[R] scaling problems in "optim"

[Spencer Graves]

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
>>
>>
>>
>>
>>
>>     
>
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