Good morning. I try to understand how beta inflated [0,1[ works (or [0,1]). For Poisson inflated or Gamma inflated, it is just a matter of changing the distribution in 0 but 0 is defined in the distribution ({0,1,2,3,...} for Poisson and [0,+\infty[ for Gamma). But for Beta, the definition of the density is on ]0,1[. So if you include zero, how does it work ? I guess there’s still the same monotonous bijection between Beta parameter space ]0,+\infty[ and ]-\infty,+\infty[ the parameter space for ]0,1[ values of the explicated variable. But how is calibrated the weight in zero ?
family = "zero_inflated_beta",
link = "logit",
link_phi = "log",
link_zi = "logit"
)
(so here zi = z I guess)
For zero-inflated, brms parametrization vignette says f_Z(y)=z+(1-z)f(0) if y=0 and f_Z(y)=(1-z)f(y) if y>0. For Hurdle family f_Z(y)=z if y=0 and f_Z(y)=(1-z)f(y)/(1-f(0)) if y>0.
I guess the question also apply for zero-one beta inflated.
Thank you!