 417232.5155 > 4 | -59604.64508 -119209.2902 -208616.2578 357627.8705 > 5 | 149011.6127 -178813.9352 -59604.64508 29802.32254 > 0 > > +--------------------------------------------------------------------- > -------+ The determinant is 2.43788e+27 which means it's certainly not > negative-definite (and you even have a 0 in the diagonal) > > Possible fix I tried: > > 1. I tried to specify it as a v-type evaluator (one that returns a row > vector) 2. I tried to scale sum of the log-likelihood by number of > observations 3. change the 2nd argument in -deriv_init_search(D, > "off")- to "bracket" or "interpolate" (which gives even worse results) > > Could anyone kindly explain me what's wrong and what I should do? > > And infact I think I lost a lot features (fast convergence, etc.) from > Newton-Raphson due to the inaccurate hessian. > > Oh in case you need, the Stata likelihood function is: > --------------------------------------------------- > program define like, nclass > qui { > args lnf XB > replace `lnf' = ln( 1 - normprob(`XB')) if $ML_y1==0 > replace `lnf' = ln( normprob(`XB')) if $ML_y1==1 > } > End > --------------------------------------------------- > Which is the common one for probit > > > > Best regards, > Sun Yutao > > > > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/faqs/resources/statalist-faq/ > * http://www.ats.ucla.edu/stat/stata/ -- --------------------------------- Maarten L. Buis WZB Reichpietschufer 50 10785 Berlin Germany http://www.maartenbuis.nl --------------------------------- * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**References**:**st: inaccurate hessian from mata: deriv()***From:*Sun Yutao <yutao.sun.statalist@outlook.com>

**Re: st: inaccurate hessian from mata: deriv()***From:*Maarten Buis <maartenlbuis@gmail.com>

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