More on fitting multilevel models

Q1. I also would also prefer to look at confidence or posterior intervals, so in the multilevel model how would you rank order the best ways to construct those intervals? - run fully Bayes posterior inference in WinBUGS or R directly (but if the data set is too big that is too slow) - run lmer() and use mcmcsamp() (but it is not working though I appreciate Bates free work!) - run lmer() and form an interval of +/- 2 Standard Errors around the Estimate (just as you and Jennifer Hill show in your ARM book on page 261)

Q2. Under what conditions is using +/- 2 standard errors of estimates a reasonable approximation of what the posterior interval would be?

Q3. May you clarify the "almost always" in your blog post? Is it reasonable to choose a lmer() model with "family=poisson" over one with "family=quasipoisson" when there are already, say, two non-nested batches of random effects taking care of the overdispersion in observed counts? I interpret those batches as capturing unobserved heterogeneity of count propensities across the individual groups in those batches, so they sufficiently reflect overdispersion; above that, an additional idiosyncratic error term for each observation seems unnecessary to the individual-level story.

My reply:

1. Full Bayes is best. Once it's working again, mcsamp() is full Bayes (I think).

2. Easiest way to evaluate this is via a fake-data simulation. See chapter 8 of ARM for some simple examples of this sort of thing.

3. I'd say to always do quasipoisson etc. But I don't actually know what glmer does here. Just today I fit a model using binomial and then quasibinomial and I was stunned to find the standard errors were smaller when I used quasibinomial. I still don't know what was going on here. Again, fake-data simulation would be the way to check this and see what to trust.