[R] logistic regression and 3PL model

Prof Brian Ripley ripley at stats.ox.ac.uk
Thu Nov 25 17:13:31 CET 2004

On Thu, 25 Nov 2004, John Fox wrote:

> Pinheiro and Bates discuss a three-parameter logistic growth model in their
> Mixed Effects Models in S and S-PLUS, but as far as I know there's no direct
> way to fit the 3PL IRT model in R. It should be possible to fit such a model
> using one of the general optimisers in R, such as nlm() or optimise(), and I

optim(), not optimize() as there are at least two free parameters, I 

> think that it would be a nice project to produce an IRT package for R.

As I understand it this is a logistic regression and not a logistic growth 
curve, the latter being fitted by least squares.

For a known baseline (which is thus a 2-free PL model but what seems asked 
for here), a glm family can be constructed to allow glm() to do the 
fitting.  This is model described at


with c known to be 0.25.  It would certainly be worth having an 
implementation of that in R, with c=0.5 being the most common case.

It is quite straightforward to fit such models by direct optimization of 
the likelihood, and MASS4 p. 445 gives you a template for logistic 
regression that could easily be modified.

>> -----Original Message-----
>> To: r-help at stat.math.ethz.ch
>> Subject: [R] logistic regression and 3PL model
>> Hello colleagues,
>> I am a novice with R and am stuck with an analysis I am
>> trying to conduct.
>> Any suggestions or feedback would be very much appreciated.
>> I am analyzing a data set of psi (ESP) ganzfeld trials.  The
>> response variable is binary (correct/incorrect), with a 25%
>> base rate.  I've looked around the documentation and other
>> online resources and cannot find how I can correct for that
>> base rate when I conduct a logistic regression.  I understand
>> that the correction would be equivalent to the three
>> parameter logistic model (3PL) in IRT but am unsure how to
>> best fit it from a logistic regression in R.

Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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