When there is a constraint like this, it is often the case that the
likelihood function may the value zero. Hence, the log-likelihood may
take the value -Inf. You could impose this constraint with something
like
if( kappa >= alpha ) {
ll <- -Inf
} else
ll <- n*log(alpha/gamma(kappa))+
kappa*alpha*sum(log(x))-
n*kappa*alpha*log(lam)-
kappa*alpha*sum(log(psi))-
lam^(-alpha)*sum((x/psi)^alpha)
}
However, if you are using the 'optim' function, or some other function
for optimization, you may prefer to impose this constraint by telling
the optimization routine not to search at values in ( kappa >= alpha ).
Also, you may find it helpful to pass the variable 'x' as part of the
function call (i.e. mll <- function(param, x). This may avoid some
hard-to-diagnose errors.
-Matt
On Mon, 2010-05-24 at 22:31 +1000, Carol Gao wrote:
> > Dear R list,
> >
> > I have a function specifying my log-likelihood, and now I need to
> set the
> > constraint that *alpha > kappa*, could anyone help me with setting
> this in
> > my function?
> >
> > the function is defined as follows:
> >
> > mll <- function(param){
> > n <- length(x)
> > psi <- numeric(n)
> > psi[1] <- 1.0
> > a0 <- exp(param[1]); a1 <-exp(param[2]); b1 <- exp(param[3]);
> *alpha *<-
> > exp(param[4]); *kappa *<- exp(param[5]);
> >
> > for (i in 2:n) {psi[i] <- a0 + a1*x[i-1] + b1*psi[i-1]}
> > lam <- gamma(kappa)/gamma(kappa+(1/alpha))
> > ll <-
> >
> n*log(alpha/gamma(kappa))+kappa*alpha*sum(log(x))-n*kappa*alpha*log(lam)-kappa*alpha*sum(log(psi))-lam^(-alpha)*sum((x/psi)^alpha)
> > return(list(maxl=-ll,vpsi=psi))
> > }
> >
> > Thanks in advance!!
> >
> > Cheers,
> >
> > Carol
> >
> > [[alternative HTML version deleted]]
> >
> > ______________________________________________
> > R-help@r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
>
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