maxLik (version 0.5-6)

maxLik: Maximum likelihood estimation

Description

This is just a wrapper for maximisation routines which return object of class "maxLik". Corresponding methods can correctly handle the likelihood-specific properties of the estimate including the fact that inverse of negative hessian is the variance-covariance matrix.

Usage

maxLik(logLik, grad = NULL, hess = NULL, start, method = "Newton-Raphson", ...)

Arguments

logLik

log-likelihood function. Must have the parameter vector as the first argument. Must return either a single log-likelihood value or a numeric vector where each component is log-likelihood corresponding to individual observations.

grad

gradient of log-likelihood. Must have the parameter vector as the first argument. Must return either single gradient vector with length equal to the number of parameters, or a matrix where each row corresponds to gradient vector of individua

hess

hessian of log-likelihood. Must have the parameter vector as the first argument. Must return a square matrix. If NULL, numeric gradient will be used.

start

numeric vector, initial value of parameters.

method

maximisation method, currently either "Newton-Rapshon", "BFGS", "BHHH", "SANN" or "NM" (for Nelder-Mead). Lower-case letters and shortcuts (as 'nr' for Newton-Raphson) allowed.

...

further arguments for the maximisation routine.

Value

• object of class 'maxLik' which inherits from class 'maxim'. Components are identical to those of class 'maxim', see maxNR.

See Also

maxNR, nlm and optim for different non-linear optimisation routines.

Examples

## ML estimation of exponential duration model:
t <- rexp(100, 2)
loglik <- function(theta) log(theta) - theta*t
gradlik <- function(theta) 1/theta - t
hesslik <- function(theta) -100/theta^2
## Estimate with numeric gradient and hessian
a <- maxLik(loglik, start=1, print.level=2)
summary(a)
## Estimate with analytic gradient and hessian
a <- maxLik(loglik, gradlik, hesslik, start=1)
summary(a)
##
##
## Next, we give an example with vector argument:  Estimate the mean and
## variance of a random normal sample by maximum likelihood
##
loglik <- function(param) {
  mu <- param[1]
  sigma <- param[2]
  ll <- -0.5*N*log(2*pi) - N*log(sigma) - sum(0.5*(x - mu)^2/sigma^2)
  ll
}
x <- rnorm(1000, 1, 2) # use mean=1, stdd=2
N <- length(x)
res <- maxLik(loglik, start=c(0,1)) # use 'wrong' start values
summary(res)