Eric Schwartz writes:

Thanks for the blog post. I have three follow up questions:

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.**

What can I use instead of mcsamp() to fit and then plot a varying-intercept, logit model. What is the equivalent of mcsamp()?

Thank you.

Quassi _usually_ means just making a simple (scalar) adjustment of the log-likelihoods based on local features at the maximum – best avoided unless you are sure the log likelihood is not multi-model (happens with exponential models with unknown scale parameters) AND the adjustment does not make things worse.

Smaller standard errors are _usually_ due to observed under-dispersion which is a strong signal of model failure – overfitting, non-independent patient responses … so _usually_ making a bad situation much worse.

Related/equivalent to robust standard errors, sandwich variance estmates – etc – desparate attempts to avoid doing full modeling – which I was warned as a graduate student was always very dangerous

Wonder if the multi-modality would make the fake data checking very challenging?

K?

desparate attempts to avoid doing full modeling… always very dangerousC'mon, these attitudes are just silly. Use of e.g. robust standard errors is just a method, not a mentality. If the user has checked – perhaps using the fake data simulation suggested above – that the method should work well for the problem at hand, it's wrong (and unhelpful) to call them 'desperate' or 'dangerous'.

Freddy – maybe a bit strong but its a blog post and not much different than the warning David Firth gave me was I was a graduate student that I did not take seriously enough at my on peril.

For an example of what can go wrong – search for "batman" is this pdf

http://www.samsi.info/200809/meta/tutorials/thesi…