st: 2-PLM (was Rasch)

[Jean-Benoit Hardouin <jean-benoit.hardouin@univ-nantes.fr>]

I completely agree with SR Millis : 2-PLM is not at all a Rasch model, 
and generally is not a good solution when the Rasch model don't fit the 
data. From a psychometrician point of view, 2-PLM (Birnbaum model) only 
is a statictician model to obtain a good fit, but is not a 
psychometrician model, because it have not good psychometrician 
properties. Generally, it is recommanded to modify a scale if the Rasch 
model don't fit it (for example, by reformulating or omitting  
problematic items...), but it is not recommanded to use 2-PLM or more 
complex model (3-PLM, 4-PLM, 5-PAM...).

Nevertheless, Zheng and Rabe-Hesketh recently have wrotten an excellent 
paper in the Stata journal, which explain how to estimate the parameters 
of the 2-PLM.

My own advice is to avoid this model, and to consider only the Rasch 
model and its extensions : there is a very interesting extension of the 
Rasch model wich is the OPLM (One Parameter Logistic Model) proposed by 
Verhelst in the reference book of Fisher and Molenaar (1997): /Rasch 
models. Foundations, recent developments and applications. / Springer 
Verlag. With the OPLM, it is possible to adjust the discriminating 
powers of the items whitout lost of the Rasch properties. This model can 
be fit with gllamm.

Concerning the programing under Stata, -gllamm- is actually the more 
important reference to estimate parameters of IRT models. Concerning the 
Rasch model, -raschtest- allows estimating the parameters of the Rasch 
model and evaluating the fit. Concerning the 2-PLM, there is no (to my 
knowledge) specific Stata module, and the only solution is to use 
-gllamm- which is in this case very slow, but other faster algorithm 
have not be developped under Stata. Concerning the OPLM, it is possible 
to estimate it with -gllamm- (marginal maximum likelihood - MML), or 
with -mmsrm- (GEE algorithm, with several restrictions, notably that the 
variance of the latent trait is lesser than 1 - this algorithm can, in 
some cases, be faster than MML).

I hope this helps
Jean-Benoit Hardouin

Davood Souri a �crit :


> You are right, I mean two-parameter item response model. I have tried
> gllamm, but it is very slow and not suitable for large datasets. I am
> wondering if there is another ado file in Stata.
>
> Thanks
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of SR Millis
> Sent: Wednesday, October 03, 2007 3:44 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: Rasch
>
> There is no such thing as a 2-parameter Rasch model.
> By definition, Rasch is a 1-parameter model.
>
> SR Millis
>
>
> --- Davood Souri <davood.souri@gmail.com> wrote:
>
>  
>
> > Dear Statalisters,
> >
> >
> >
> > Can anybody help me to estimate a two-parameter
> > Rasch model by Stata.
> >
> >
> >
> > Thanks
> >
> >    
> Scott R Millis, PhD, MEd, ABPP (CN,CL,RP), CStat
> Professor & Director of Research
> Dept of Physical Medicine & Rehabilitation
> Wayne State University School of Medicine
> 261 Mack Blvd
> Detroit, MI 48201
> Email:  smillis@med.wayne.edu
> Tel: 313-993-8085
> Fax: 313-966-7682
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--
Jean-Benoit Hardouin, PhD
Maitre de Conf�rences - Assistant Professeur
Team of Biostatistics, Clinical Research and Subjective Measures in Health Sciences

Departement of Biomathematics and Biostatistics
Faculty of Pharmaceutical Sciences
University of Nantes
1, rue Gaston Veil - BP 53508 
44035 Nantes Cedex 1 - FRANCE 
Email : jean-benoit.hardouin@univ-nantes.fr
Personal website : http://www.anaqol.org

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