Thanks @paul.buerkner.
For those interested, the relevant function in the link appears to be posterior_epred_trunc_gaussian(). Here’s how I used elements from that function to replicate the behavior of fitted() by working directly with the posterior samples.
# extract the posterior samples
posterior_samples(m1) %>%
# wrangle
expand(nesting(b_Intercept, b_x, sigma),
x = seq(from = min(d_t_1e3$x), to = max(d_t_1e3$x), length.out = 30)) %>%
mutate(mu = b_Intercept + b_x * x) %>%
mutate(lb = -1,
ub = Inf) %>%
mutate(zlb = (lb - mu) / sigma,
zub = (ub - mu) / sigma) %>%
mutate(trunc_zmean = (dnorm(zlb) - dnorm(zub)) / (pnorm(zub) - pnorm(zlb))) %>%
mutate(trunc_mu = mu + trunc_zmean * sigma) %>%
group_by(x) %>%
tidybayes::mean_qi(trunc_mu) %>%
# plot!
ggplot(aes(x = x)) +
geom_point(data = d_t_1e3,
aes(y = y),
size = 1/4) +
geom_ribbon(aes(ymin = .lower, ymax = .upper),
alpha = 1/4) +
geom_line(aes(y = trunc_mu),
color = "blue")
