SMPracticals (version 1.3-1)

lik.ci: 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

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)