mgcv (version 1.8-5)

ziP: GAM zero-inflated Poisson regression family

Description

Family for use with gam, implementing regression for zero inflated Poisson data when the complinetart log log of the zero probability is linearly dependent on the log of the Poisson parameter. Use with care, noting that simply having many zero response observations is not an indication of zero inflation: the question is whether you have too many zeroes given the specified model.

Usage

ziP(theta = NULL, link = "identity")

Arguments

theta

the 2 parameters controlling the slope and intercept of the linear transform of the mean controlling the zero inflation rate. If supplied (and second element is positive) then treated as fixed parameters ($\theta_1$ and $\exp(\theta_2)$), otherwise esti

link

The link function: only the "identity" is currently supported.

Value

• An object of class extended.family.

WARNINGS

Zero inflated models are often over-used. Having lots of zeroes in the data does not in itself imply zero inflation. Having too many zeroes *given the model mean* may imply zero inflation.

Details

The probability of a zero count is given by $1-p$, whereas the probability of count $y>0$ is given by the truncated Poisson probability function $p\mu^y/((\exp(\mu)-1)y!)$. The linear predictor gives $\log \mu$, while $\eta = \log(-\log(1-p))$ and $\eta = \theta_1 + \exp(\theta_2) \log \mu$. The theta parameters are estimated alongside the smoothing parameters.

Note that the fitted values for this model are the log of the Poisson parameter. Use the predict function with type=="response" to get the predicted expected response.

See Also

ziplss

Examples

rzip <- function(gamma,theta= c(-2,.3)) {
## generate zero inflated Poisson random variables, where 
## lambda = exp(gamma), eta = theta[1] + exp(theta[2])*gamma
## and 1-p = exp(-exp(eta)).
   y <- gamma; n <- length(y)
   lambda <- exp(gamma)
   eta <- theta[1] + exp(theta[2])*gamma
   p <- 1- exp(-exp(eta))
   ind <- p > runif(n)
   y[!ind] <- 0
   np <- sum(ind)
   ## generate from zero truncated Poisson, given presence...
   y[ind] <- qpois(runif(np,dpois(0,lambda[ind]),1),lambda[ind])
   y
} 

library(mgcv)
## Simulate some beta data...
set.seed(1);n<-400
dat <- gamSim(1,n=n)
dat$y <- rzip(dat$f/4-1)

b <- gam(y~s(x0)+s(x1)+s(x2)+s(x3),family=ziP(),data=dat)
b$outer.info ## check convergence!!
b
plot(b,pages=1)
## plot deviance residuals against expected response
plot(predict(b,type="response"),residuals(b))