# Zero inflated (hurdle) Poisson location-scale model family The `ziplss` family implements a zero inflated (hurdle) Poisson model in which one linear predictor controls the probability of presence and the other controls the mean given presence. Useable only with `gam`, the linear predictors are specified via a list of formulae. Should be used with care: simply having a large number of zeroes is not an indication of zero inflation. Requires integer count data. ```r ziplss(link=list("identity","identity")) zipll(y,g,eta,deriv=0) ``` ## Arguments - `link`: two item list specifying the link - currently only identity links are possible, as parameterization is directly in terms of log of Poisson response and complementary log log of probability of presence. - `y`: response - `g`: gamma vector - `eta`: eta vector - `deriv`: number of derivatives to compute ## Returns For `ziplss` An object inheriting from class `general.family`. ## Details `ziplss` is used with `gam` to fit 2 stage zero inflated Poisson models. `gam` is called with a list containing 2 formulae, the first specifies the response on the left hand side and the structure of the linear predictor for the Poisson parameter on the right hand side. The second is one sided, specifying the linear predictor for the probability of presence on the right hand side. The fitted values for this family will be a two column matrix. The first column is the log of the Poisson parameter, and the second column is the complementary log log of probability of presence.. Predictions using `predict.gam` will also produce 2 column matrices for `type` `"link"` and `"response"`. The null deviance computed for this model assumes that a single probability of presence and a single Poisson parameter are estimated. For data with large areas of covariate space over which the response is zero it may be advisable to use low order penalties to avoid problems. For 1D smooths uses e.g. `s(x,m=1)` and for isotropic smooths use `Duchon.spline`s in place of thin plaste terms with order 1 penalties, e.g `s(x,z,m=c(1,.5))` --- such smooths penalize towards constants, thereby avoiding extreme estimates when the data are uninformative. `zipll` is a function used by `ziplss`, exported only to allow external use of the `ziplss` family. It is not usually called directly. ## Author(s) Simon N. Wood simon.wood@r-project.org ## References Wood, S.N., N. Pya and B. Saefken (2016), Smoothing parameter and model selection for general smooth models. Journal of the American Statistical Association 111, 1548-1575 tools:::Rd_expr_doi("10.1080/01621459.2016.1180986") ## WARNINGS Zero inflated models are often over-used. Having many zeroes in the data does not in itself imply zero inflation. Having too many zeroes *given the model mean* may imply zero inflation. ## Examples ```r library(mgcv) ## simulate some data... f0 <- function(x) 2 * sin(pi * x); f1 <- function(x) exp(2 * x) f2 <- function(x) 0.2 * x^11 * (10 * (1 - x))^6 + 10 * (10 * x)^3 * (1 - x)^10 n <- 500;set.seed(5) x0 <- runif(n); x1 <- runif(n) x2 <- runif(n); x3 <- runif(n) ## Simulate probability of potential presence... eta1 <- f0(x0) + f1(x1) - 3 p <- binomial()$linkinv(eta1) y <- as.numeric(runif(n)0 eta2 <- f2(x2[ind])/3 y[ind] <- rpois(exp(eta2),exp(eta2)) ## Fit ZIP model... b <- gam(list(y~s(x2)+s(x3),~s(x0)+s(x1)),family=ziplss()) b$outer.info ## check convergence summary(b) plot(b,pages=1) ```

ziplss function