[R] scaling problems in "optim"

[Peter Dalgaard]

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
>
>
>
>
>   
Well, the gist is that optim is happiest when the function values 
f(beta) are not too large and not too small, and ditto for df/dbeta. You 
may e.g. get convergence issues if your data or your "covariates" are 
Molar concentrations when the actual values are on the order of 
microMolar.  "Covariates" in quotes because this is not linear, but the 
gradient df/dbeta plays the part in the local linearization. So you get 
the opportunity to rescale function values and parameters.

-- 
   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)              FAX: (+45) 35327907