I am back with another question trying to figure out my priors for an ordinal mixed effects regression with a categorical predictor, two random effects, and a random slope for the predictor by one of the random effects. The question I have is how to specify a prioir for the random slope.
Here is where I am:
model2 ← brm(
data = NSgjt, family = cumulative(probit), rating ~ Type + (1+Type | Subject) + (1 | ITEM), prior = c(prior(normal(-0.84, 1), class = Intercept, coef = 1), prior(normal(-0.25, 1), class = Intercept, coef = 2), prior(normal( 0.25, 1), class = Intercept, coef = 3), prior(normal( 0.84, 1), class = Intercept, coef = 4), prior(normal(0, 1), class = b), prior(exponential(1), class = sd)), cores = 2, seed = 1, iter = 5000, init_r = 0.2)
The model was adapted from https://solomonkurz.netlify.app/blog/2021-12-29-notes-on-the-bayesian-cumulative-probit/ which I also used to come up with the priors for the intercepts of each level of the dependent outcome(priors for coef 1-4), the categorical predictor Type ( prior(normal(0, 1), class = b) and the random effect (prior(exponential(1), class = sd))). I am not sure whether I need to specify one for each random effect or if one is enough for both. Solomon Kurz only specifies one even though he has two random effects.
The data in a nutshell is unordered ordinal data where the DV ranges from 1-5, likert-scale-like. I followed Verissimo (2021) (https://osf.io/7n92b) for the rest of the analysis after running the model. That is for looking at model fit through posterior predictive checks and the distribution of the posterior through conditional_effects. I also integrated R codes for running Bayes factor analyses to test for main effects or model fit with and without random effects from https://vasishth.github.io/bayescogsci/book/index.html and am using the same book to interpret main effects of my categorical predictor Type.
The Bayes factor analysis shows the random slope is needed in that a model without it is inferior to one with it ( ```
Thank you in advance for any advice. Francesco