add proj_epred()

[avehtari]

Currently there are proj_predict() and proj_linpred(), but no proj_epred(). proj_epred() would be useful for ordinal models (e.g. family = cumulative("logit"), but would also otherwise match what is available for brms and rstanarm

[fweber144]

Yes, I agree that proj_epred() should exist. It should be relatively easy to implement, as a wrapper of proj_linpred() with transform = TRUE.

[avehtari]

I'm confused, as for ordinal models

• brms::posterior_linpred(..., transform = TRUE) is not equivalent to brms::posterior_epred(...)
• output of proj_linpred(..., transform=TRUE) does not match in structure of the output of brms::posterior_linpred(..., transform = TRUE)

[fweber144]

It seems brms::posterior_linpred() with the default of transform = FALSE returns the linear predictor excluding the latent-category thresholds. Building upon that, brms::posterior_linpred() with transform = TRUE returns the no-threshold latent predictor transformed to response scale (here: the probability space [0, 1]). In contrast, brms::posterior_epred() seems to take the latent-category thresholds into account and then returns probabilities (for each response category). Example:

data(inhaler, package = "brms")

# brms --------------------------------------------------------------------

bfit <- brms::brm(
  formula = rating ~ period + carry + treat,
  data = inhaler,
  family = brms::cumulative(),
  iter = 500,
  chains = 1,
  seed = 25569
)

bpl <- brms::posterior_linpred(bfit)
dim(bpl)
#> [1] 250 572
bpl_t <- brms::posterior_linpred(bfit, transform = TRUE)
dim(bpl_t)
#> [1] 250 572
all.equal(bpl_t, plogis(bpl))
#> [1] TRUE
bpe <- brms::posterior_epred(bfit)
dim(bpe)
#> [1] 250 572   4
all(0 <= bpe & bpe <= 1)
#> [1] TRUE

Currently, projpred's proj_linpred() behavior is to always take the latent-category thresholds into account (even for transform = FALSE):

# projpred ----------------------------------------------------------------

library(projpred)
#> This is projpred version 2.10.0.
refm <- get_refmodel(bfit, brms_seed = 99664)
prj <- project(
  refm,
  predictor_terms = c("carry", "treat"),
  ndraws = 25,
  seed = 70244
)

ppl <- proj_linpred(prj)
dim(ppl$pred)
#> [1]  25 572   3
ppl_t <- proj_linpred(prj, transform = TRUE)
dim(ppl_t$pred)
#> [1]  25 572   4

^{Created on 2026-03-29 with reprex v2.1.1}

Not taking the latent-category thresholds into account would seem a bit arbitrary and too family-specific to me, and it would also lead to the confusing behavior you observed in brms.

Hence, I would prefer proj_epred() to be a simple wrapper of proj_linpred() with transform = TRUE. The return value of proj_epred() would then be consistent with brms::posterior_epred().