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From |
jverkuilen <jverkuilen@gc.cuny.edu> |

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

Subject |
RE: st: IRT with GLLAMM |

Date |
Fri, 6 Mar 2009 10:46:07 -0800 |

The usual 2PL model has only one random effect but the model is bilinear. Let t_i be the random trait of subject i. Then for item j logit(p_ij) = a_j * t_i + b_j Usually specify T ~ N(0,1). There are other specifications. Estimation is then MML with integration over T. The Rasch model restricts a_j = a, or, equivalently, estimates the variance of T. This model can be easily fit by MML using -xtlogit- or -xtmelogit- by stacking the data long and using item dummies as fixed effects. There is a nice example out there showing how to do this with -clogit- by Phil Ender on ATS web page (Google for it, I can't dig it out right now). JV -----Original Message----- From: "Joseph Coveney" <jcoveney@bigplanet.com> To: statalist@hsphsun2.harvard.edu Sent: 3/5/2009 10:07 AM Subject: RE: st: IRT with GLLAMM I'm not sure what kind of convergence problems you're experiencing with -gllamm-. Is it just slowness? With the two-parameter model, my understanding is that you'd be fitting 30 random effects--something that would require a great deal of patience with -gllamm- at least with more than a few integration points and without multiple processors. There are some examples of these kinds of models fitted with -gllamm- in Xiaohui Zheng & Sophia Rabe-Hesketh. (2007) Estimating parameters of dichotomous and ordinal item response models with gllamm. _The Stata Journal_ 7(3):313-33. They limit themselves to a relative few test items, nowhere near 30. As far as fitting an analogous model with -xtmelogit-, couldn't you set up an equation on the random effects side of the double-pipe for student-by-test item interaction terms (the 30 random effects)? It would seem that the common tactic of omitting the first test item in the random effects equation (omitting it from the equation as the constant) identifies the model by fixing the first test item's loading factor (allowing the variance for the random effect for students to be free). I think that traditionally with IRT models, the random effects for students would be constrained to unit variance, which allows for all of the item factor loadings to be estimated (free)--they're held to be equal for the Rasch model (a single random effect, fitted with -xtlogit- as Jay mentions and as you show below) and allowed to be independently estimated in the two-parameter model * * 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:*"Joseph Coveney" <jcoveney@bigplanet.com>

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