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st: 2-PLM (was Rasch)

From   Jean-Benoit Hardouin <>
Subject   st: 2-PLM (was Rasch)
Date   Fri, 05 Oct 2007 10:01:30 +0200

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 écrit :

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.


-----Original Message-----
[] On Behalf Of SR Millis
Sent: Wednesday, October 03, 2007 3:44 PM
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 <> wrote:

Dear Statalisters,

Can anybody help me to estimate a two-parameter
Rasch model by Stata.


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
Tel: 313-993-8085
Fax: 313-966-7682
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Jean-Benoit Hardouin, PhD
Maitre de Conférences - 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 :
Personal website :

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