Understanding Beta inflated brms

Modeling
1

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.

2

You might find this helpful Matti’s homepage - How to analyze visual analog (slider) scale data?

Phi is precision
Zoi is zero or one inflation
Coi is conditional one inflation

1 Like
3

Thank you !