Intercept from brms model summary is different to posterior draws plot. What am I missing?

```
library(tidyverse)
library(brms)
library(tidybayes)
library(cmdstanr)
library(modelr)
setseed(1234)
# adjusted from
# https://willemsleegers.com/content/posts/18-bayesian-tutorial-simple-regression/bayesian-tutorial-simple-regression.html
options(
mc.cores = 4,
brms.threads = 4,
brms.backend = "cmdstanr",
brms.file_refit = "on_change"
)
data <- read_csv("https://willemsleegers.com/content/posts/18-bayesian-tutorial-simple-regression/Howell1.csv")
data <- filter(data, age >= 18)
data <- mutate(data, weight_mc = weight - mean(weight))
m1 <- brm(
data = data,
height ~ weight_mc,
family = gaussian,
prior = c(
prior(normal(160, 10), class = "Intercept"),
prior(cauchy(5, 5), class = "sigma"),
prior(normal(0, 3), class = "b")
),
sample_prior = TRUE,
seed = 4,
silent = 2,
file = "m1.rds"
)
m1
lm(data = data,
height ~ weight_mc)
weight_mean <- data %>%
pull(weight) %>%
mean()
predicted_slopes_qi <- data_grid(data, weight_mc = round(weight_mc)) |>
add_predicted_draws(m1) |>
median_qi() |>
mutate(weight = weight_mc + weight_mean)
pdraw<-data_grid(data, weight_mc = round(weight_mc)) |>
add_predicted_draws(m1) |>
mutate(weight = weight_mc + weight_mean)
lm(data = pdraw%>%sample_n(100)%>%mutate(height=.prediction),
height ~ weight_mc)
linpred=data_grid(data, weight_mc = round(weight_mc)) |>
add_linpred_draws(m1) |>
median_qi()|>
mutate(weight = weight_mc + weight_mean)
p1=ggplot() +
geom_abline(intercept=154.61, slope=0.9, color="red")+
geom_ribbon(
aes(ymin = .lower, ymax = .upper, x = weight),
data = predicted_slopes_qi,
alpha = .25
) +
geom_line(
aes(x = weight, y = .prediction),
data = predicted_slopes_qi
) +
geom_point(
aes(x = weight, y = .prediction),color="skyblue2",pch="*", size=3,
data = pdraw%>%sample_n(100)
) +
geom_point(
aes(x = weight, y = height),
data = data,
alpha = .25
) +
geom_ribbon(
aes(ymin = .lower, ymax = .upper, x = weight),color="salmon",
data = linpred,
alpha = .5
)+
labs(x = "Weight", y = "Height")+
coord_cartesian(xlim = c(0, 60), ylim=c(140,180))
p1
```

Thanks

Herry

- brms Version: 2.21.0’

OS:

platform x86_64-pc-linux-gnu

arch x86_64

os linux-gnu

system x86_64, linux-gnu

status

major 4

minor 3.2

year 2023

month 10

day 31

svn rev 85441

language R

version.string R version 4.3.2 (2023-10-31)

nickname Eye Holes