[R] glmer with multiple random slopes

[Ben Bolker]

David Kikuchi <dwkikuchi <at> gmail.com> writes:

> 
> Hi all,
> 
> I'm modeling the probability that a subject attacks or rejects a prey 
> item based on its proportion of yellow coloration and size. There are 
> two populations of prey, one defended and the other undefended, so 
> subjects should reject one type and accept others. Each subject has a 
> unique rejection threshold that is a line on a contour plot with 
> coloration and size on the x and y axes. I want to estimate the error 
> around that line's slope, and believe that I need to estimate two random 
> slopes per subject to do so, one in the color dimension and the other in 
> the size dimension. The code that I think I should use to do this is: 
> glmer(attack ~ prop.color + size + (prop.color + size|subject, family = 
> binomial), but I cannot find a reference or example for fitting random 
> slopes in different continuous dimensions. I would appreciate any 
> pointers in the right direction.
> 
> Thanks,
> David

     This seems perfectly reasonable.  It might be more on-topic 
on r-sig-mixed-models at r-project.org (send follow-ups there please).

My only concern with this model is the size of your data set -- you
probably need a reasonably large number of trials per subject (20-30, or more?),
and a reasonably large number of subjects (at least 10, preferably >20?)
in order to estimate the among-subject variation in the response reasonably
well.

You should be able to use lme4's simulate method to simulate data and
try a power analysis -- the hardest part is figuring out what the 'theta'
(random-effects) parameters mean (the among-subject variance-covariance
matrix is a 3*3 matrix (intercept, color, size), the parameters fill in
a lower-triangular matrix

  t1  0  0
  t2  t4 0
  t3  t5 t6

which is multiplied by its transpose 

  t1  t2  t3
  0   t4  t5
  0    0  t6

to get the variance-covariance matrix.