[R] psychometric functions

[Jonathan Baron]

On 08/21/08 17:48, Mario Maiworm wrote:
> >>> Two comments.  First, it isn't clear to me why you want the upper
> >>> bound to differ from 1.  Apparently you have some theoretical reason
> >>> for using a cumulative gaussian.  Wouldn't the same theory tell you
> >>> that the upper bound should be 1?
> 
> the reason why I use cumulative gaussians is that I am interested in the
> sigma values of the underlying gaussian, which is a measure of perceptual
> uncertainty. In my experiments, people are supposed to judge a stimulus
> feature (in a 2AFC task). In theory, if subjects are presented with a
> stimulus that has the maximum value for that feature (and the experiment ist
> properly designed), there is a probability of 1 that people respond with
> "yes". In practice, subjects do make unspecific errors due to a whole bunch
> of reasons even at high stimulus intensities. If I let the computational
> routine that is supposed to fit my data sets assume that the probability for
> response is 1 at high stimulus intensities (i.e. fix the asymptote at 1),
> the estimated parameters are very sensitive to those outliers and I get a
> strongly biased result if the subject only made one or very few mistakes at
> high stimulus intesities.

This makes sense.  Sorry I didn't think of it.

> Unfortunately, I cannot make this code run. You mean the 'lower' and 'upper'
> parameters of nls()?

Given all the other comments, I don't think you should bother with my
code.  My point was simply that there are many tools in R for doing
the kind of model fitting you want to do.  Probably optim() itself is
better for this, but it seems that there are many other options.

The model I fit made exactly the same assumption you describe, namely,
that the upper asymptote was less than 1, because (for example) some
of the best students understand the question differently from what the
test makers intended.  And the lower asymptote depends on what the
worst students tend to guess.

I think ltm should allow a flexible upper bound, for these reasons.
(I haven't tried it.)

Jon
-- 
Jonathan Baron, Professor of Psychology, University of Pennsylvania
Home page: http://www.sas.upenn.edu/~baron