RE: st: maximum simulated likelihood

["Jun Xu" <mystata@hotmail.com>]

Dear Professor Jenkins and other listers,

1. Thanks for correcting my incorrect terminology. I should use msl (maximum 
simulated likelihood)
2. So I would say that we HAVE to create those random variables outside the 
loop first, right?
3. With slight change in the last line, my new code now is
*****************************
    forval i = 1/100   {
       tempname ed`i'
       gen double `ed`i'' = -ln(uniform()) // just a very ad hoc way of 
creating random vars
    }

    qui forval i = 1/100 {
        replace `sp'= `sp' * (invlogit(`xb' + `ed`i'')) if $ML_y1 == 1
        replace `sp'= `sp' * (invlogit(-(`xb' + `ed`i''))) if $ML_y1 == 0
    }

    qui replace `lnf' = (ln(`sp')/100)
********************************
One more question:
I use simplest lf method. I am not quite sure why I need to have
    "qui replace `lnf' = `lnf' + (ln(`sp')/100)" (say Option A) instead of 
"qui replace `lnf' = (ln(`sp')/100)" (say Option B). For Option A, I cannot 
get it converged. Option B converged. Regardless of the convergence, I am 
just wondering which one is right.

Thanks a lot




Jun Xu
Ph.D. Candidate
Department of Sociology
Indiana University at Bloomington






> From: Jenkins S P <stephenj@essex.ac.uk>
> Reply-To: statalist@hsphsun2.harvard.edu
> To: statalist@hsphsun2.harvard.edu
> Subject: st: maximum simulated likelihood Date: Sun, 28 Aug 2005 14:10:31 
> +0100 (BST)
>
>
> > Date: Sat, 27 Aug 2005 12:15:36 -0500
> > From: "Jun Xu" <mystata@hotmail.com>
> > Subject: st: simulate maximum likelihood estimation--where to
> > construct the random variables
> >
> > A while ago, Professor Stephen P. Jenkins and Arne Uhlenforff
> > had exchanges
> > on this:
> >
> > Arne Uhlenforff <auhlendorff@diw.de> wants to estimate a MNL
> > model with a
> > random intercept using simulated ML (rather than using -gllamm-).
> >
> > **********
> > I haven't looked at your program in detail, but one thing
> > that strikes me is
> > that I think you are not treating the pseudo-random uniform
> > draws correctly.
> > You want 50 replications/draws per ML iteration, but are
> > creating them anew
> > every iteration -- you shouldn't. They should be created just
> > once. (See
> > e.g. the gory details of the code underlying -mvprobit- or
> > associated SJ
> > article.) I don't know if this is having knock-on effects elsewhere.
> >
> > good luck
> > Stephen
> > ***********
> >
> > I am also trying to write some codes on simulated ml as
> > practice. I did it
> > in two ways, a first method is to generate 100 random
> > variables outside the
> > loop as below; a second method is to create `ed`i' (the
> > random variable)
> > anew in each iteration.
> >
> > Method 1:
> >      forval i = 1/100   {
> >         tempname ed`i'
> >         gen double `ed`i'' = ...whatever ways to generate the random
> > variable
> >      }
> >
> >      qui forval i = 1/100 {
> >          replace `sp'= `sp' * (invlogit(`xb' + `ed`i'')) if
> > $ML_y1 == 1
> >          replace `sp'= `sp' * (invlogit(-(`xb' + `ed`i'')))
> > if $ML_y1 == 0
> >      }
> >
> >    qui replace `lnf' = ln(`sp')
> >
> > Method 2:
> >      forval i = 1/100   {
> >         tempname ed`i'
> >
> >      }
> >
> >      qui forval i = 1/100 {
> >         gen double `ed`i'' = ...whatever ways to generate the random
> > variable
> >          replace `sp'= `sp' * (invlogit(`xb' + `ed`i'')) if
> > $ML_y1 == 1
> >          replace `sp'= `sp' * (invlogit(-(`xb' + `ed`i'')))
> > if $ML_y1 == 0
> >      }
> >
> >    qui replace `lnf' = ln(`sp')
> >
> > Strangely enough Method 1 will converge and Method 2 will
> > never converge. I
> > am not sure if this is what Professor Jenkins talked about
> > and why it is so?
> > I will appreciate any thoughts on this.
> There were 2 points raised by Arne Uhlendorff and myself in the earlier 
> discussion:
> 1. the need to create the pseudo-random variables "outside" the -ml- 
> iteration loop, doing it once and for all ab initio. [Your method 1.]
> 2. (Arne's follow-up point) the need to average the simulated
> likelihoods (the average is over the simulations) per -ml- iteration.
>
> Remember that the method is really "maximum simulated likelihood" (not 
> "simulated maximum likelihood").  The draws, outside the loop as you phrase 
> it, are used to calculate the simulated likehood at each iteration. That 
> calculation also requires averaging.  Your code appears not to average. If 
> you look inside "mvprob_ll.ado", the subroutine associated with the 
> -mvprobit- program, you will see a line like
>         replace `lnf' = `lnf' + `sp$S_MLE_M'/$S_MLE_D This is related to 
> the averaging process.
>
> A third point, implicit in Arne's discussion, was the use of another 
> program, -gllamm- in his case,  to check (or more generally, "certify") 
> that his program was giving the results expected. [I conjecture that Arne 
> was writing his own specialist program because -gllamm- was slow-running 
> for his particular problem.]  An alternative is to generate some simulated 
> data and equations with 'known' coefficients, and then to estimate this 
> with your model.  [There is an example of this in the Stata Journal SJ 3-3 
> article about -mvprobit-. The program itself was updated in SJ 5-2.]
> When you have got your program running, I suggest some of this sort of 
> checking.
>
>
> Stephen
> =============================================
> Professor Stephen P. Jenkins <stephenj@essex.ac.uk>
> Institute for Social and Economic Research (ISER)
> University of Essex, Colchester CO4 3SQ, UK
> Phone: +44 1206 873374.  Fax: +44 1206 873151.
> http://www.iser.essex.ac.uk
> Survival Analysis Using Stata: 
> http://www.iser.essex.ac.uk/teaching/degree/stephenj/ec968/index.php
>
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