# Cumulative probit regressions - trouble with interaction terms and guidance setting priors for differing predictors

Hello,

I have been looking into Bayesian cumulative probit regressions with brms. I have an ordinal outcome variable (rating: 1-4) with one categorical predictor (group: A/B) and two continuous predictors (both which are centered).

I am thinking about a mixed model structured as such

``````bf.form = bf(rating ~ group * cont_pred1 * cont_pred2 + (1|ID) + (1|stimulus_no) + (1|stimulus_origin)
``````

but have encountered issues with the interaction terms and setting priors, particularly for the continuous predictors (range of cont_pred1: -0.09 - 0.25; range of cont_pred2: -41.2 - 32.7).

Below is the code I have used to implement the model:

``````intercept.priors = tibble(rating = 1:4) %>%
mutate(proportion = 1/4) %>%
mutate(cumulative_proportion = cumsum(proportion)) %>%
mutate(probit_threshold = qnorm(cumulative_proportion))

priors = c(
prior(normal(-0.674, 1), class = Intercept, coef = 1),
prior(normal(0, 1), class = Intercept, coef = 2),
prior(normal(0.674, 1), class = Intercept, coef = 3),
prior(normal(0, 1), class = b)))

mod.fake = brm(bf.form, data = df, prior = priors, family = cumulative("probit"))

``````

Using shuffled data, I have been able to run the model using a formula without the interactions terms but get the following error with the interaction terms:

``````"Error in sampler\$call_sampler(args_list[[i]]): Initalization failed"

Chain 1: Rejecting initial value:
Chain 1:   Log probability evaluates to log(0), i.e. negative infinity.
Chain 1:   Stan can't start sampling from this initial value.

``````

Likewise, I have been trying to estimate the priors using `sample_priors = "only"` and have been unsuccessful in determining ones that fit the simulated data.

``````mod.sample = brm(bf.form, data = df, prior = priors, sample_prior = "only", family = cumulative("probit"))

``````

My questions are:

1. Can a cumulative probit model with brms include interaction terms? If so, why might I be getting this error?
2. Does anyone have suggestions for setting the beta priors?
3. Are there alternative models/approaches that could be considered?