Dear all,
First a bit of background: I currently work on an anlysis of
phenotypic plasticity of avian phenology in response to temperature.
Using a random regression model I found that individual reaction
norms (defined by slope and intercept) vary among individuals, i.e.
some individuals change their phenology more strongly in response to
temperatures than others and also that some individuals have a
consistently earlier phenology than others.
I now want to test whether there is selection on reaction norm
slopes, i.e. whether individuals with steeper/shallower slope have a
higher/lower fitness. This means I have to fit a bivariate random
regression model but only one trait (phenology) should be regressed
against temperature. For the random effects part this should give me
a 3x3 covariance matrix with variation in slopes, intercepts,
fitness plus all the covariances and then the covariance between
slope and fitness indicates selection on reaction norm slopes.
I figured how to regress only phenology and not fitness against
temperature for the fixed effects part but am still struggling with
the syntax for the random effects part.
The univariate random regression model (omitting obvious syntax parts) is:
phenology~age + temp, random=~us(1+temp):individual
For the multivariate model I came up with:
cbind(phenology,fitness)~trait:age + at.level(trait,1):temp,
random=~us(at.level(trait,1):(1+mt2):at.level(trait,2):1):individual,
rcov=~us(trait):units
but curiously this fits only a single variance for individual and
not the desired 3x3 matrix...
I hope I managed to explain my problem clearly enough (maybe there
was too much non-technical detail...). Any ideas to fit the desired
model are highly welcome!
Best,
Phillip