I am keen to get a detailed grasp of the relationship of some non-linear models analysed with **mgcv** vs. **brms**. The syntax is virtually the same, apart from the functions themselves `gam()`

vs. `brm()`

. But the summary tables differ. To illustrate this, I am using the first toy-example from **mgcv**:

```
require(mgcv)
require(brms)
# example from mgcv
set.seed(2)
dat <- gamSim(1, n=400, dist='normal', scale=2)
# gam from mgcv
summary(gam1 <- gam(y ~ s(x0) + s(x1) + s(x2) + s(x3), data=dat))
# Parametric coefficients:
# Estimate Std. Error t value Pr(>|t|)
# (Intercept) 7.83328 0.09878 79.3 <2e-16
# Approximate significance of smooth terms:
# edf Ref.df F p-value
# s(x0) 2.500 3.115 6.921 0.000131
# s(x1) 2.401 2.984 81.858 < 2e-16
# s(x2) 7.698 8.564 88.158 < 2e-16
# s(x3) 1.000 1.000 4.343 0.037818
# brm from brms
summary(brm1 <- brm(y ~ s(x0) + s(x1) + s(x2) + s(x3), data=dat))
# Smooth Terms:
# Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
# sds(sx0_1) 2.18 1.19 0.74 5.11 1.00 1856 2533
# sds(sx1_1) 2.05 1.11 0.70 4.88 1.00 1928 2416
# sds(sx2_1) 19.74 5.03 12.16 32.31 1.00 1142 1741
# sds(sx3_1) 0.90 0.91 0.03 3.23 1.00 1468 1731
# Population-Level Effects:
# Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
# Intercept 7.83 0.10 7.64 8.03 1.00 5138 3185
# sx0_1 -1.06 3.77 -8.79 6.21 1.00 2113 2201
# sx1_1 9.31 3.74 1.90 17.20 1.00 2019 2222
# sx2_1 35.47 11.85 11.58 58.22 1.00 2581 2655
# sx3_1 -0.61 2.44 -4.89 5.45 1.00 1881 1648
# Family Specific Parameters:
# Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
# sigma 1.98 0.07 1.84 2.13 1.00 4643 3062
```

So, all four smooths are significant according to the `gam`

. Equally, by `brm`

, CIs do not contain zeros. Nicely, `x3`

is flagged weak by both, so to say.

However, how should I interpret `Population-Level Effects`

from `brm`

? Are these simple comparisons with the Intercept? Is there more to it? Interestingly enough, besides x3 x0 also does not differ from the Intercept.

- Operating System: macOS Monterey (12.5.1)
- brms Version: 2.17.0

Thanks!