Prior specification for ordinal probit model

Interfaces brms
1

I’m having difficulties in specifying prior distribution for the cut-off (I think it is coded as “Intercept” in brms).

fit1=brm(y ~ x1+x2 +x3+ x4 +(1|UserId), data = dat1,family=cumulative(“probit”), sample_prior = “only”, set_prior(“normal(0,0.1)”,class=“b”), set_prior(“student_t(3, 0, 1)”, class = “Intercept”),chains = 4, ,seed=10001,autocor=NULL)

Running the above code and looking at the result of prior_summary(fit1) gives me exactly the priors I specified for the population effects “b” but the prior for the “Intercept” stays as the default student_t(3, 0, 10) rather than the one I specified. In addition, looking at the result of ppc_hist () the distributions of replicated data yrep from the prior distribution doesn’t seem to be in line with empirical distribution of the data y.

Additional information
X1 is a dummy variable taking value 0/1

summary(Fit1 $data$x2)
Min. 1st Qu. Median Mean 3rd Qu. Max.
22.00 47.00 52.00 54.07 63.00 72.00

summary(Fit1 $data$x3)
Min. 1st Qu. Median Mean 3rd Qu. Max.
-5.443 2.367 5.833 6.229 9.865 18.746

summary(Fit1 $data$x4)
Min. 1st Qu. Median Mean 3rd Qu. Max.
969 1009 1017 1015 1023 1044

I didn’t expect the effect of x3 and x4 to be outside [-0.5,0.5].
ppc_hist

2

Try writing prior = set_prior(“normal(0,0.1)”,class=“b”) + set_prior(“student_t(3, 0, 1)”, class = “Intercept”). Right now, you actually just pass the first prior to the prior argument.

3

Thank you Paul! Now I can see my prior for the “Intercept” as I specified. Do you have any recommendation about the prior to be used for the “Intercept”?. As you see from the attached figure the observed outcome is some what symmetrical. I am trying different scale parameter but I am having high standard error for the cutoff’s.

4

That’s a hard one. I can’t really give you any good adcive on this. However, usually, estimating the thresholds should not be a major issue. What is “high standard error” for you?

5

Thank you Paul. I got a high standard error because I wasn’t looking at the right summary result. I have the result which I expect now.