Dear list members,

I measured individual behaviours with age in different 2 density levels
(High/Low), and found that there are significant variation of random
coefficients among individuals by comparing 2 models with and without the
random slope, (age|ID).

But I am also wondering whether random coefficients vary bewteen densitiy
levels or not.

At first time, I tried to test by comparing 2 models with/without density
effect.
1) y ~ age + density + (1+age|ID)
2) y ~ age + (1+age|ID)
However, this comparison just test the difference of mean levels of
populations.

Recently, I found a good reference introducing the method to compare random
slopes between populations. The method is described in a supporting
material in detail (see below link).

Dingemanse, N. J., Bouwman, K. M., van de Pol, M., van Overveld, T.,
Patrick, S. C., Matthysen, E. and Quinn, J. L. (2012), Variation in
personality and behavioural plasticity across four populations of the great
tit Parus major. Journal of Animal Ecology, 81: 116–126

http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2656.2011.01877.x/suppinfo

They combined each model from each population into a single model. But they
used a random intercept term for individual only, but had a seperate random
intercept term for individual for each population (using so-called partial
random intercepts for each population). Similarly, I want to give a
separate random intercepts for individuals for each density condition. My
data is much simpler. Can I make such a nested design with R? or should I
use MLwin instead of R package?

Density ID AGE Y
L 1 1 1
L 1 2 1
L 1 3 2
L 2 1 9
L 2 2 9
L 2 3 77
H 108 1 150
H 108 2 21
H 108 3 17
H 109 1 43
H 109 2 23
H 109 3 15
...

Cheers,

Chang

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