R help - Jul 2007 - fit a nonlinear model using nlm()

I am trying to fit a nonlinear model using nlm().
My application of nlm() is a bit complicated.
Here is the story behind the model being fit:

The observer is trying to detect a signal corrupted by noise.
On each trial, the observer gets stim=signal+rnorm().

In the simulation below I have 500 trials. Each row of stim is a new trial.
On each trial, if the cross-correlation between the stim and
the signal is above some criterion level (crit=.5 here), the
observer says "signal" (resp=1), else he says "no signal"
(resp=0).

So the situation is this: I know resp and stim for each trial.
I would like to estimate crit and signal from these.
(You might say that I already know the signal and crit. But the
idea here is that the observer cross-correlates the stim with an
internal template that will not be identical to the actual signal.
I want to estimate this template. Also the observer's crit may
differ from the "correct" one.)

In the code below, please help me get the f() and nlm() bits right.
I want to estimate signal and crit given stim and resp.

Thanks very much for any help!
Bill


x<-1:100
con<-.1
signal<-con*cos(2*pi*3*x/length(x))

crit<-.5
noisesd<-.1

# each row is a new stim (trial). 500 trials
resp<-array(dim=500)
stim<-matrix(nrow=500,ncol=100)
for (i in 1:500)
{
stim[i,]<-signal+rnorm(n=length(signal), mean=0, sd=noisesd)
if (sum(stim[i,]*signal)>crit) (resp[i]<-1) else (resp[i]<-0)
}


f<-function(signalest)
{
r<-array(dim=500)
for (i in 1:500)
{
r[i]<-sum(stim[i,]*signalest)>critest
}
sum((r-resp)^2)
}

fit<-nlm(f, stim[1,])

William Simpson <william.a.simpson <at> gmail.com> writes:
> 
> I am trying to fit a nonlinear model using nlm().
> The observer is trying to detect a signal corrupted by noise.
> On each trial, the observer gets stim=signal+rnorm().
> 
> In the simulation below I have 500 trials. Each row of stim is a new trial.
> On each trial, if the cross-correlation between the stim and
> the signal is above some criterion level (crit=.5 here), the
> observer says "signal" (resp=1), else he says "no
signal"
> (resp=0).
> 
> Thanks very much for any help!
> Bill
> 
> 
It sounds like you are doing a classification image experiment.  
You can use tapply() to get means for each x as a function of the 
observer's classifications and then combine them as a function of 
hits, false alarms, misses, correct rejections using the weights
 1 -1, -1, 1, as in Ahumada's original approach.
You can do this with lm() if you set it up so that the noise is 
the response and the classifications are a 4 level factor that prediccts 
them and the contrasts are set up as above.  
I think that it would be better to set it up as a glm, however,
where the responses of the observer are binary responses, the 
noise and the presence/absence of the signal are predictor variables, 
with a binomial family. 

I have example code that does each of these if you are 
interested and if it is only for simulation, see 

@Article{pmid16277294,
   Author="Thomas, James P and Knoblauch, Kenneth",
   Title="{{F}requency and phase contributions to the detection of 
   temporal luminance modulation}",
   Journal="J Opt Soc Am A Opt Image Sci Vis",
   Year="2005",
   Volume="22",
   Number="10",
   Pages="2257--2261",
   Month="Oct"
}

for which I can send you the code also.

Ken