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
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
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
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
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.)