I'm looking for an example of a data set that can be fitted using a GLMM with at least 3 separate random effects. I've taken a look at a few books on GLMM's including the one by McCulloch and Searle, but their examples always stop at 2 random effects. I don't know why I'm having so much trouble wrapping my head around a practical example of 3 or more random effects but I am.

In the national youth tobacco survey for example, counties were the PSU's. Within sampled counties, schools were then randomly selected along with students. So if I understand it correctly it would make sense to perhaps treat both counties and schools as random. I suppose if they sampled classrooms within each school we could then have 3 nested random effects - one for each of county, school and classroom. Is that correct?

Any help would be greatly appreciated.


Yes your intuition is correct. Another 3-level clustering would be School>Classroom>Student. (Clearly a 4-level would be Country>School>Classroom>Student)

Reference-wise: Linear Mixed Models: A Practical Guide Using Statistical Software by West et al. actually has a three level example both for clustered (Chapt.4) and longitudinal data (Chapt.7). As you say, not many 3-level examples exists in the literature and I find that being true also.

  • $\begingroup$ Thanks for the reference. I'll definitely take a look. I find that even with national studies, it isn't so easy to find one in which it would make sense to model more than 2 random effects. I'm sure that's because survey methodologists prefer to keep their sampling designs as simple as possible, but it just makes my search a little tougher. I'm thinking longitudinal or repeated measures surveys might also be a good place to look for data of this type. Thanks again! $\endgroup$
    – user21386
    Feb 28 '13 at 14:50
  • $\begingroup$ Good luck with the rest of you analysis. $\endgroup$
    – usεr11852
    Mar 1 '13 at 15:59

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