Choosing family and link

For Bayesian IRT models you may want to take a look at https://arxiv.org/abs/1905.09501

For more details and a tutorial on ordinal models see https://psyarxiv.com/x8swp/

In both papers, models are fitted with brms.

Thank you for your advice Guido, and your resources Paul. The first beginning of page 20 of the ordinal model paper appears to confirm that there is a way that multiple items assessing the same construct can be modelled in brms in other ways that averaging across items. Paul, are there any resources regarding this that go into more detail? Is this similarly to a latent modelling approach as suggested by Guido? Thanks.

I believe I also have ordinal examples in the IRT paper I linked to above. Not sure how that relates to what Guido suggested, as I haven’t seen the exact mathematical formulation of this.

@paul.buerkner’s IRT paper does what I tried to explain (I remember see a reference to Paul’s paper on twitter). The connection between IRT analysis and latent variable modeling is that the ability parameter that can be estimated in an IRT analysis is a latent variable.

In my understanding, IRT analysis is a special form of a hierarchical logistic or ordinal regression, which is the reason it is straight forward to implement in brms.

Brilliant, thank you!