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Re: st: IRT with GLLAMM

From   Jean-Benoit Hardouin <>
Subject   Re: st: IRT with GLLAMM
Date   Mon, 16 Mar 2009 19:22:23 +0100

Verkuilen, Jay a écrit :
Jean-Benoit Hardouin wrote:

I just figured I'd offer some alternative perspective on Jean-Benoit's
very informative comments.

I think your sample is too small to envisage a complex IRT models like

the 2 parameters logictic model (2PLM or Birnbaum model) (60 parameters=30 discriminating powers (factor loadings) minus 1 (identifiability constraint), 30 difficulty parameters (fixed effects), and the variance of the latent variable (which generally is not fixed to

one). Even for the Rasch model (1PLM) which consider only 31 parameters (30 difficulty parameters and the variance of the latent variable), your

sample is small !!<<

This is where Bayesian estimation (deterministic or stochastic) can be
VERY helpful. You can fit a model that's a compromise between the Rasch
and 2PL by using a hyper-parameter on the slopes, for instance, to
shrink things towards a common mean value. Make this prior very
informative and you have a Rasch model. Make it very uninformative and
you have a 2PL model.

There is two a frequentist appoach which is the ONE Parameter Logistic Model (OPLM) which is different of the 1-PLM(=Rasch model). The OPLM allows defining a value of slope (discriminating power) different for each item. The difference with the 2PLM is that this slopes are a priori fixed by the user. The properties of the OPLM are very close of the Rasch model (objective measure, exhaustivity of the score), with a besser flexibility compare to the Rasch model. This is possible to implement this model with gllamm
For most of psychometricians, the Rasch model (and its polytomous
extensions like the Rating scale model or the Partial Credit Model) is the only one (IRT) model which allows obtaining an objective measure (a measure independent of the sample, and independent of the responded items), so the others IRT models are not recommanded.<<

Just to note this is an area of substantial dispute.
Yes !!
The 2PL model is
the Spearman factor model analog for logistic regression. If you like
the Spearman factor model but hate the 2PL, there's a conflict in
I don't hate the 2PLM but I don't see any advantage of this model compared to the Rasch family model (which have nice measurement properties) or compared to the Classical Test Theory (where the measure generally is more reliable). I think the 2PLM is a pretty statistical tool to verify the proposition "the model should have a good fit to the data", but is not a very usefull model for a practical use (in the idea to create a measure with good properties (psychometric point of view) or reliable (practical point of view)).

Generally, we
don't obtain a better measure with a complex IRT model than by using the

classical score computed as the number of correct responses. A complex IRT model can only be a way to understand the items functionning (is a guessing effect, a strong discrimination power...). So I always recommand to use the Rasch model in a first intention.<<

Agreed. If you're *making* a test, use the Rasch model if at all
possible. The problem with it is the fact that often we don't get to
pick the dataset we're analyzing. When you fit a Rasch model to data
from a different population, it can do some decidedly odd things.
If the Rasch model don't agree with another population than this one used to check the fit, then there is Differential Item Functionning which is well described in the literatture and which can be taking account, even with the Rasch model !


Jean-Benoit Hardouin, PhD
Maitre de Conférences - Assistant Professor
EA 4572 "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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