R help - Oct 2006 - Fitting a cumulative gaussian

Dear R-Experts,

I was wondering how to fit a cumulative gaussian to a set of empirical 
data using R. On the R website as well as in the mail archives, I found 
a lot of help on how to fit a normal density function to empirical data, 
but unfortunately no advice on how to obtain reasonable estimates of m 
and sd for a gaussian ogive function.
Specifically, I have data from a psychometric function relating the 
frequency a subject's binary response (stimulus present / absent) to the 
strength of a physical stimulus. Such data is often modeled using a 
cumulative gaussian function. I have tried to implement such a fitting 
algorithm in R, but unfortunately, I was not successful. Maybe anyone on 
the list already coded a script for such purposes or could help me 
otherwise???

Thanks in advance,
Matthias

Gamer, Matthias <gamer <at> uni-mainz.de> writes:
> Specifically, I have data from a psychometric function relating the 
> frequency a subject's binary response (stimulus present / absent) to
the
> strength of a physical stimulus. Such data is often modeled using a 
> cumulative gaussian function. 
Well, more often by a logistic function, and there are quite a few tools
powerful for doings this around, for example glm, or lmer/lme4, glmmPQL/MASS,
glmmML/glmmML . The latter three are the tools of choice when you have within
subject repeats, as it's standard in psychophysics. See
http://finzi.psych.upenn.edu/R/Rhelp02a/archive/33737.html for a comparison.

If you really want a cumlative gaussian, you can misuse drfit/drfit, which is
primarily for dose/response curves and ld50 determination. I think there is a
fitdistr/MASS example around (somewhere in the budworms chapter), but I
don't
have the book at hand currently.

Dieter

If the data asymptote at 0 and 1, then you can use glm with the 
binomial family
with either the logistic or probit links.  If the data are from an 
n-alternative
forced choice procedure or if the data do not asymptote at 0 and 1 for 
some
reason or other, then you need to try other procedures.  Two 
possibilities are to
use the PsychoFun package available here

http://www.kyb.tuebingen.mpg.de/~kuss

and described in

Kuss, M., F. Jäkel and F.A. Wichmann: Bayesian inference for 
psychometric functions. Journal of Vision 5(5), 478-492 (2005)

or tools from some of Jim Lindsey's packages, described here

Yssaad-Fesselier R, Knoblauch K. Modeling psychometric functions in R. 
Behav Res Methods. 2006 Feb;38(1):28-41.

HTH

ken


> Gamer, Matthias <gamer <at> uni-mainz.de> writes:
>
> > Specifically, I have data from a psychometric function relating the
> > frequency a subject's binary response (stimulus present / absent)
to
> the
> > strength of a physical stimulus. Such data is often modeled using a
> > cumulative gaussian function.
>
> Well, more often by a logistic function, and there are quite a few 
> tools
> powerful for doings this around, for example glm, or lmer/lme4, 
> glmmPQL/MASS,
> glmmML/glmmML . The latter three are the tools of choice when you have 
> within
> subject repeats, as it's standard in psychophysics. See
> http://finzi.psych.upenn.edu/R/Rhelp02a/archive/33737.html for a 
> comparison.
>
> If you really want a cumlative gaussian, you can misuse drfit/drfit, 
> which is
> primarily for dose/response curves and ld50 determination. I think 
> there is a
> fitdistr/MASS example around (somewhere in the budworms chapter), but 
> I don't
> have the book at hand currently.
>
> Dieter
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