Question

I am trying to optimise my likelihood function of R_j and R_m using optim to estimate al_j, au_j, b_j and sigma_j. This is what I did.

a = read.table("D:/ff.txt",header=T)
attach(a)   
a

  R_j         R_m
1  2e-03 0.026567295
2  3e-03 0.009798475
3  5e-02 0.008497274
4 -1e-02 0.012464578
5 -9e-04 0.002896023
6  9e-02 0.000879473
7  1e-02 0.003194435
8  6e-04 0.010281122

The parameters al_j, au_j, b_j and sigma_j need to be estimated.

llik=function(R_j,R_m)
 if(R_j< 0)
 {
 sum[log(1/(2*pi*(sigma_j^2)))-(1/(2*(sigma_j^2))*(R_j+al_j-b_j*R_m))^2]
 }else if(R_j>0)
 {
 sum[log(1/(2*pi*(sigma_j^2)))-(1/(2*(sigma_j^2))*(R_j+au_j-b_j*R_m))^2]
 }else if(R_j==0)
 {
 sum(log(pnorm(au_j,mean=b_j*R_m,sd=sigma_j)-pnorm(al_j,mean=b_j*R_m,sd=sigma_j)))
 }

start.par=c(al_j=0,au_j=0,sigma_j=0.01,b_j=1) 
out1=optim(llik,par=start.par,method="Nelder-Mead")

Error in pnorm(au_j, mean = b_j * R_m, sd = sigma_j) : 
  object 'au_j' not found

Answer 1

It is difficult to tell where to start on this.

As @mac said, your code is difficult to read. It also contains errors.

For example, if you try sum[c(1,2)] you will get an error: you should use sum(c(1,2)). In any case, you seem to be taking the sum in the wrong place. You cannot use if and else if on vectors, and need to use ifelse. You have nothing to stop the standard deviation going negative. There is more.

The following code runs without errors or warnings. You will still have to decide whether it does what you want.

a <- data.frame( R_j = c(0.002,0.003,0.05,-0.01,-0.0009,0.09,0.01,0.0006),
                 R_m = c(0.026567295,0.009798475,0.008497274,0.012464578,
                         0.002896023,0.000879473,0.003194435,0.010281122) )

llik = function(x) 
   { 
    al_j=x[1]; au_j=x[2]; sigma_j=x[3];  b_j=x[4]
    sum(
        ifelse(a$R_j< 0, log(1/(2*pi*(sigma_j^2)))-
                           (1/(2*(sigma_j^2))*(a$R_j+al_j-b_j*a$R_m))^2, 
         ifelse(a$R_j>0 , log(1/(2*pi*(sigma_j^2)))-
                           (1/(2*(sigma_j^2))*(a$R_j+au_j-b_j*a$R_m))^2,
                          log(pnorm(au_j,mean=b_j*a$R_m,sd=sqrt(sigma_j^2))-
                           pnorm(au_j,mean=b_j*a$R_m,sd=sqrt(sigma_j^2))))) 
       )
   } 

start.par = c(0, 0, 0.01, 1) 
out1 = optim(llik, par=start.par, method="Nelder-Mead")