# [R] maximizing a function

Uwe Ligges ligges at statistik.uni-dortmund.de
Sun Oct 28 16:36:37 CET 2007

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Nigel.Walker at studentmail.newcastle.edu.au wrote:
> Hi list,
> I would like to maximize a likelihood function to obtain estimates. The problem is that i first have to have functions other functions that are in the likelihood that depend on the parameters. I was thinking of using optim but i do not know how to go about starting. A example of what i wish to do is given below. The parameters i wish to estimate are phi and gamma.
>
> How would i go about maximizing the likelihood function to obtain estimates?
>
> Any help would be much appreciated
>
> Nigel
>
> # initial starting points
> phi<-0.2
> gamma<-0.1
> n<-200
> h<-c()
> h[1]<-1
> e<-c()
> e[1]<-1
> for (i in 2:n){
> h[i]<-phi*e[i-1]+gamma*h[i-1]+3
> e[i]<-rnorm(1,0,h[i])
> }
> likelihood<- sum(log(h)+e^2/2*h)

You want

lik <- function(par, n=200){
phi <- par[1]
gamma <- par[2]
h <- numeric(n)
h[1] <- 1
e <- numeric(n)
e[1] <- 1
for (i in 2:n){
h[i] <- phi*e[i-1] + gamma*h[i-1] + 3
e[i] <- rnorm(1,0,h[i])
}
## optim minimizes, hence using negative sum:
-sum(log(h) + e^2/2*h)
}

set.seed(1)
optim(c(phi=0.3, gamma=0.1), lik, n=200)

and you will find that your function is highly dependend on the random
numbers you are generating, hence using a seed. I wonder where the
random term comes from. Probably there is some error in the likelihood?

Uwe Ligges

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