Good morning,

I’m trying to understand what the output of the inflated beta regression are in brms.

Wheter I’m on [0,1[ or [0,1] I’d like to use :

```
zero_inflated_beta(link = "logit", link_phi = "log", link_zi = "logit")
```

or

```
zero_one_inflated_beta(
link = "logit",
link_phi = "log",
link_zoi = "logit",
link_coi = "logit"
)
( https://rdrr.io/cran/brms/man/brmsfamily.html )
```

But I don’t see what zi, zoi and coi are. In the brms vignette, there’s just the density mentionned but no explanation of what to do with the output. So for instance I get :

```
Family: zero_one_inflated_beta
Links: mu = logit; phi = identity; zoi = identity; coi = identity
Formula: y ~ 1 + x_1 + x_2
Data: df (Number of observations: 10000)
Draws: 3 chains, each with iter = 5000; warmup = 100; thin = 10;
total post-warmup draws = 1470
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept -0.01 0.03 -0.07 0.06 1.00 1572 1509
x_1 0.27 0.01 0.25 0.29 1.00 1593 1468
x_2 -1.88 0.01 -1.90 -1.85 1.00 1628 1428
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
phi 2.94 0.05 2.84 3.05 1.00 1577 1428
zoi 0.04 0.00 0.04 0.05 1.00 1534 1354
coi 1.00 0.00 0.99 1.00 1.00 698 873
```

So I understand x_1, x_2 and phi but how to interpret the inflated related part ?

I tried to refer to Raydonal Ospina a, Silvia L.P. Ferrar (2012) *A general class of zero-or-one inflated beta regression models* but I still fail to understand what to think of zi, zoi and coi. Could someone explain it to me please ?

Have a good day.