I see. Since I am not really sure where I want this to get shrunk, I
probably won't be trying these quasi-Bayesian routes. (Writing
MataBUGS can be an exciting year-long project on its own though :))
I'll go over my list of questions, and restrict the parameters to be
equal if the same (low) number of students have missed those
questions. That might kill my sensitivity parameter on these questions
though.
For -xtmelogit-, it looks to me like the covariance structure you need
is the matrix of ones... which is kinda stupid to deal with. Anyway I
hope Bobby G would chime in.
The Rasch model would then be just
g byte ones = 1
eq ones : ones
gllamm Correct [question dummies], ... eq( ones )
or
xtmelogit Correct [question dummies], nocons || studentID :
so that the random factor weighs equally on all questions, right?
On 3/5/09, jverkuilen <[email protected]> wrote:
> Stas,
>
> Sounds like an empirical unidentification problem to me, just as you say, and my advice is exactly the same as Joseph Coveney's: Run the Rasch model, which can be done simply as a random intercept logistic regression in -xtlogit-, -xtmelogit- or -clogit- (the latter for conditional ML favored by many Rasch-ies).
>
> If you can figure out how to run the 2PL in -xtmelogit- that would be great I messed around a little on that but don't know how to specify the requisite bilinear form in terms of the random effects covariance matrices.
>
> For your data, you may need to impose a prior. This can often be done by adding some pseudo-observations to your dataset that fit the model towards which you want to shrink. Having read the original papers of Bock et al on the estimation, the slope parameter has more need for a prior than the location (unsurprisingly). (All this is summarized in F Baker and SH Kim, 2002, Item Response Theory Estimation, CRC Press.)
>
> JV
>
>
> -----Original Message-----
> From: "Stas Kolenikov" <[email protected]>
> To: [email protected]; "Multilevel modelling discussion list" <[email protected]>
> Sent: 3/4/2009 6:46 PM
> Subject: st: IRT with GLLAMM
>
> 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.
>
> --
> Stas Kolenikov, also found at http://stas.kolenikov.name
> Small print: I use this email account for mailing lists only.
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>
>
> *
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>
--
Stas Kolenikov, also found at http://stas.kolenikov.name
Small print: I use this email account for mailing lists only.
*
* 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/
