findL3 {ELYP} | R Documentation |
This program is the sister program to the findU3( ). It uses simple search to find the lower 95% Wilks confidence limits based on the log likelihood function supplied.
findL3(NPmle, ConfInt, LogLikfn, Pfun, level=3.84, dataMat)
NPmle |
a vector containing the two NPMLE: beta1 hat and beta2 hat. |
ConfInt |
a vector of length 3. |
LogLikfn |
a function that compute the loglikelihood. Typically this has three parameters: beta1, beta2 and lam, in a Yang-Prentice model context. |
Pfun |
a function that takes the input of 3 parameter values (beta1,beta2 and Mulam) and returns a parameter that we wish to find the confidence Interval of (here only the Lower Value). |
level |
confidence level. Default to 3.84 for 95 percent. |
dataMat |
a matrix. |
The empirical likelihood for Y-P model has parameters: beta1, beta2 and a baseline. The baseline is converted to a 1-d parameter feature via Hfun, and then amount controled by lam.
Basically we repeatedly testing the value of the parameter, until we find those which the -2 log likelihood value is equal to 3.84 (or other level, if set differently).
A list with the following components:
Lower |
the lower confidence bound. |
minParameterNloglik |
Final values of the 4 parameters, and the log likelihood. |
Mai Zhou
Zhou, M. (2002). Computing censored empirical likelihood ratio by EM algorithm. JCGS
## Here Mulam is the value of int g(t) d H(t) = Mulam
## For example g(t) = I[ t <= 2.0 ]; look inside myLLfun().
Pfun <- function(b1, b2, Mulam) {
alpha <- exp(-Mulam)
TrtCon <- 1/(alpha*exp(-b1) + (1-alpha)*exp(-b2))
return(TrtCon)
}
data(GastricCancer)
# The following will take about 10 sec. to run on i7 CPU.
# findL3(NPmle=c(1.816674, -1.002082), ConfInt=c(1.2, 0.5, 10),
# LogLikfn=myLLfun, Pfun=Pfun, dataMat=GastricCancer)