Many facets rasch model in brms

Interfaces brms
1

Hi,
I was interested in using the Many Facets Rasch model with the brms package. Is there a way to implement it? And a way to plot the results?
Thank you in advance!

2

There probably is, brms is very flexible. And if not you can probably implement it directly in Stan.

I am familiar with Rasch models, but I’m not sure what a “many facets” model is. Could you explain, or state the model equation?

Have you tried any code yet? What problems did you run into?

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3

Thanks for your answer! I have 5 facets, i.d. rater, student, lexeme, trial, criteria (criteria contains 5 different items, two rated binomially and three on a 1-4 scale). The Winsteps model statement I want to reproduce has the following formula
Model = ?,?,?,?,1-2,D,1
?,?,?,?,3-5,R4,1
Here there are two models where all the “facets” rater, student, lexeme, and trail interact, and we define that items 1 and 2 are dichotomous, while items 3 to 5 are on a different rating scale (1-4).

I was thinking of using a multivariate multilevel model approach like this, but the model does not seem to converge. In particular, I don’t know how to set the random incept correctly without making the model too complex (I’m new to brms).

Thank you very much for any ideas you may have!

4

I’m not familiar with Winsteps, unfortunately. And your description of the data didn’t immediatly make sense to me.

I read quickly about the many facets model, and it seems to me like a hierarchical cumulative logit model with mostly random effects on the right hand side of the model equation?

Anyway, this paper seems relevant to you, they actually implement a revised many facets rasch model in Stan: A generalized many-facet Rasch model and its Bayesian estimation using Hamiltonian Monte Carlo | Behaviormetrika

5

Thank you for your answer. I am not familiar with this, but I don’t think it is possible to account for different response variables (binary and ordered) in the same model.

I will have a look at the paper, thank you!

6

I’m pretty sure it’s possible to specify such a model in Stan, and perhaps also in brms. Might be difficult to fit, but at least possible to try.

Are the different responses measures of the same latent construct (ability in IRT-terms)? Or are they measures of correlated but distinct latent variables?