QRPEM is parallelized with MPI (as are all the Phoenix NLME methods) and runs on multiple cores/cpus.
In all of the other methods, the parallelization is over subjects, so for example, with two processors, the likelihood for the even numbered subjects is computed and accumulated on processor 0 and for the odd number subjects on processor 1.
It turns out that due to a synchronization requirement imposed by the use of QR sampling and also the fundamentally different nature of the EM type methods, that it is much easier to parallelize the QRPEM method over the sampling points, rather than the subjects.
It seems to work quite well.
