  Composite likelihood inference has gained much popularity thanks to its
computational manageability and its theoretical properties. Unfortunately,
performing composite likelihood ratio tests is inconvenient because of their
awkward asymptotic distribution. There are many proposals for adjusting
composite likelihood ratio tests in order to recover an asymptotic chi square
distribution, but they all depend on the sensitivity and variability matrices.
The same is true for Wald-type and score-type counterparts. In realistic
applications sensitivity and variability matrices usually need to be estimated,
but there are no comparisons of the performance of composite likelihood based
statistics in such an instance. A comparison of the accuracy of inference based
on the statistics considering two methods typically employed for estimation of
sensitivity and variability matrices, namely an empirical method that exploits
independent observations, and Monte Carlo simulation, is performed. The results
in two examples involving the pairwise likelihood show that a very large number
of independent observations should be available in order to obtain accurate
coverages using empirical estimation, while limited simulation from the full
model provides accurate results regardless of the availability of independent
observations.
