Hi,

I’m wondering whether there is a way to use brms to fit a psychometric lapsing model for a multi-response (*categorical* rather than bernoulli-distributed) outcome? To make this more concrete, I’m trying to analyze which of 8 English vowels (“had”, “hid”, “head”, etc.") listeners heard based on the acoustic properties of the input *while also accounting for an unknown proportion of trials on which listeners have attentional lapses* (or for other reasons do not respond based on the input). On those lapsing trials, I’d like to either assume that all 8 vowels have the same uniform probability (1/8) of being responded or I might try to also fit the response bias. A concise summary of what I have in mind is given on p5 of https://www.biorxiv.org/content/10.1101/260976v2.full.pdf. (fwiw, this type of data is quite common but researchers often simplify it to ‘correct’ and ‘incorrect’ answers since they have no easy way of analyzing the data if it’s not binary).

I’ve previously used both the non-linear formula syntax (gamma + (1 - gamma - lambda) * perceptual model) and mixture syntax (lapse * bias + (1-lapse) * perceptual model) to run such models for binary outcomes. But the same approach does not seem to work when there are more than two possible categorical outcomes. For example, mixture(“categorical”, “categorical”) is not allowed:

```
Error: Some of the families are not allowed in mixture models.
```

My first question is for @paul.buerkner (if you have time) to see whether there are any plans to allow the special case when *all* mixture components are categorical, since that would seem to be well-formed.

My second question is whether anybody has some thoughts on how to fit such a model using brms::brm(). My first thought was that one might be able to put together a multivariate model that consists of 7 models, each predicting a binary outcome(vowel 2 vs. not vowel 2; vowel 3 vs. not vowel 3; etc.) through a non-linear or mixture formula. Is that even possible in brms? And would there be a way to constrain the lapse rate to be consistent across all seven models? Any feedback or alternative suggestions would be appreciated. It’s quite likely that I’m missing something more fundamental. Thank you in advance!