[R] selection of optim parameters

[Charles C. Berry]

On Mon, 5 Jul 2010, Fabian Gehring wrote:

> Hi all,
>
> I am trying to rebuild the results of a study using a different data set. I'm 
> using about 450 observations. The code I've written seems to work well, but I 
> have some troubles minimizing the negative of the LogLikelyhood function 
> using 5 free parameters.
>
> As starting values I am using the result of the paper I am rebuiling. The 
> system.time of the calculation of the function is about 0.65 sec. Since the 
> free parameters should be within some boundaries I am using the following 
> command:
>
> optim(fn=calculateLogLikelyhood, c(0.4, 2, 0.4, 80000, 0.8), 
> lower=c(0,0,0,0,0), upper=c(1, 5, Inf, Inf, 1), control=list(trace=1, 
> maxit=1000))
>
> Unfortunately the result doesn't seem to be reasonable. 3 of the optimized 
> parameters are on the boundaries.

You haven't said why this is unreasonable.

A suggestion: Profile the loglikelihood around the starting value and 
around the putative maximum. (This might help with the parscale issue.)

Also, you might try something like

apply(rbind(0,eps*as.matrix(expand.grid(rep(list(c(-1,0,1)),5)))),1,
 	function(x) calculateLogLikelyhood( x + y ) )

where y is the starting value (or the value achieved by optim()) and 'eps' 
is small enough to make small changes in the function value might help you 
see what gives. (It might be necessary to scale each column in 
as.matrix(...) separately, 'though.)

In addition to inspecting the results by eyeball, you can fit the results 
to a quadratic form in rbind(...) using lm() and then figure out roughly 
where to go to find the maximum of your function.

If this isn't enough to get you started, at least it might enable you to 
say more clearly what is not reasonable about your results.

HTH,

Chuck

>
> Unfortunately I don't have much experience using optimizatzion methods. 
> That's why I am asking you. Do you have any hints for me what should be 
> taken into account when doing such an optimization.
>
> Is there a good way to implement the boundaries into the code (instead of 
> doing it while optimizing)? I've read about parscale in the help-section. 
> Unfortunately I don't really know how to use it. And anyways, could this 
> help? What other points/controls should be taken into account?
>
> I know that this might be a bit little information about my current code. But 
> I don't know what you need to give me some advise. Just let me know what you 
> need to know.
>
> Thankds
>
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Charles C. Berry                            (858) 534-2098
                                             Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu	            UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901