# Choosing family and prior in brms

Hey

I’d like to use brms to estimate whether there’s compelling evidence in favour of certain factors in a model.

My dependent variable has 3 levels - 1/0/-1. It is a subtraction of two binary variables for a given item - hit (1/0) minus false alarm (1/0). My fixed effects are both categorical and continuous

I’m not sure which family and linking function are the correct ones to use. The dependent variable isn’t exactly categorical, as it has levels, but also doesn’t seem to fit any of the ordinal types described in an ordinal regression tutorial (since there is no underlying continuous variable).

I’m also not sure how to set a prior when I have no prior estimation of the different predictors.

And just to make sure I’ve got the next bit right - after I figure out the top two questions, I compare models with/without each effect using bayes_factor in order to assess the evidence in favour of that effect?

Any help with these issues would be much appreciated
Thanks!

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It might be more straightforward if, instead of coding your DV as hits and false alarms, you let your DV be a binary factor (0 or 1) indicating the participants’ responses (`response_level`), and let that be predicted with the `true_level` (0 or 1) which interacts with your predictors `X` of interest. So

`response_level ~ true_level * (X1 + X2 + X3 + ...)`

Then you have a simple Bernoulli family model. The effects of the `X1, X2, ...` show how the “bias” – the tendency to respond 1 regardless of the true value – is influenced by `X1, X2, ...`; the effect of, for example, `true_level:X1` shows how the “discriminability” of the true value is changed by `X1`. If the link function is probit, the results can be phrased in terms of z-scores/d-prime, which might be useful. Relevant material can be found at https://vuorre.netlify.app/post/2017/10/09/bayesian-estimation-of-signal-detection-theory-models-part-1/ and https://psyarxiv.com/5ue9a/

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