[R] Optim: Function definition

[Serguei Kaniovski]

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
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