plkhci {Bhat} R Documentation

## Profile-likelihood based confidence intervals

### Description

function to find prob*100% confidence intervals using profile-likelihood. Numerical solutions are obtained via a modified Newton-Raphson algorithm. The method is described in Venzon and Moolgavkar, Journal of the Royal Statistical Society, Series C vol 37, no.1, 1988, pp. 87-94.

### Usage

plkhci(x, nlogf, label, prob = 0.95, eps = 0.001, nmax = 10, nfcn = 0)


### Arguments

 x a list with components 'label' (of mode character), 'est' (the parameter vector with the initial guess), 'low' (vector with lower bounds), and 'upp' (vector with upper bounds) nlogf the negative log of the density function (not necessarily normalized) for which samples are to be obtained label parameter for which confidence bounds are computed prob probability associated with the confidence interval eps a numerical value. Convergence results when all (logit-transformed) derivatives are smaller eps nmax maximum number of Newton-Raphson iterations in each direction nfcn number of function calls

### Value

2 component vector giving lower and upper p% confidence bounds

### Note

At this point, only a single parameter label can be passed to plkhci. This function is part of the Bhat exploration tool

### Author(s)

E. Georg Luebeck (FHCRC)

dfp, newton, logit.hessian

### Examples


# generate some Poisson counts on the fly
dose <- c(rep(0,50),rep(1,50),rep(5,50),rep(10,50))
data <- cbind(dose,rpois(200,20*(1+dose*.5*(1-dose*0.05))))

# neg. log-likelihood of Poisson model with 'linear-quadratic' mean:
nlogf <- function (x) {
ds <- data[, 1]
y  <- data[, 2]
g <- x[1] * (1 + ds * x[2] * (1 - x[3] * ds))
return(sum(g - y * log(g)))
}

# for example define
x <- list(label=c("a","b","c"),est=c(10.,10.,.01),low=c(0,0,0),upp=c(100,20,.1))

# get MLEs using dfp:
r <- dfp(x,f=nlogf)
x$est <- r$est
plkhci(x,nlogf,"a")
plkhci(x,nlogf,"b")
plkhci(x,nlogf,"c")
# e.g. 90% confidence bounds for "c"
plkhci(x,nlogf,"c",prob=0.9)



[Package Bhat version 0.9-12 Index]