# Choosing informative priors for Bayesian ordered logistic regression

Crossposted from CV; I thought to post it there first because this isn’t a Stan-centric question necessarily, but I’m thinking this community might give me the best answer.

What are some guidelines for choosing weakly informative priors in a Bayesian ordinal regression? Consider the following model from the Stan manual (version 2.17.0, section 9.8, page 138):

``````data {
int<lower=2> K;
int<lower=0> N;
int<lower=1> D;
int<lower=1,upper=K> y[N];
row_vector[D] x[N];
}
parameters {
vector[D] beta;
ordered[K-1] c;
}
model {
for (n in 1:N)
y[n] ~ ordered_logistic(x[n] * beta, c);
}
``````

We specify the likelihood as `ordered_logistic`, but improper flat priors are left on all `beta` and `c`.

I can reason how to specify more informative priors on `beta`, because it is simply how much how much the log odds change for each unit increase in each predictor in `x`. These, for instance, could simply be `beta ~ normal(0, 3)` or something, depending on how the predictors are scaled.

However, how does one specify priors on the cutoff points `c`? They have to be ordered, but I am not sure how to specify that. Also, I am not sure how to think about them being distributed. Anybody know of guides for informative priors for ordinal regression?

The Stan community very briefly touches on it on GitHub, but it isn’t a fully-realized or explained section.

This can be problematic for identification, especially if there’s an intercept colum in the `x` matrix.

That’s covered in the manual example.

I’m afraid that’s about as far as we’ve gotten.

The example manual says

If the cutpoints were assigned independent priors, the constraint effectively truncates the joint prior to support over points that satisfy the ordering constraint.

Does this also hold if I am running a hierarchical ordered logistic regression?

I am thinking

``````c~normal(mu_c, sigma_c)
``````

I will also use appropriate diffuse hyperpriors on mu_c and sigma_c.

I have Conjoint data in which respondents answer choice questions with ordered outcomes. Thanks.