maxLik (version 0.5-6)

hessian: Hessian matrix

Description

This function extracts the Hessian of the M-estimator of statistical model. It should be supplied by the underlying optimisation algorithm, possibly using approximations.

Usage

hessian(x, ...)
## S3 method for class 'default':
hessian(x, \dots)

Arguments

x

a M-estimator based statistical model

...

other arguments for methods

Value

• A numeric matrix, the Hessian of the model at the estimated parameter values. If the maximum is flat, the Hessian is singular. In that case you may want to invert only the non-singular part of the matrix. You may also want to fix certain parameters (see activePar).

See Also

maxLik, activePar

Examples

# log-likelihood for normal density
# a[1] - mean
# a[2] - standard deviation
ll <- function(a) sum(-log(a[2]) - (x - a[1])^2/(2*a[2]^2))
x <- rnorm(1000) # sample from standard normal
ml <- maxLik(ll, start=c(1,1))
# ignore eventual warnings "NaNs produced in: log(x)"
summary(ml) # result should be close to c(0,1)
hessian(ml) # How the Hessian looks like
sqrt(-solve(hessian(ml))) # Note: standard deviations are on the diagonal
#
# Now run the same example while fixing a[2] = 1
mlf <- maxLik(ll, start=c(1,1), activePar=c(TRUE, FALSE))
summary(mlf) # first parameter close to 0, the second exactly 1.0
hessian(mlf)
# Now look at the Hessian.  Note that the second component has is not
# related to the curvature of the object function:
sqrt(-solve(hessian(mlf))) # works in current case, although you may get
                           # warnings.  
# now invert only the free parameter part of the Hessian
sqrt(-solve(hessian(mlf)[activePar(mlf), activePar(mlf)]))
# gives the standard deviation for the mean