Hi all,
I need help calculating the error rate of an optimal responder to a
multidimensional discrimination task. I have been trying to use pmnorm
to do this, but am not sure about its functionality. I'm working with a
dataset of responses (binary, attack/not attack) of subjects who were
asked to discriminate between two different, overlapping categories of
stimuli. The stimuli subjects viewed were bivariate normal in their
distributions (squares with different mean blue:yellow ratios and
sizes). It is easy to find a threshold (a line) on the bivariate plane
that describes the optimal discrimination function. It is a diagonal. To
find the error rate committed by this optimal responder, I need to find
the cumulative distribution function for a bivariate normal that lies
above the line. However, pmnorm only seems to calculate rectangular
probabilities, i.e. only uses limits of integration perpendicular to the
axes. Is there another function I could use?
Thanks,
David
The problem is visualized with the code below:
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)