Function to compute estimated and profile likelihood based confidence intervals for twinstim objects. Computations might be cumbersome!

WARNING: the implementation is not well tested, simply uses optim (ignoring optimizer settings from the original fit), and does not return the complete set of coefficients at each grid point.

## Usage

# S3 method for twinstim
profile(fitted, profile, alpha = 0.05,
control = list(fnscale = -1, maxit = 100, trace = 1),
do.ltildeprofile=FALSE, ...)

## Arguments

fitted

an object of class "twinstim".

profile

a list with elements being numeric vectors of length 4. These vectors must have the form c(index, lower, upper, gridsize).

index:

index of the parameter to be profiled in the vector coef(fitted).

lower, upper:

lower/upper limit of the grid on which the profile log-likelihood is evaluated. Can also be NA in which case lower/upper equals the lower/upper bound of the respective 0.3 % Wald confidence interval (+-3*se).

gridsize:

grid size of the equally spaced grid between lower and upper. Can also be 0 in which case the profile log-likelihood for this parameter is not evaluated on a grid.

alpha

$$(1-\alpha)\%$$ profile likelihood based confidence intervals are computed. If alpha <= 0, then no confidence intervals are computed. This is currently not implemented.

control

control object to use in optim for the profile log-likelihood computations. It might be necessary to control maxit or reltol in order to obtain results in finite time.

do.ltildeprofile

If TRUE calculate profile likelihood as well. This might take a while, since an optimisation for all other parameters has to be performed. Useful for likelihood based confidence intervals. Default: FALSE.

...

unused (argument of the generic).

## Value

list with profile log-likelihood evaluations on the grid, and -- not implemented yet -- highest likelihood and Wald confidence intervals. The argument profile is also returned.

Michael Höhle

## Examples

# profiling takes a while
if (FALSE) {
#Load the twinstim model fitted to the IMD data
data("imdepi", "imdepifit")
# for profiling we need the model environment
imdepifit <- update(imdepifit, model=TRUE)

#Generate profiling object for a list of parameters for the new model
names <- c("h.(Intercept)","e.typeC")
coefList <- lapply(names, function(name) {
c(pmatch(name,names(coef(imdepifit))),NA,NA,11)
})

#Profile object (necessary to specify a more loose convergence
#criterion). Speed things up by using do.ltildeprofile=FALSE (the default)
prof <- profile(imdepifit, coefList,
control=list(reltol=0.1, REPORT=1), do.ltildeprofile=TRUE)

#Plot result for one variable
par(mfrow=c(1,2))
for (name in names) {
with(as.data.frame(prof\$lp[[name]]),
matplot(grid,cbind(profile,estimated,wald),
type="l",xlab=name,ylab="loglik"))
legend(x="bottomleft",c("profile","estimated","wald"),lty=1:3,col=1:3)
}
}