fitted value for zeroinflatedpoisson0 family

[Aria]

Hello,

I have a question about the fitted value of a zero-inflated distribution. Here is a simple example:

>Y=list(c(0,1,1,0,0,rep(NA,5)), c(rep(NA,5),NA,2,4,NA,NA))
>covariant = data.frame(x1 = c(1:5,rep(NA,5)), x2 = c(rep(NA,5),1:5))
>model = inla(Y ~  x1 + x2, family = c("binomial","zeroinflatedpoisson0"), data=covariant, control.predictor = list(link = 2))
>model$summary.fitted.values$mean[6:10]

[1]  2.328542  2.319196  3.375467  7.179170 22.307927

I was wondering if the fitted value for the zeroinflatedpoisson0 provides the expectation of the count given that the count is greater than 0, i.e.  E(Y|Y>0). If not, what predictions does it provide?

Thank you!

[Håvard Rue]

The fitted values are as for the poisson,

fitted.values = exp(lin.predictor)

This might not be what you want for the inflated model, which have to be
computed/estimated offline, either using a plugin-approach, or through sampling,
using inla.posterior.sample() and inla.posterior.sample.eval(). There is a
vignette about its use

best
H

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[Aria]

Thank you very much for your reply. I'm not sure if I'm correct. For the 'zeroinflatedpoisson0' model, I have the linear predictor log(E(Y)) and fitted.values = E(Y), where E(Y) = ∑ (1−p)*Poisson(y∣y>0)*y. Can I get E(Y∣Y>0) through fitted.values/(1-p), where p is given as a hyperparameter in the 'zeroinflatedpoisson0' model?

[Denis Rustand]

Hi Aria,
You can just skip the estimation of p as it seems useless in your case, it looks like you just want the truncated at zero Poisson from zeroinflatedPoisson0 likelihood. As Haavard said, the p is not taken into account for the computation of fitted values in the Poisson part, so it is not needed to "remove" its contribution there. See attached code.
Best,
Denis Rustand
he...@r-inla.org