Can I fit a Thurstonian IRT model with mirt?

[Seongho Bae]

Hello, Phil.

Can I fit a Thurstonian IRT model with mirt.model()?

An example paper is this;

Brown, A., & Maydeu-Olivares, A. (2012). Fitting a Thurstonian IRT model to forced-choice data using Mplus. Behavior research methods, 44(4), 1135-1147.

I don't like the bivariate empty cell in SEM framework in Brown & Maydeu-Olivares paper. So I'm seeking another method what I can replace it.

Can I Fit a Thurstonian IRT model with mirt.model()?

Best regards,

Seongho Bae

[Phil Chalmers]

In principle I don't see why you couldn't estimate these models in mirt, though for now you'd have to switch to the Rsolnp optimizer to account for the reverse-sign equality constraints in the transformed loadings matrix (what they call $\breve{\Lambda}$). There may be a problem with high-dimensionality as well, but I'm not familiar enough with the models to confirm that. 

Otherwise, if you wanted to use the default optimizers for unbounded parameters, I would have to add a 'signed' argument somewhere to indicate that there are equality constraints but that their signs are flipped (i.e., instead of a1_1 = a1_2, it would have to be a1_1 = -a1_2), or more generally a transformation matrix for the entire parameter set (which I already use, but it's generally built up from inputs rather than directly accessible by the user). The latter would be the most general, so I'll probably consider adding that sometime in the future anyway.

Phil

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[Seongho Bae]

Can I try Rsolnp optimizer now for fit the Thurstonian Model? How can I apply that? Please give hints to me.

Seongho

2015년 9월 28일 월요일 오후 9시 31분 37초 UTC+9, Phil Chalmers 님의 말:

[Phil Chalmers]

Here's an example of using the optimizer: http://philchalmers.github.io/mirt/html/Three-Rasch.html. For this you would need to set up the more complicated Lambda matrix presented in the paper, which probably requires some hand calculations to see how it should look after transformation. Sorry I can't offer more in depth examples at the time (busy with other things). Cheers.

Phil