parameters of ZIB type 2

[Camille Morlighem]

Dear INLA developers and experts, 

I'm using a zero-inflated binomial model of type 2 to model malaria prevalence and I want to make sure I understand the parameters properly (from zeroinflated.pdf). 

The probability of an excess zero t_i at location i is: 

t_i = 1 - [Eexp(η_i)/(1+ Eexp(η_i))] ^ alpha 

Where η_i is the linear predictor at location i. 

Is this correct ? 

Also, does the model parameter called "zero-probability parameter for zero-inflated binomial_2" represent alpha ? 

Many thanks in advance. 

Camille 

[Helpdesk (Haavard Rue)]

Here is code to simulate from this model and estimate it back, and then you see


n = 10000
s = 0.1
x = rnorm(n,sd=s)
z = rnorm(n,sd=s)
y = numeric(n)
## I want to be able to look at this one
p = numeric(n)
N = 1+rpois(n, lambda = 50)
alpha = 0.3

for(i in 1:n) {
eta = x[i] + z[i]
m = exp(eta)
## OOPS: q = 1-p
p[i] = 1-(m/(1+m))^alpha
prob = exp(eta)/(1+exp(eta))
xx = 0:N[i]
d = dbinom(xx, size = N[i], prob = prob)
len = length(d)
d[1] = p[i] + (1-p[i])*d[1]
d[2:len] = (1-p[i])*d[2:len]
y[i] = sample(xx, 1, prob=d)
}

i = 1:n
formula = y ~ f(i, model="iid") + z
data = data.frame(y=y, x=x, z=z, N=N, i=i)

r = inla(formula, family = "zeroinflatedbinomial2", data=data, Ntrials=N,
verbose=TRUE)
summary(r)

> --
> You received this message because you are subscribed to the Google Groups "R-
> inla discussion group" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to r-inla-discussion...@googlegroups.com.
> To view this discussion, visit
> https://groups.google.com/d/msgid/r-inla-discussion-group/751367ef-4c0c-45ed-8f94-ccf2efccf9b3n%40googlegroups.com
> .

--
Håvard Rue
he...@r-inla.org

[Camille Morlighem]

It worked great, many thanks !