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How do I know how large to make $M$?

In our experience $M=1000$ is sufficient for most analyses. However, one check on the adequacy of $M$ is to verify that the means of the simulated parameters are equal to the estimated parameters within the desired degree of precision. If they are not, increase $M$ until you achieve the desired precision. Be aware that in larger models increasing $M$ may add to the computer time and memory required for simulation.