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From |
"Verkuilen, Jay" <JVerkuilen@gc.cuny.edu> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: IRT with GLLAMM |

Date |
Mon, 16 Mar 2009 12:22:57 -0400 |

Jean-Benoit Hardouin wrote: I just figured I'd offer some alternative perspective on Jean-Benoit's very informative comments. >>I think your problem of convergence is a consequence of your small sample size. You have only N=40 subjects for J=30 items. Generally in IRT, we consider to be in good conditions if J<<N. In order to achieve this requierement, sample size are generally important (2000-30000 subjects) if the test (questionnaire) is long (typically in Educational Sciences) or if the sample size is small (100-300 individuals), the test is short (J=5-10) (typically in Health Sciences).<< True enough but I guess I'd say that you can relax this somewhat provided you know what you're doing. Certainly Stas qualifies as "knows what he's doing." >>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. >>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. 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 reasoning. >>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. >>Concerning the fit of a 2PLM, if you have SAS, you can easily test the convergence of the estimations by using the %anaqol macro-program (available on http:\\www.anaqol.org). This macro use the NLMIXED procedure which is based on the same technics of estimation than -gllamm-, so these two procedure are comparable (even on the computing time, usually very long !!!!!).<< NLMIXED has one really big advantage over -gllamm- in many circumstances. It uses analytic derivatives via automatic differentiation rather than numerical derivatives. This is a potentially huge speedup because it cuts the number of fevals down a lot. I have gotten quite complex models to run in NLMIXED quite rapidly (seconds to minutes) given good starting values. Sure, it's not as quick as, say, BILOG, but it's a whole lot more flexible. It is imperative that it have good starting values, however. One of my mentors, Carolyn Anderson, has done some nice work on pseudo-likelihood estimation of very large IRT models. She's got a more technical article somewhere in the Psychometrika pipeline, but for a simpler version see: Anderson, C. J., Li, Z., & Vermunt, J. K. (2007). Estimation of models in a Rasch family for polytomous items and multiple latent variables. Journal of Statistical Software, 20(6), 1-36. All of these models could be ported in Stata quite easily. JV * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: IRT with GLLAMM***From:*Jean-Benoit Hardouin <jean-benoit.hardouin@univ-nantes.fr>

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

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