On 14-04-2011, at 09:00, Kristian Lind wrote:
> HI Berend,
>
> Thank you for your reply.
>
> ......
> Finally the likelihood function at the end of your code
>
> #Maximum likelihood estimation using mle package
> library(stats4)
> #defining loglikelighood function
> #T <- length(v)
> #minuslogLik <- function(x,x2)
> #{ f <- rep(NA, length(x))
> # for(i in 1:T)
> # {
> # f[1] <- -1/T*sum(log(transdens(parameters = parameters, x =
> c(v[i],v[i+1])))-log(Jac(outmat=outmat, x2=c(v[i],r[i])))
> # }
> # f
> # }
>
> How do the arguments of your function x and x2 influence the calculations in
> the likelihood function?
>
> What I was thinking was that the x and x2 would be the input for the
> transdens() and Jac() functions, but I guess that is already taken care of
> when defining them.
>
Huh?
If you define zz <- function(x) {...} x is an argument which must be specified
when using the function.
> As written now with argument x and x2 not being used in the body of the
> function, there is nothing to optimize.
>
> That is correct and that is the problem. The likelihood need to be stated as
> a function of the parameters, here the vector "parameters". Because in the
> maximum likelihood estimation we want to maximize the value of the likelihood
> function by changing the parameter values. The likelihood function is a
> function of the parameters but only through the functions, for example
> Kristian() is a function of "parameters" which feeds into Bo(), transdens()
> and Jac(). Do you have any suggestions how to get around this issue?
>
What kind of problem?. Why don't you then do (parameters and outmat already
known globally)
f[i] <- -1/T*sum(log(transdens(parameters = parameters, x =
x))-log(Jac(outmat=outmat, x2=x2)))
You should pass the arguments used by the optimizer in calling your likelihood
function to the functions you defined. That way f[] will depend on x and x2 and
so will the likelihood.
> Shouldn't f[1] be f[i] because otherwise the question is why are looping
> for( i in 1:T)?
> But then returning f as a vector seems wrong here. Shouldn't a likelihood
> function return a scalar?
>
> The likelihood function should return a scalar. I think the fix could be to
> make the function calculate the function value at each "i" and then make it
> return the mean of all the f[i]s.
>
Is the mean a likelihood?
Berend
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