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Background: I have a dataset, which consists of waterlevel measurements over time at different locations. However, the locations are irregularly measured in different years. Therefore my data consists of more gaps than actual data. Additionally, some of my data is nested. That means that some of my measurements can be grouped under another measurement, while others are not.

How can I best test whether there is a difference between the waterlevels of various locations given these features of the data?

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Just for my learning, how is the data nested? By location (i.e. multiple water levels around a lake)? – Wayne Aug 11 '12 at 11:53

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This is definitely a job for multilevel models (aka hierarchical models, mixed models and other terms). It's a big field, but the essential idea is to deal with non-independent data, which you have, certainly in terms of time and possibly place as well.

There are tools for this in SAS (PROC MIXED, NLMIXED or GLIMMIX, you probably want MIXED) and R (a couple of packages, such as nlme).

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...and in Stata too! (xtmixed, xtlogit, xtpoisson...) – andrea Apr 12 '12 at 12:04
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It sounds like the dependence structure is a nuisance and primary interest focuses on differences in means. Is there a particular reason you're suggesting random effects models rather than something like GEE which has the nice property of consistency of regression coefficient estimates even when the association structure is misspecified? – Macro Apr 12 '12 at 13:24
@macro In general, I find mixed models more intuitive, perhaps just because I am more used to them. You're right that GEE could be good here. – Peter Flom Apr 12 '12 at 15:36
@Macro: I'd suggest giving your comment as a separate answer. I, too, know little about GEE's, except that they address population means when there are various correlation issues. – Wayne Aug 11 '12 at 11:56
@PeterFlom: R's lme4 package is more intuitive for me, but not as flexible in regard to correlation structure. (I like lme4 a lot, but I'm just a rookie at this and don't have a firm grasp on the correlation part: just parroting what "they" say.) – Wayne Aug 11 '12 at 11:57
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