How to set parameters constraints in a function? (Matt Shotwell)

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

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

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