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

lme4-nlmemixed modelrreferencesrepeated measures

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?

Best Answer

Update 3 (May, 2013): Another really good paper on mixed models in Psychology was released in the Journal of Memory and Language (although I do not agree with the authors conclusions on how to obtain p-values, see package afex instead). It very nicely discusses on how to specify the random effects structure. Go read it!

Barr, D. J., Levy, R., Scheepers, C., & Tily, H. J. (2013). Random effects structure for confirmatory hypothesis testing: Keep it maximal. Journal of Memory and Language, 68(3), 255–278. doi:10.1016/j.jml.2012.11.001

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"

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

Original Response:

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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