[R] Optim: Function definition

[Spencer Graves]

      Have you tried making contour plots of your objective function, 
e.g., using expand.grid and 'contour' or 'contourplot', as described in 
Venables and Ripley (2002) Modern Applied Statistics with S (Springer)? 

      Hope this helps. 
      Spencer Graves

Serguei Kaniovski wrote:
> Hi all,
>
> I apply "optim" to the function "obj", which minimizes the goodness of 
> fit statistic and obtains Pearson minimum chi-squared estimate for x[1], 
> x[2] and x[3]. The vector "fr" contains the four observed frequencies.
>
> Since "fr[i]" appears in the denominator, I would like to substitute "0" 
> in the sum if fr[i]=0.
>
> I tried an "ifelse" condition which works, but in some cases the 
> solution seems rather odd. Is there anything wrong with the way second 
> objective function is coded?
>
> obj<-function(x){
> (fr[1]-x[1]*x[2]-x[3]*sqrt(x[1]*(1-x[1])*x[2]*(1-x[2])))^2/fr[1]+
> (fr[2]-(1-x[1])*x[2]+x[3]*sqrt(x[1]*(1-x[1])*x[2]*(1-x[2])))^2/fr[2]+
> (fr[3]-x[1]*(1-x[2])+x[3]*sqrt(x[1]*(1-x[1])*x[2]*(1-x[2])))^2/fr[3]+
> (fr[4]-(1-x[1])*(1-x[2])-x[3]*sqrt(x[1]*(1-x[1])*x[2]*(1-x[2])))^2/fr[4]
> }
>
> obj<-function(x){
> ifelse(fr[1]==0,0,(fr[1]-x[1]*x[2]-x[3]*sqrt(x[1]*(1-x[1])*x[2]*(1-x[2])))^2/fr[1])+
> ifelse(fr[2]==0,0,(fr[2]-(1-x[1])*x[2]+x[3]*sqrt(x[1]*(1-x[1])*x[2]*(1-x[2])))^2/fr[2])+
> ifelse(fr[3]==0,0,(fr[3]-x[1]*(1-x[2])+x[3]*sqrt(x[1]*(1-x[1])*x[2]*(1-x[2])))^2/fr[3])+
> ifelse(fr[4]==0,0,(fr[4]-(1-x[1])*(1-x[2])-x[3]*sqrt(x[1]*(1-x[1])*x[2]*(1-x[2])))^2/fr[4])
> }
>
> sval=rep(0.1,3)
> fr<-c(0,0.1,0.2,0.3)
>
> optim(sval,obj, method="BFGS")$par
>
> Thank you,
> Serguei
>