[R] Prediction intervals for zero inflated Poisson regression

[ONKELINX, Thierry]

Dear all,

I'm using zeroinfl() from the pscl-package for zero inflated Poisson
regression. I would like to calculate (aproximate) prediction intervals
for the fitted values. The package itself does not provide them. Can
this be calculated analyticaly? Or do I have to use bootstrap?

What I tried until now is to use bootstrap to estimate these intervals.
Any comments on the code are welcome. The data and the model are based
on the examples in zeroinfl().

#aproximate prediction intervals with Poisson regression
fm_pois <- glm(art ~ fem, data = bioChemists, family = poisson)
newdata <- na.omit(unique(bioChemists[, "fem", drop = FALSE]))
prediction <- predict(fm_pois, newdata = newdata, se.fit = TRUE)
ci <- data.frame(exp(prediction$fit + matrix(prediction$se.fit, ncol =
1) %*% c(-1.96, 1.96)))
newdata$fit <- exp(prediction$fit)
newdata <- cbind(newdata, ci)
newdata$model <- "Poisson"

library(pscl)
#aproximate prediction intervals with zero inflated poisson regression
fm_zip <- zeroinfl(art ~ fem | 1, data = bioChemists)
fit <- predict(fm_zip)
Pearson <- resid(fm_zip, type = "pearson")
VarComp <- resid(fm_zip, type = "response") / Pearson
fem <- bioChemists$fem
bootstrap <- replicate(999, {
    yStar <- pmax(round(fit + sample(Pearson) * VarComp, 0), 0)
    predict(zeroinfl(yStar ~ fem | 1), newdata = newdata)
})
newdata0 <- newdata
newdata0$fit <- predict(fm_zip, newdata = newdata, type = "response")
newdata0[, 3:4] <- t(apply(bootstrap, 1, quantile, c(0.025, 0.975)))
newdata0$model <- "Zero inflated"

#compare the intervals in a nice plot.
newdata <- rbind(newdata, newdata0)
library(ggplot2)
ggplot(newdata, aes(x = fem, y = fit, min = X1, max = X2, colour =
model)) + geom_point(position = position_dodge(width = 0.4)) +
geom_errorbar(position = position_dodge(width = 0.4))


Best regards,

Thierry

------------------------------------------------------------------------
----
ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature
and Forest
Cel biometrie, methodologie en kwaliteitszorg / Section biometrics,
methodology and quality assurance
Gaverstraat 4
9500 Geraardsbergen
Belgium 
tel. + 32 54/436 185
Thierry.Onkelinx op inbo.be 
www.inbo.be 

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