Non linear, sequential model using results of cumulative regression in a bernoulli regression

Hi all,
I was interested in modeling something like this (but I don’t realy know how to categorise/name it): I have data about the descission for or against keeping a testitem in the itempool after a expert rating made by the head of study in binary form. I want to do a logistic regression for this process to get a hint what argument might have been most important for this descission.

The arguments include:the importance of the item (as seen by the experts) and if the experts found the items to be problematic in some way. The importance was rated on a rating scale.

So the base formula looks something like this using brmsfamily(“bernoulli”, “logit”):

resp_desc ~ 1 + impotance + error

Now my idea was to model the importance rating of an item with the cumulative link via based on the data given by the experts

importance_rating ~ 1 + (1 | item)

and use these values for the item’s importance in the first formula in the importance term. This seems to require some kind of sequential model fitting in each step. First the values for the items importance have to be estimated. And then the logistic regression on the descissions could follow. Is something like this possible? Or is it possible to do this simultaneousely and combine both fomulae?

Sincerely Simon Schäfer

I think what you need is a mixture model where you combine a Cumulative with Bernoulli? However, since you say there’s an “importance rating” then Cumulative is not the only option. Perhaps a Sequential (i.e., sratio in brms) or Adjacent-category (i.e., acat in brms) could also be an option? I’ve never tried to combine these families with Bernoulli however,

Thanks for your answer. I found that my question seems to be realted to seome of the open issues at github for brms like SEM (#304) and more specific #1093 “Specify random effects of one response as predictors of another”. As far as I understood the answers there this might not be implemented but I’ll try the latent variable work around specified there (and in this blog entry) after informing myself more about SEMs. At least now I can specify my question and relate it to a superordinated topic. Another thing I’ll will try is using the new blavaan-Stan approch.