# Interpret hurdle coefficients in brms

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).

You are right that zero-inflated and hurdle models give the probability of being in the structural zero state, rather than the probability of clearing the hurdle.

The most reliable way to check this is to simulate some data under known parameters and fit the model :)

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