I’m using the cumulative() family in brms. In other software implementations of the graded response model, each of the thresholds is freely estimated and so they can be out of order (e.g., the threshold between “Not sure” and “Agree” being larger than the “Agree”–“Strongly agree” threshold). That can be useful to detect poorly functioning items within the model.
Can anyone tell me if the estimation procedure in brms permits such disordered thresholds or does it constrain them to have the “proper” order?
The cumulative() family implies ordered thresholds, if you don’t want ordered thresholds then you’ll be after the acat (adjacent category) or sequential family.
There’s a pretty thorough coverage of the different ordinal models and their brms mappings in this paper: https://journals.sagepub.com/doi/full/10.1177/2515245918823199
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Yes, I’ve read that paper many times. What isn’t clear to me from the paper or the brms docs is what estimation constraints are imposed on the thresholds in a cumulative model.
Most implementations of the graded response model freely estimate each threshold. Does the Stan cumulative model also do that or does it constrain the thresholds to be in order?
It’s not an estimation constraint, but a fundamental component of a cumulative model. The cumulative model implies a single latent variable with thresholds indicating the latent position at which the next observed category is observed.
Using Figure 1 from that paper:
The only thing that determines which threshold corresponds to which category is their ordering.
Are you thinking of the generalised partial credit model? That doesn’t require ordered thresholds (uses the adjacent-category family). If not, can you point to an example of the graded response model without ordered thresholds so I can see how it’s implemented?
The brms generated Stan code enforeces the ordering.
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