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I would like to know more about interaction in LMM using lmer. Can you recommend me any books, articles, websites?

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2 Answers 2

Bookwise: The uber-classic is Mixed-Effects Models in S and S-PLUS by Bates and Pinheiro; it shows its years at time but it is still an excellent read. I have also read Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Stroup; it is quite new and based on software I have never used (SAS) but it very well-written and clear. I like it a lot. I believe those two resources will cover most questions. I have also found Linear Mixed Models: A Practical Guide Using Statistical Software by West, Welch and Galecki to be a good read but I would not pick it over the previous two. Finally Mixed Effects Models and Extensions in Ecology with R by Zuur, Ieno, Walker, Saveliev and Smith seems to be popular but I have not used personally.

The Centre for Multilevel Modelling (CMM) in the University of Bristol has a fuller web-catalogue of good books that can be found here.

Paper-wise: This list can be endless and probably you can find works specific to your field of application. Having said that the paper: Generalized linear mixed models: a practical guide for ecology and evolution by Bolker, Brooks, Clark, Geange, Poulsen, Stevens and White is pretty darn good (I like TREE papers).

And a side-comment: Given lmer/lme/fitlme/genstat are coherent pieces of software, what you want is to understand how Wilkinson notation works. There is not "magic" surrounding how you define interactions and nesting, just some rules that are (generally) not software-specific.

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Kris Preacher's website (under "Hierarchical Linear Modeling") provides online tools to decompose either 2-way or 3-way interactions in LMMs, and distinguishes between same-level and cross-level interactions. Above each tool, he gives a brief tutorial for each type of interaction. He also provides references for further reading at the bottom.

EDIT:

I should also mention two books which should be useful. A reference in the field of LMMs is Raudenbush & Bryk's (2002) book (cited over 20,000 times according to Google Scholar). A more beginner-friendly book is that of Hox (2010). Both books are most relevant to the social sciences. A third book is very beginner-friendly as well, but concerns only LMMs as applied to longitudinal data (observations nested under participants): Singer & Willett (2003).

Since there is much overlap between interactions in LMMs and interactions in single-level regression, I would recommend Cohen, Cohen, West, & Aiken's (2003) book on linear regression (cited 30,000 times!). They talk at length about interactions involving different types of predictors (continuous, dummy coded), in very accessible fashion.

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Patrick Coulombe, I have roughly read that website, but found that it is quite difficult to understand. Could I ask you why I need decompose three-way interaction? –  user3288202 Apr 5 at 21:00
    
I'll try to studied those sources. Thanks very much Patrick Coulombe. –  user3288202 Apr 6 at 5:01
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