[R] logistic regression and 3PL model

Dimitris Rizopoulos dimitris.rizopoulos at med.kuleuven.ac.be
Thu Nov 25 17:51:30 CET 2004

I don't know if I am missing something, but isn't there also a latent 
variable (trait) that must be integrated out using maybe Gauss-Hermite 
which might complicate a bit the calculations? So is this possible 
with `glm()'?


Dimitris Rizopoulos
Ph.D. Student
Biostatistical Centre
School of Public Health
Catholic University of Leuven

Address: Kapucijnenvoer 35, Leuven, Belgium
Tel: +32/16/336899
Fax: +32/16/337015
Web: http://www.med.kuleuven.ac.be/biostat

----- Original Message ----- 
From: "Prof Brian Ripley" <ripley at stats.ox.ac.uk>
To: "John Fox" <jfox at mcmaster.ca>
Cc: <r-help at stat.math.ethz.ch>
Sent: Thursday, November 25, 2004 5:13 PM
Subject: RE: [R] logistic regression and 3PL model

> 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 
> believe.
>> 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
> http://work.psych.uiuc.edu/irt/modeling_dich1.asp
> 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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