The theory behind profile likelihood (PL) confidence intervals (CIs) is clear to me. (See here, for example).
SAS is surprisingly quick in calculating the PL CIs for all the covariates in a given model. Therefore I was wondering if there is another way of calculating PL CIs that does not require the time-consuming loop of maximizing the likelihood (over the nuisance parameters) given different fixed values of the parameter of interest.
Example: I run a logistic regression in SAS on ~43000 subjects with 10 covariates (+ the intercept). It took 0.6 seconds to fit this model without asking for PL CIs, and only 3 seconds when I required also the PL CIs for all the 10 covariates (option
proc logisitc). In Stata, the same model was fit in 0.35 seconds (without PL CIs) and in 10 seconds when asking the PL CIs for just one of the 10 covariates in the model (I used the
pllf command, which iteratively fixes values of the parameter of interest and maximizes the likelihood over the remaining ones).