R: One-inflated Positive Poisson Distribution Family Function

oipospoisson {VGAM} | R Documentation

## One-inflated Positive Poisson Distribution Family Function

### Description

Fits a 1-inflated positive Poisson distribution.

### Usage

    oipospoisson(lpstr1 = "logitlink", llambda = "loglink",
       type.fitted = c("mean", "lambda", "pobs1", "pstr1", "onempstr1"),
       ilambda = NULL, gpstr1 = (1:19)/20, gprobs.y = (1:19)/20,
       imethod = 1, zero = NULL)

### Arguments

`lpstr1, llambda` | For `lpstr1`: the same idea as `zipoisson` except it applies to a structural 1.
`ilambda, gpstr1, gprobs.y, imethod` | For initial values. See `CommonVGAMffArguments` for information.
`type.fitted, zero` | See `CommonVGAMffArguments` for information.

### Details

The 1-inflated positive Poisson distribution is a mixture distribution of the positive (0-truncated) Poisson distribution with some probability of obtaining a (structural) 1. Thus there are two sources for obtaining the value 1. It is similar to a zero-inflated Poisson model, except the Poisson is replaced by a positive Poisson and the 0 is replaced by 1. This distribution is written here in a way that retains a similar notation to the zero-inflated Poisson, i.e., the probability P[Y=1] involves another parameter phi. See `zipoisson`.

This family function can handle multiple responses.

### Value

An object of class `"vglmff"` (see `vglmff-class`). The object is used by modelling functions such as `vglm`, `rrvglm` and `vgam`.

### Warning

Under- or over-flow may occur if the data is ill-conditioned.

### Author(s)

Thomas W. Yee

### See Also

`Oipospois`, `pospoisson`, `oapospoisson`, `otpospoisson`, `zipoisson`, `poissonff`, `simulate.vlm`.

### Examples

     set.seed(1)
    pdata <- data.frame(x2 = runif(nn <- 1000))  # Artificial data
    pdata <- transform(pdata, pstr1 = 0.5, lambda = exp(3 - x2))
    pdata <- transform(pdata, y1 = roipospois(nn, lambda, pstr1 = pstr1))
    with(pdata, table(y1))
    fit1 <- vglm(y1 ~ x2, oipospoisson, data = pdata, trace = TRUE)
    coef(fit1, matrix = TRUE)

[Package VGAM version 1.1-3 Index]