[R-sig-ME] Logistic and nonlinear mixed models: Accounting for guessing probability

[Robert Miller]

Hello everyone,

Recently i tried to predict the discrimination probability of a chemosignal
by its concentration and an experimental manipulation factor (term:
concentration*x + test*b + concentration*test*c + d) with nested factor
"manipulation" within "participants". For statistical analysis i needed to
incorporate a fixed guessing probability into my model (similiar to a 3-PL
IRT model) resulting in the following equation:

P(correct) = 0.33 + 0.67*(exp(term)/(1 + exp(term)))

As i found no way to do so via the glmer()-function of the lme4-package, i
tried to use nlmer() but unfortunately even the simplest analysis with just
the concentration factor and intercept resulted in cryptic error messages.

Syntax:
library(lme4)
rawdata <- read.csv2("http://dl.dropbox.com/u/7147679/AND_data.csv")

mod1 <- glmer(Correct ~ log(Concentrat) * Test + (Test|Code), family =
binomial, data=rawdata) #works fine but is inappropriate
mod2 <- nlmer(Correct ~ .33 + .67*(exp(log(Concentrat)*a+d))
/(1+exp(log(Concentrat)*a+d)) ~ (Test|Code), start = c(a = 0.1, d = -3),
data = rawdata) #doesnt work
mod3 <- nlmer(Correct ~ .33 + .67*(exp(log(Concentrat)*a + Test*b +
log(Concentrat)*Test*c + d))/(1+exp( log(Concentrat)*a + Test*b +
log(Concentrat)*Test*c + d)) ~ (Test|Code), start = c(a = 0.115,b = -0.05,
c= 0.065, d= -3), data = rawdata) #doesnt work either

Even without specifying random effects nls() doesnt work, but brute force
ML-parameter estimation on the aggregated data produces reasonable results.

Right now I'm quite desperate and would appreciate any help.
Thank you
Robert Miller