We are using the brms package to estimate the zero inflation parameter. Our data is a survey sample. We are interested in the proportion W of subjects in the sample that have experienced a medical condition that may or may not have symptoms. Unfortunately, the data is binary and only contains Yes\No answers to the question of whether a subject experienced the condition in the past 12 months. Yes answers are coded as Y=1, No answer as Y=0. We believe some of the zeros are subjects with the condition but no symptoms (hence, zero-inflation).

We do not have precise information, only a rough estimate, about the likelihood of having no symptoms. We want to use a zero-inflated Bernoulli model to estimate the prevalence W of the condition and how it depends on a set of demographic factors X_1, X_2, X_3.

Letting Z be the zero-inflation parameter, we think of the proportion of zero in the data as being Z + (1-Z)(1-W).

Our question is about the output of the brms package. In the code W is called MEDCOND. Here is the code we are using:

```
fit_zibin <- brm(MEDCOND |trials(1) ~ X_1 + X_2 + X_3,
data = df, family = zero_inflated_binomial(),
set_prior("beta(19, 17)", class= "zi"))
```

Is this correct? That is, is the reported z_i the estimated inflation parameter? Do the reported regression coefficients of the explanatory variables X_i measure their impact on the true proportion W of subjects with the condition? (The beta prior reflects data from a few previous studies).

Thanks