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From |
"Joseph Coveney" <jcoveney@bigplanet.com> |

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

Subject |
st: RE: IRT with GLLAMM |

Date |
Thu, 5 Mar 2009 11:21:23 +0900 |

Have you tried simplifying the model, e.g., fitting a one-parameter IRT (Rasch) model, to see whether you can achieve convergence? If so, then use the fit as starting values for the two-parameter IRT model. If the condition number of the Rasch model is not good, then empirical underidentification will be even worse for the two-parameter IRT model. If you have access to MPlus, you might give it a try. Example 5.5 in the user's manual is for a two-parameter IRT model with binary test items as I recall. I must be misconstruing your description of the data: from your post, it seems that there are test items with identical scores--e.g., several test items where everyone got them all right or everyone got them wrong, or the one student who got the first item wrong (right) is the only person who got the second and subsequent items wrong (right). If this is the case, then you might have better luck if you discard all but one of these kinds of items. It's been my belief that multiple items with identical scores is trouble. My only experience with Rasch and two-parameter IRT models is with ordered-categorical responses, so I haven't looked into -xtmelogit-. But, to my knowledge, none of official Stata's mixed-model commands allows -constraints()-. (It's been on my wish list since -xtmixed- first appeared.*) Without the ability to impose constraints, I'm not sure how you'd set up these kinds of factor models. Joseph Coveney * The announcement yesterday of Bobby Gutierrez's course http://www.icpsr.umich.edu/cocoon/sumprog/course/0042.xml piqued my interest: "The theme of the third day can best be described as tricks of the trade, covering . . . models with complex and grouped constraints on covariance structures." Stas Kolenikov: My data set consists of students (CourseID variable), their test questions (Question) and 0/1 indicator of whether they've answered the question correctly. The data are in the long form appropriate for GLLAMM. I am modeling the questions as fixed/parameters of the model, and students as random factors. Here's what I have: * generate dummy variables for questions xi i.Question, noomit * specify the equation for the random factor: the dummy variables from the previous command eq diff : _IQ* * variance of the random factor identification constr 55 [Cou1_1]_IQuestion_4 == 1 * call to gllamm: 2-parameter IRT gllamm Correct _IQ* , fam( bin ) link( logit ) i( CourseID ) eq( diff ) nocons constr(55) I am specifying -nocons- so that each question has its own intercept (sensitivity times difficulty, in IRT terms), and the factor loadings from -eq()- option should give me the sensitivity. -gllamm-, however, has trouble converging. Does it have to do with empirical underidentification? Do I need to search for a better identifying variable? Question 4 above was the first on the list that had any variability; everybody answered the first three questions. It is probably not a terrific question to give identification, too: only a couple people missed it. My sample sizes are not terrific, either: I have about 40 students and about 30 questions. And there are lots of easy questions that were missed by one or two or three students only. If I have only one student who missed a question, then I probably won't be able to identify two parameters for that question, right? Finally, since we are talking about random effects logit in Stata, is there any way to run this with -xtmelogit-? It should be faster, at least. * * 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/

**References**:**st: IRT with GLLAMM***From:*Stas Kolenikov <skolenik@gmail.com>

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