[R] Likelihood returning inf values to optim(L-BFGS-B) other options?

[Michael Jungbluth]

Thank you very much for your postings. Rewriting the likelihood with  
lgamma helps a lot and the mistake with "fnscale" was quite stupid  
(Sorry for that!).

The model is working for most of the parameter sets but I am still  
facing some inf-returns on my (with lgamma updated and negative)  
loglikelihood if I am putting in some extreme parameter values (e.g.  
u-shaped beta densities for the simulation data which generates x,t_x  
and T). Actually these are the ones which are really interesting for  
my project. So, is there another similar optimization algorithm which  
can deal with inf-returns?

Thanks a lot!

Best regards,
Michael

Zitat von Prof Brian Ripley <ripley at stats.ox.ac.uk>:

> On Thu, 5 Apr 2007, Ravi Varadhan wrote:
>
>> In your code, the variables x (which I assume is the observed data), Tvec,
>> and flag are not passed to the function as arguments.  This could be a
>> potential problem.
>
> I think scoping will probably find them.
>
>> Another problem could be that you have to use "negative"
>> log-likelihood function as input to optim, since by default it "minimizes"
>> the function, whereas you are interested in finding the argmax of
>> log-likelihood.  So, in your function you should return (-ll) instead of ll.
>
> OR set fnscale.  This is the most serious problem.
>
>> If the above strategies don't work, I would try different initial values (it
>> would be best if you have a data-driven strategy for picking a starting
>> value) and different optimization methods (e.g. conjugate gradient with
>> "Polak-Ribiere" steplength option, Nelder-Mead, etc.).
>
> It looks to me as if the calculations are very vulnerable to
> overflow/underflow, as they use gamma and not lgamma.  They could be
> rearranged to be much stabler by computing the sum of logs for each
> sub-expression.
>
> There were over 50 warnings, which we were not shown.  They probably
> explained the problem.
>
> Beyond that, the feasible region seems to be the interior of the
> positive orthant, in which case transforming the parameters (e.g.
> working with their logs) would be a good idea.
>
> Finally, always supply analytical gradients when you can (as would be
> easy here).
>
>
>> -----Original Message-----
>> From: r-help-bounces at stat.math.ethz.ch
>> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of r at micom-solutions.de
>> Sent: Thursday, April 05, 2007 6:12 AM
>> To: r-help at stat.math.ethz.ch
>> Subject: [R] Likelihood returning inf values to optim(L-BFGS-B) other
>> options?
>>
>> Dear R-help list,
>>
>> I am working on an optimization with R by evaluating a likelihood
>> function that contains lots of Gamma calculations (BGNBD: Hardie Fader
>> Lee 2005 Management Science). Since I am forced to implement lower
>> bounds for the four parameters included in the model, I chose the
>> optim() function mith L-BFGS-B as method. But the likelihood often
>> returns inf-values which L-BFGS-B can't deal with.
>>
>> Are there any other options to implement an optimization algorithm
>> with R accounting for lower bounds and a four parameter-space?
>>
>> Here is the error message I receive (german):
>> --
>>>
>> out=optim(c(.1,.1,.1,.1),fn,method="L-BFGS-B",lower=c(.0001,.0001,.0001,.000
>> 1,.0001))
>> Fehler in optim(c(0.1, 0.1, 0.1, 0.1), fn, method = "L-BFGS-B", lower
>> = c(1e-04,  :
>> 	L-BFGS-B benötigt endliche Werte von 'fn'
>> Zusätzlich: Es gab 50 oder mehr Warnungen (Anzeige der ersten 50 mit
>> warnings())
>> --
>> And this is the likelihood function:
>> --
>> fn<-function(p) {
>>    A1=(gamma(p[1]+x)*p[2]^p[1])/(gamma(p[1]))
>>    A2=(gamma(p[3]+p[4])*gamma(p[4]+x))/(gamma(p[4])*gamma(p[3]+p[4]+x))
>>    A3=(1/(p[2]+Tvec))^(p[1]+x)
>>    A4=(p[3]/(p[4]+x-1))*((1/(p[2]+t_x))^(p[1]+x))
>>    ll=sum(log(A1*A2*(A3+flag*A4)))
>>    return(ll)
>> }
>>
>> Thank you very much for your help in advance!
>>
>> Best regards,
>>
>> Michael
>>
>> ______________________________________________
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>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>> ______________________________________________
>> R-help at stat.math.ethz.ch mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
> -- 
> Brian D. Ripley,                  ripley at stats.ox.ac.uk
> Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
> University of Oxford,             Tel:  +44 1865 272861 (self)
> 1 South Parks Road,                     +44 1865 272866 (PA)
> Oxford OX1 3TG, UK                Fax:  +44 1865 272595



-- 
Michael Jungbluth
Research Associate
Department of Marketing
Ingolstadt School of Management
CU-Eichstaett-Ingolstadt
Germany