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I do not know if this has been asked before, but I do not found anything about it. My question is if anyone can provide a good reference to learn how to obtain the proportion of variance explained by each one of the fixed and random factors in a mixed-effects model.

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Good question, but I don't have (a reference for) a good answer. There's more than one level of variation in mixed models, so there's more than one component of variance to explain, plus it's debateable whether random effects can really be said to 'explain' variance. I think the whole concept of 'proportion of variance explained' is less useful in mixed models. – onestop Feb 15 '11 at 9:18

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I can provide some references:

Xu, R. (2003). Measuring explained variation in linear mixed effects models. Statistics in Medicine, 22, 3527-3541. DOI:10.1002/sim.1572

Edwards, L. J., Muller, K. E., Wolfinger, R. D., Qaqish, B. F., & Schabenberger, O. (2008). An $R^2$ statistic for fixed effects in the linear mixed model. Statistics in Medicine, 27, 6137-6157. DOI:10.1002/sim.3429

Hössjer, O. (2008). On the coefficient of determination for mixed regression models. Journal of Statistical Planning and Inference, 138, 3022-3038. DOI:10.1016/j.jspi.2007.11.010

Happy reading!

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@onestop: Thanks for adding the DOIs/links. – Wolfgang Feb 15 '11 at 16:22
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Here is some more discussion on the topic: https://stat.ethz.ch/pipermail/r-sig-mixed-models/2010q1/003363.html

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Very good link, but please give some context, so if the link is dead, there still would be some idea about what is in it. – mpiktas Aug 3 '11 at 12:42

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