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][1] 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][2]][2]
[![enter image description here][3]][3]

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



  [1]: https://drive.google.com/open?id=0BzrHpe_fGynadHlpYS1qcGw4WkU
  [2]: https://i.sstatic.net/IChuZ.png
  [3]: https://i.sstatic.net/I1aFz.png