Rafael pointed me toward some great stuff at the UCLA statistics website, including a page on Multilevel modeling that’s full of great stuff (No link yet to our forthcoming book, but I’m sure that will change…) It would also benefit from a link to R’s lmer() package.
Fixed and random (whatever that means)
One funny thing is that they link to an article on “distingushing between fixed and random effects.” Like almost everything I’ve ever seen on this topic, this article treats the terms “random” and “fixed” as if they have a precise, agreed-upon definition. People don’t seem to be aware that these terms are used in different ways by different people. (See here for five different definitions that have been used.)
del.icio.us isn’t so delicious
At the top of UCLA’s multilevel modeling webpage is a note saying, “The links on this are being superseded by this link: Statistical Computing Bookmarks“. I went to this link. Yuck! I like the original webpage better. I suppose the del.icio.us page is easier to maintain, so it’s probably worth it, but it’s too bad it’s so much uglier.
Andrew,
Regarding definition 5:
(5) Fixed effects are estimated using least squares (or, more generally, maximum likelihood) and random effects are estimated with shrinkage ("linear unbiased This definition is standard in the multilevel modeling literature (see, for example, Snijders and Bosker, 1999, Section 4.2) and in econometrics.prediction" in the terminology of Robinson, 1991).
I think this definition is becoming less common in econometrics. (At least this is the case if estimating with shrinkage means using GLS. I am not sure).
The more common definition is the one I gave in my original post:
1. An effect is fixed if the effect is correlated with the error term.
2. An effect is random if the effect is not correlated with the error term.
This is true at least for empirical microeconomics research.
Eric,
No problem. This adds a sixth definition to the list, which I think reinforces my point that the different definitions have different meanings.