[R] glmer with multiple random slopes

[David Kikuchi]

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

In case I've given a poor description of the problem, below is code to 
visualize the rejection threshold, using an optimal decision threshold 
rather than one estimated from the data:

library(mnormt)
library(lattice)

modelms<- 31.2
mimicms<- 24
sds<- 4*4
modelmc<- 0.7
mimicmc<- 0.4
sdc<- 0.15*0.15
xv<-seq(0,1,0.01)
yv<-seq(10,50,0.1)

ys <- matrix(NA,length(xv),length(coeffs[1,]))
for(i in 1:length(xv)) ys[i,] <- 
(coeffs[1,]+coeffs[2,]*xv[i])/(coeffs[3,]*-1)

mu <- c(modelmc,modelms) #model
sigma <- matrix(c(sdc,0,0,sds),2,2)
z1<-NULL
for(x in xv){
   f <- dmnorm(cbind(x,yv), mu, sigma)
   z1<-rbind(z1,f)
}
contour(xv,yv,z1, nlevels = 5,col = "blue", lty = "solid", lwd = 1.8, 
xlab = "proportion yellow", ylab = "size")

mu <- c(mimicmc,mimicms) #mimic
sigma <- matrix(c(sdc,0,0,sds),2,2)
z2<-NULL
for(x in xv){
   f <- dmnorm(cbind(x,yv), mu, sigma)
   z2<-rbind(z2,f)
}
contour(xv,yv,z2, nlevels = 5,add = TRUE,col = "red", lty = "solid", lwd 
= 1.8)
contour(xv,yv,z2-z1, nlevels = 1,add = TRUE, col = "black", lty = 
"solid", lwd = 2.5)