R-Sessions 25: Book – Mixed Effects Models in S and S-PLUS (Pinheiro & Bates, 2000)

November 22, 2024Rense Nieuwenhuis


Despite the reference to S and S-PLUS in the title of this book, it offers an excellent guide for the nlme-package in R-Project. Reason for this is the close resemblance between R and S. The nlme-package, available in R-Project for estimation of both linear and non-linear multilevel models, is written and maintained by the authors of this book.

The book is not an introduction to R. Basic knowledge of R-Project (or S / S-PLUS) is required to get the most out of it, as well as some knowledge on multilevel theory. Although the book forms a thorough introduction to multilevel modeling, addressing both some theory, the mathematics and of course the estimation and specification in R-Project (or S / S-PLUS), the learning curve it offers is quite steep. The authors are not shunned to apply matrix algebra and specify exactly the used estimation procedures.

Not only the specification of basic models is described, but many other subjects are brought up. A specific grouped-data object is considered, as well as ways to visualize hierarchical data and multilevel models. Heteroscedasticity, often a violation of assumptions, can be caught in the models easily, as is described clearly in one of the chapters. Finally, not only linear models are tackled, but non-linear models as well.

All in all, this book is an excellent addition for those who have prior knowledge of both R-Project and multilevel analysis. Using real-data examples and by providing tons of output, the authors accomplish to make clear the necessity of the more complex models and thereby invite the reader to invest time for the more fundamental aspects of multilevel analysis.

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R-Sessions is a collection of manual chapters for R-Project, which are maintained on Curving Normality. All posts are linked to the chapters from the R-Project manual on this site. The manual is free to use, for it is paid by the advertisements, but please refer to it in your work inspired by it. Feedback and topic requests are highly appreciated.
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5 comment on “R-Sessions 25: Book – Mixed Effects Models in S and S-PLUS (Pinheiro & Bates, 2000)”

  • I really like the book as it offers a thorough discussion of the linear and non-linear mixed effects models (BTW: not multilevel models, Doug Bates mentioned that issue in Dortmund ;-). But chapter 2 is really hard stuff, especially for a non-statistician.

  • Ah, thanks for the comment. I must admit I can’t remember what Douglas Bates stated about the difference between mixed and multilevel models. I always thought these terms were used rather interchangeably. Perhaps you can elaborate?

  • It’s on Doug’s slides (p39, “Models with crossed random eff ects”): “Many people believe that mixed-e ffects models are equivalent to hierarchical linear models (HLMs) or ‘multilevel models’. This is not true. The plate and sample factors in fm2 are crossed. They do not represent levels in a hierarchy.”

  • Ah yes, that makes sense. Somehow, when I read ‘hierarchical model’ my brain reads something like ‘model with any kind of hierarchy’, bringing it to some sort of synonym. However, taking a more strict understanding of the term is much more clear. Thanks again!

    Oh: for those who do not know what Bernd refers to: We both attended a tutorial session on mixed models by Douglas Bates at the useR! 2008 conference (in Dortmund).

  • … and here’s the URL: Douglas Bates “Using lme4: Mixed-E ffects Modeling in R“.

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