Hi,
I’m working with ordinal models (the cumulative model to be precise) and I have a question concerning the default behavior of brms.
I read in this paper from DeYoreo and Kottas (https://doi.org/10.1080/10618600.2017.1316280) that the first cut-off point of the ordinal regression models is typically set to 0 for identifiability. From what I understand, this is not how the cumulative family of models is coded in BRMS. Is there a specific reason? If not, how can I set to a constant? Even if not for identifiability reasons, I’m guessing it could improve performance.
Best,
brms::cumulative() fixes the first threshold to 0 for identification. For a model with k levels in the response, k - 1 thresholds are estimated.
Hi Bwiernik,
I believe what you mean is that estimating k-1 thresholds imply the existence of an additional threshold, say \tau_0 that is set to 0? If so, I don’t believe that’s correct.
While it is true that the cumulative logit model for an ordinal outcome y_n \in \{ 1, ... , k \} has k - 1 thresholds \tau_1, ..., \tau_{k-1} , none of them are set to 0 either. The model implicitly assumes that \tau_0 = -\infty and \tau_k = \infty , as stated in this article by @paul.buerkner (see page 92).
**Note that the reference could be a bit confusing as they define k as the number of categories of the outcome variable minus one, while we are simply defining k as the number of categories.
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