Understanding cumulative probit ordinal priors

Interfaces brms
,
1

As I am dealing with 7-item Likert data, I am trying to get my hand around cumulative probit models, and how they are implemented in brms

I don’t have much prior information, so I planned to use the technique mentioned by @Solomon in
this post: Understanding odd estimates from cumulative probit model - #14 by Solomon

However, my actual data are quite skewed, but do not contain the highest ranked category.
This means that brms will not allow me to specify an intercept for \tau_6

Running the code:

validate_prior(prior = c(prior(normal(-1.068, 1), class = Intercept, coef = 1),
                         prior(normal(-0.566, 1), class = Intercept, coef = 2),
                         prior(normal(-0.18, 1), class = Intercept, coef = 3),
                         prior(normal( 0.18, 1), class = Intercept, coef = 4),
                         prior(normal( 0.566, 1), class = Intercept, coef = 5),
                         prior(normal( 1.068, 1), class = Intercept, coef = 6),
                         prior(exponential(1), class = sd)),
               data=data_without_cat_7,
               family=cumulative(probit),
               formula=response ~ 1 + (1 | id) + (1 | name))

yields the error message:
Error: The following priors do not correspond to any model parameter: Intercept_6 ~ normal(1.068, 1)

I can of course introduce synthetic data to fix the issue, e.g:

d <- rbind(data_without_cat_7, data.frame(response=c(7), id=c("a"), name=c("extra")))
validate_prior(prior = c(prior(normal(-1.068, 1), class = Intercept, coef = 1),
                         prior(normal(-0.566, 1), class = Intercept, coef = 2),
                         prior(normal(-0.18, 1), class = Intercept, coef = 3),
                         prior(normal( 0.18, 1), class = Intercept, coef = 4),
                         prior(normal( 0.566, 1), class = Intercept, coef = 5),
                         prior(normal( 1.068, 1), class = Intercept, coef = 6),
                         prior(exponential(1), class = sd)),
               data=d,
               family=cumulative(probit),
               formula=response ~ 1 + (1 | id) + (1 | name))

This gives PPC checks that align reasonably well with my assumption of equal probability among responses (and it also shows the skewedness of the actual responses):

image
image799×612 14.3 KB

But this would of course not work when I want to analyse the actual data set.
It does not make sense (to me) to add data to “fill out categories”, but I would still like the model to have some indication into how many 6 responses and 7 responses I could expect, given the posterior.
What am I missing? Appreciate your thoughts on the issue (and as you probably know, I am very much a newbie on ordinal regression using brms, though I found this blog post immensely useful: Notes on the Bayesian cumulative probit | A. Solomon Kurz

  • Operating System: Ubuntu 22.04, R 4.5.0
  • brms Version: 2.22.0
2

Hey @epkanol, when you say

However, my actual data are quite skewed, but do not contain the highest ranked category. This means that brms will not allow me to specify an intercept for \tau_6,

that’s not quite right. You can use the resp_thres() helper function to tell brm() how many thresholds you expect. That could look like this

my_fit <- brm(
  family = cumulative(probit),
  formula = response | thres(6) ~ 1 + (1 | id) + (1 | name),
  ...)

Note I’m using the shorthand alias thres(). You can learn about this function in the Additional response information subsection of the brmsformula section of the brms reference manual.

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3

Amazing, thanks @Solomon (again!)

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