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From |
Jean-Benoit Hardouin <jean-benoit.hardouin@univ-nantes.fr> |

To |
statalist@hsphsun2.harvard.edu |

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'svery informative comments.I think your sample is too small to envisage a complex IRT models likethe 2 parameters logictic model (2PLM or Birnbaum model) (60parameters=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 toone). Even for the Rasch model (1PLM) which consider only 31 parameters(30 difficulty parameters and the variance of the latent variable), yoursample 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 andyou have a 2PL model.

For most of psychometricians, the Rasch model (and its polytomousextensions like the Rating scale model or the Partial Credit Model) isthe only one (IRT) model which allows obtaining an objective measure (ameasure independent of the sample, and independent of the respondeditems), 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 inreasoning.

Generally, wedon't obtain a better measure with a complex IRT model than by using theclassical score computed as the number of correct responses. A complexIRT model can only be a way to understand the items functionning (is aguessing effect, a strong discrimination power...). So I alwaysrecommand 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 datafrom a different population, it can do some decidedly odd things.

Best, Jean-Benoit -- Jean-Benoit Hardouin, PhD Maitre de Conférences - Assistant Professor EA 4572 "Biostatistics, Clinical Research and Subjective Measures in Health Sciences" http://www.sante.univ-nantes.fr/biostat/ Departement of Biomathematics and Biostatistics Faculty of Pharmaceutical Sciences University of Nantes

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**Follow-Ups**:**RE: st: IRT with GLLAMM***From:*"Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>

**References**:**Re: st: IRT with GLLAMM***From:*Jean-Benoit Hardouin <jean-benoit.hardouin@neuf.fr>

**RE: st: IRT with GLLAMM***From:*"Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>

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