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I did a simple experiment with trees: 5 species (sp) and two management (trt). I assessed the diameter (diam) through the time (month=1:24) and I'm interesting in the factors interaction effect, I mean if the management is suitable for some species.

The dataset has some limitations since it is not balanced, so in 2 out of 10 factors combinations (sp*trt) I have 4 trees (subjects) and for the rest there are 5 trees: 

       sp    trt trees
1       A      L     5
2       A      W     5
3       B      L     5
4       B      W     5
5       C      L     5
6       C      W     5
7       P      L     4
8       P      W     5
9       T      L     5
10      T      W     4

I fitted the following model:

m1 <- lmer(diam ~ trt * sp * month + (1|tree), data = dat1)

I'm not sure if I'm doing right, mainly if the model is right...

enter image description here enter image description here

If the model is correct, and the anova is the following table:

Analysis of Variance Table
             Df  Sum Sq Mean Sq F value
trt           1 0.12110 0.12110 17.3756
sp            4 0.06761 0.01690  2.4251
month         1 0.33917 0.33917 48.6659
trt:sp        4 0.00436 0.00109  0.1564
trt:month     1 0.15814 0.15814 22.6900
sp:month      4 0.24445 0.06111  8.7687
trt:sp:month  4 0.19109 0.04777  6.8547
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  • $\begingroup$ I vote to reopen. I don't understand why this was closed as off-topic. The question asks about how RM-ANOVA analogue can be performed via a mixed mode. This definitely does require a lot statistical expertise to answer! In fact, it's likely a duplicate, we have a bunch of threads on this topic, and they are well-upvoted and open. $\endgroup$
    – amoeba
    Commented Mar 30, 2017 at 20:12
  • $\begingroup$ Juanchi, your lmer formula looks fine to me. $\endgroup$
    – amoeba
    Commented Mar 30, 2017 at 20:15
  • $\begingroup$ thanks @amoeba. I didn't understand either why they closed it. Anyway.. I am oserving that residuals of this model are not so normally distributed (I added the plot to the OP). I also have the doubt if do I need to add the time to the subject (tree) as nested in the random effect... $\endgroup$
    – Juanchi
    Commented Mar 31, 2017 at 0:00

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