lik.ci {SMPracticals} | R Documentation |
Likelihood Confidence Intervals for Scalar Parameter
Description
A simple function for computing confidence intervals from the values of a likelihood function for a scalar parameter. It prints the maximum likelihood estimate (MLE) and its standard error, and confidence intervals based on normal approximation to the distribution of the MLE and on the chi-squared approximation to the distribution of the likelihood ratio statistic.
Usage
lik.ci(psi, logL, conf = c(0.975, 0.025))
Arguments
psi |
Vector containing parameter values, the range of which contains the MLE |
logL |
Vector containing corresponding log likelihood values |
conf |
Vector containing levels for which confidence interval limits needed |
Value
See above
Note
This uses the spline functions in library(modreg).
Author(s)
Anthony Davison (Anthony.Davison@epfl.ch)
References
Davison, A. C. (2003) Statistical Models. Cambridge University Press. Sections 4.4.2, 4.5.1.
Examples
# likelihood analysis for mean of truncated Poisson data
y <- c(1:6)
n <- c(1486,694,195,37,10,1)
logL <- function(x, y, n.obs) # x is theta
{ f <- dpois(y,x)/(1-dpois(0,x)) # dpois is Poisson PDF
sum(n*log(f)) } # log likelihood
theta <- seq(from=0.8, to=1, length=200)
L <- rep(NA, 200)
for (i in 1:200) L[i] <- logL(theta[i], y, n)
plot(theta, L, type="l", ylab="Log likelihood")
lik.ci(theta, L)