VGAM (version 1.0-4)

# oipospoisson: One-inflated Positive Poisson Distribution Family Function

## Description

Fits a 1-inflated positive Poisson distribution.

## Usage

oipospoisson(lpstr1 = "logit", llambda = "loge",
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.

## 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.

## 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.

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

## Examples

Run this code
# NOT RUN {
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)
# }


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