I have a simple doubt about the interpretation of hurdle coefficients when using hurdle models through brms. I adapted one example from the brms vignette on distributional models [link].

In the output below the coefficient `hu_child`

would be the log odds of catching 0 fish, i.e, for each child in the visiting group the model predicts odds 3 times higher (exp(1.13)) of catching 0 fish. Therefore, the plot below shows the predicted probability of catching 0 fish according to number of children.

Is this a correct interpretation?

```
zinb <- read.csv("https://paul-buerkner.github.io/data/fish.csv")
library(brms)
fit_hu <- brm(bf(count ~ persons + child + camper, hu ~ child),
data = zinb, family = hurdle_poisson())
summary(fit_hu)
#> Family: hurdle_poisson
#> Links: mu = log; hu = logit
#> Formula: count ~ persons + child + camper
#> hu ~ child
#> Data: zinb (Number of observations: 250)
#> Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
#> total post-warmup samples = 4000
#>
#> Population-Level Effects:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> Intercept -0.84 0.17 -1.18 -0.51 1.00 3767 2545
#> hu_Intercept -0.39 0.17 -0.73 -0.06 1.00 4589 2877
#> persons 0.84 0.04 0.75 0.92 1.00 3632 2946
#> child -1.15 0.09 -1.33 -0.96 1.00 3650 2974
#> camper 0.74 0.09 0.56 0.93 1.00 4080 2563
#> hu_child 1.13 0.21 0.74 1.57 1.00 3753 2579
#>
#> Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
#> and Tail_ESS are effective sample size measures, and Rhat is the potential
#> scale reduction factor on split chains (at convergence, Rhat = 1).
plot(conditional_effects(fit_hu, effects = "child", dpar = "hu"))
```

Looking at a similar question [link] I get the idea that this should be correct. But I got confused because bernoulli models in brms are interpreted in the opposite way. In any case, I would also like to know which should be the most reliable source to check this (beyond this example or distribution family).