p.s. With proper scaling, 'optim' gives the correct answer in this case:
(mle2 <- optim(rep(0, 2), dmvnorm, method='CG',
control=list(fnscale=-10, trace=9),
mean=1:2, hessian=TRUE, log=TRUE))
$par
[1] 0.9999917 1.9999833
However, as noted below, with parscale = c(0.3, 3), only a
difference of a factor of 9 in the scaling between the two parameters,
the first parameter = 0.735 rather than 1; the second is identified
correctly.
Spencer
Spencer Graves wrote:
> ALL:
>
> Can anyone explain why optim returns c(0.75, 2) for what I think
> should be the maximum of a bivariate normal density with mean = 1:2?
>
>
> KATHIE:
>
> Apart from 'optim' giving an answer I don't understand, the
> following should illustrate the use of 'fnscale' and 'parscale' -- while
> perhaps illustrating the need to use these parameters.
>
> Hope this helps.
> Spencer Graves
>
> library(mvtnorm)
> (mle2 <- optim(rep(0, 2), dmvnorm, method='CG',
> control=list(fnscale=-10, parscale=c(.3, 3), trace=9),
> mean=1:2, hessian=TRUE, log=TRUE))
> Conjugate gradients function minimizer
> Method: Fletcher Reeves
> tolerance used in gradient test=3.63798e-12
> 0 1 0.433788
> parameters 0.00000 0.00000
> i> 1 3 0.234892
> parameters 0.03000 0.60000
>
> <snip>
>
> i> 100 201 0.187167
> parameters 2.46674 0.66667
> $par
> [1] 0.7352784 2.0000004 # = approximately c(2.46674, 0.66667) * parscale
>
> $value
> [1] -1.871671 # = 0.187167 * fnscale
>
> $counts
> function gradient
> 201 101
>
> $convergence
> [1] 1
>
> $message
> NULL
>
> $hessian
> [,1] [,2]
> [1,] -1.00000e+00 -9.94586e-11
> [2,] -9.94586e-11 -1.00000e+00
>
> # Checks:
> > dmvnorm(c( 0.7352784, 2.0000004), mean=1:2, log=TRUE)
> [1] -1.872916
> > dmvnorm(1:2, mean=1:2, log=TRUE)
> [1] -1.837877
>
>
> kathie wrote:
>
>> Dear R users,
>>
>> I am trying to figure out the control parameter in "optim," especially,
>> "fnscale" and "parscale."
>>
>> In the R docu.,
>>
>> ------------------------------------------------------
>> fnscale
>>
>> An overall scaling to be applied to the value of fn and gr during
>> optimization. If negative, turns the problem into a maximization problem.
>> Optimization is performed on fn(par)/fnscale.
>>
>> parscale
>>
>> A vector of scaling values for the parameters. Optimization is performed
>> on par/parscale and these should be comparable in the sense that a unit
>> change in any element produces about a unit change in the scaled value.
>> ------------------------------------------------------
>>
>> I cannot understand these two statements.
>>
>> "Optimization is performed on fn(par)/fnscale." and
>>
>> "Optimization is performed on par/parscale and these should be comparable in
>> the sense that a unit change in any element produces about a unit change in
>> the scaled value."
>>
>> Would you please explain these things?
>>
>> Thank you in advance.
>>
>> Kathryn Lord
>>
>>
>>
>>
>>
>>
>
> ______________________________________________
> R-help@r-project.org 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.
>
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