`stan_glmer()` and `offset()` formula term

Summary:

A stan_glmer() fit with offset() in the formula seems to be handled incorrectly in posterior_linpred().

Description:

Unlike a stan_glm() fit, a stan_glmer() fit with offsets specified via offset() in the formula doesn't include the offsets in the linear predictors returned by posterior_linpred(). This might be related to issue #541.

Reproducible Steps:

library(rstanarm)
options(mc.cores = parallel::detectCores(logical = FALSE))
data("kidiq")
kidiq_gr <- within(kidiq, {
  agegr <- cut(mom_age,
               breaks = unique(quantile(mom_age)),
               include.lowest = TRUE)
  levels(agegr) <- paste0("lvl", seq_len(nlevels(agegr)))
})
set.seed(3492)
kidiq_gr$offs_col <- rnorm(nrow(kidiq))
glmm_fit <- stan_glmer(kid_score ~ mom_iq + (1 | agegr) + offset(offs_col),
                       data = kidiq_gr,
                       seed = 734572)
glmm_pl <- posterior_linpred(glmm_fit)

glmm_drws <- as.matrix(glmm_fit)
glmm_pl_man <- glmm_drws[, "(Intercept)"] +
  glmm_drws[, "mom_iq", drop = FALSE] %*%
  t(kidiq_gr[, "mom_iq", drop = FALSE]) +
  glmm_drws[, paste0("b[(Intercept) agegr:", kidiq_gr$agegr, "]"), drop = FALSE]
all.equal(unname(glmm_pl), unname(glmm_pl_man), tolerance = 1e-15)

with that last line returning TRUE, so the offsets are not included in the linear predictors. In contrast, for stan_glm(), the offsets are included in the linear predictors:

glm_fit <- stan_glm(kid_score ~ mom_iq + offset(offs_col),
                    data = kidiq_gr,
                    seed = 734572)
glm_pl <- posterior_linpred(glm_fit)

glm_drws <- as.matrix(glm_fit)
glm_pl_man <- glm_drws[, "(Intercept)"] +
  glm_drws[, "mom_iq", drop = FALSE] %*%
  t(kidiq_gr[, "mom_iq", drop = FALSE]) +
  matrix(kidiq_gr$offs_col,
         nrow = nrow(glm_drws),
         ncol = nrow(kidiq_gr),
         byrow = TRUE)
all.equal(unname(glm_pl), unname(glm_pl_man), tolerance = 1e-15)

(with that last line returning TRUE).

RStanARM Version:

2.21.2 (from https://mc-stan.org/r-packages/)

R Version:

4.1.0

Operating System:

Ubuntu 20.04.2

Reproduce the issue using the supplied kidiq example, comparing posterior_linpred() for stan_glmer() and stan_glm() with offset() terms. Trace how posterior_linpred() constructs linear predictors for each fit type; done means the stan_glmer() result includes the formula offset and no longer matches the manually computed version that omits it.