Logistic and nonlinear mixed models: Accounting for guessing probability

Unfortunately an nlmer model is not appropriate for a binary response,
because it doesn't appropriately weight the residuals.

Incorporating a non-zero guessing parameter requires a generalized
nonlinear mixed model if you need to estimate the guessing parameter.
The long term plan is to allow such a model. ?This is the reason that
Martin and I worked on factoring out the internal code dealing with
different kinds of models for the expected response. ?Nonlinear models
affect these in one way and generalized linear models in another so
you need to chain these effects.

For the particular case that Robert is considering, in which the
guessing parameter is fixed at 0.33 I think it may be possible to use
the mafc.logit link from the psyphy package with lme4a, the
development version of lme4. ?I am currently installing the necessary
packages to see if I can make it work. ?My thanks to Robert for making
the data available so we can test it.

On Mon, Sep 27, 2010 at 11:25 AM, Manuel Morales
<Manuel.A.Morales at williams.edu> wrote:

I found this link doing a search for your error message on Google:
https://stat.ethz.ch/pipermail/r-sig-mixed-models/2007q4/000408.html

Following the recipe:
grModel <- function(x,y,a,b,c,d) .33 + .67*(exp(log(x)*a+y*b+log(x)*y*c
+ d))/
?(1+exp( log(x)*a + y*b +log(x)*y*c + d))

grModg <- deriv(body(grModel), namevec = c("a","b","c","d"),
function.arg=grModel)

mod3 <- nlmer(Correct~grModg(Concentrat,Test,a,b,c,d)~(Test|Code),
? ? ? ? ? ? ?start = c(a = 0.115, b=-0.1, c=0.65, d=-3),
? ? ? ? ? ? ?data = rawdata)
Which appears to work.

My messages haven't been posted to R, so you may want to post again with
this solution if it works for you.

Best,

Manuel

On Mon, 2010-09-27 at 15:54 +0200, Robert Miller wrote:

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

--
http://mutualism.williams.edu