Example reports for mixed-model analysis using lmer in biology, psychology and medicine?

Question

As the general consensus seems to be to use mixed-models via lmer() in R instead of classical ANOVA (for the often cited reasons, like unbalanced designs, crossed random effects etc.), I would like to give it a try with my data. However I am worried that I would be able to "sell" this approach to my supervisor (who is expecting classical analysis with a p-value in the end) or later to the reviewers.

Could you recommend some nice examples of published articles that used mixed-models or lmer() for different designs like repeated-measures or multiple within- and between-subject designs for the field biology, psychology, medicine?

Answer 1

I do not have a number of examples, only one (see below), but know some paper you should cite from Psychology/Cognitive Sciences. The most important one is definitely:

Baayen, R. H., Davidson, D. J., & Bates, D. M. (2008). Mixed-effects modeling with crossed random effects for subjects and items. Journal of Memory and Language, 59(4), 390–412. doi:10.1016/j.jml.2007.12.005

Another one from Baayen is:

Baayen, R. H., & Milin, P. (2010). Analyzing Reaction Times. International Journal of Psychological Research, 3(2), 12–28.

I actually totally liked his book, too, which also has a nice introductory chapter on mixed model (and is pretty cheap for a stats book): Baayen, R. H. (2008). Analyzing linguistic data : a practical introduction to statistics using R. Cambridge, UK; New York: Cambridge University Press.

I probably guess he also has a lot of papers using lme4, but as my main interest is not psycholinguistics, you might wanna check his homepage.

From my field (reasoning), I know of this one paper that uses lme4:

Fugard, A. J. B., Pfeifer, N., Mayerhofer, B., & Kleiter, G. D. (2011). How people interpret conditionals: Shifts toward the conditional event. Journal of Experimental Psychology: Learning, Memory, and Cognition, 37(3), 635–648. doi:10.1037/a0022329

(although I have the feeling they use a likelihood ratio test to compare models which only differ in the fixed parameters, which I have heard is not the correct way. I think you should use AIC instead.)

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UPDATE1: Another paper describing lme4

Kliegl, R., Wei, P., Dambacher, M., Yan, M., & Zhou, X. (2011). Experimental effects and individual differences in linear mixed models: estimating the relationship between spatial, object, and attraction effects in visual attention. Frontiers in Quantitative Psychology and Measurement, 1, 238. doi:10.3389/fpsyg.2010.00238

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Update 2 (July, 2012): A paper advocating the use in (Social) Psychology when there are crossed (e.g., participants and items) random effects.
The big thing is: It shows how to obtain p-values using the pbkrtest package:

Judd, C. M., Westfall, J., & Kenny, D. A. (2012). Treating stimuli as a random factor in social psychology: A new and comprehensive solution to a pervasive but largely ignored problem. Journal of Personality and Social Psychology, 103(1), 54–69. doi:10.1037/a0028347
(only available as a Word .doc)

Jake Westfall told me (per mail) that an alternative for obtaining p-values to the advocated Kenward-Rogers approximation (used in pbkrtest) is the (less optimal) Satterthwaite approximation, which can be found in the MixMod package using the anovaTab function.

Small update to last update: My R package afex contains function mixed() to conveniently obtain p-values for all effects in a mixed model. Alternatively, the car package now also obtains p-values for mixed models in Anova() using test.statistic = "F"

Answer 2

This is a highly-cited paper on mixed models for ecology and evolution:

• Bolker et al. (2009) Generalized linear mixed models: a practical guide for ecology and evolution Trends in Ecology & Evolution Vol. 24 pp127-135 (PDF) (from ScienceDirect with links to Supplementary Content).

Answer 3

The following article endeavours to promote the use of multilevel modelling in social science settings:

• Bliese, P. D. & Ployhart, R. E. (2002). Growth Modeling Using Random Coefficient Models: Model Building, Testing, and Illustrations, Organizational Research Methods, Vol. 5 No. 4, October 2002 362-387. PDF

To quote the abstract:

In this article, the authors illustrate how random coefficient modeling can be used to develop growth models for the analysis of longitudinal data. In contrast to previous discussions of random coefficient models, this article provides step-by-step guidance using a model comparison framework. By approaching the modeling this way, the authors are able to build off a regression foundation and progressively estimate and evaluate more complex models. In the model comparison framework, the article illustrates the value of using likelihood tests to contrast alternative models (rather than the typical reliance on tests of significance involving individual parameters), and it provides code in the open-source language R to allow readers to replicate the results. The article concludes with practical guidelines for estimating growth models.

An examination of the articles listed on Google Scholar as citing this paper suggest several other useful leads.

Answer 4

An excellent example of using mixed models in ecology is:

• "Demography and management of the invasive species Hypericum perforatum. I. Using multi-level mixed-effects models for characterizing growth, survival and fecundity in a long-term data set" (Buckely, Briese and Rees 2003).

Unfortunately it uses older R libraries.