oapospoisson: One-Altered Positive-Poisson Distribution In VGAMdata: Data Supporting the 'VGAM' Package

 oapospoisson R Documentation

One-Altered Positive-Poisson Distribution

Description

Fits a one-altered positive-Poisson distribution based on a conditional model involving a Bernoulli distribution and a 1-truncated positive-Poisson distribution.

Usage

```oapospoisson(lpobs1 = "logitlink", llambda = "loglink",
type.fitted = c("mean", "lambda", "pobs1", "onempobs1"),
ipobs1 = NULL, zero = NULL)
```

Arguments

 `lpobs1` Link function for the parameter pobs1 or phi, called `pobs1` or `phi` here. See `Links` for more choices. `llambda` See `pospoisson` for details. `type.fitted` See `CommonVGAMffArguments` and `fittedvlm` for information. `ipobs1, zero` See `CommonVGAMffArguments` for information.

Details

The response Y is one with probability pobs1, or Y has a 1-truncated positive-Poisson distribution with probability 1-pobs1. Thus 0 < pobs1 < 1, which is modelled as a function of the covariates. The one-altered positive-Poisson distribution differs from the one-inflated positive-Poisson distribution in that the former has ones coming from one source, whereas the latter has ones coming from the positive-Poisson distribution too. The one-inflated positive-Poisson distribution is implemented in the VGAM package. Some people call the one-altered positive-Poisson a hurdle model.

The input can be a matrix (multiple responses). By default, the two linear/additive predictors of `oapospoisson` are (logit(phi), log(lambda))^T.

Value

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

The `fitted.values` slot of the fitted object, which should be extracted by the generic function `fitted`, returns the mean mu (default) which is given by

mu = phi + (1- phi) A

where A is the mean of the one-truncated positive-Poisson distribution. If `type.fitted = "pobs1"` then pobs1 is returned.

Note

This family function effectively combines `binomialff` and `otpospoisson` into one family function.

Author(s)

T. W. Yee

`Oapospois`, `pospoisson`, `oipospoisson`, `CommonVGAMffArguments`, `simulate.vlm`.

Examples

```## Not run: odata <- data.frame(x2 = runif(nn <- 1000))
odata <- transform(odata, pobs1  = logitlink(-1 + 2*x2, inverse = TRUE),
lambda =  loglink( 1 + 1*x2, inverse = TRUE))
odata <- transform(odata, y1 = roapospois(nn, lambda = lambda, pobs1 = pobs1),
y2 = roapospois(nn, lambda = lambda, pobs1 = pobs1))
with(odata, table(y1))

ofit <- vglm(cbind(y1, y2) ~ x2, oapospoisson, data = odata, trace = TRUE)
coef(ofit, matrix = TRUE)