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# Re: st: inaccurate hessian from mata: deriv()

 From Maarten Buis To statalist@hsphsun2.harvard.edu Subject Re: st: inaccurate hessian from mata: deriv() Date Thu, 25 Oct 2012 20:41:54 +0200

```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latter is obsolete.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)
> 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
>
>
>
>
> *
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> *   http://www.ats.ucla.edu/stat/stata/

--
---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

http://www.maartenbuis.nl
---------------------------------

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```