VGAM (version 1.0-4)

# quasipoissonff: Quasi-Poisson Family Function

## Description

Fits a generalized linear model to a Poisson response, where the dispersion parameter is unknown.

## Usage

```quasipoissonff(link = "loge", onedpar = FALSE,
parallel = FALSE, zero = NULL)```

## Arguments

Link function. See `Links` for more choices.

onedpar

One dispersion parameter? If the response is a matrix, then a separate dispersion parameter will be computed for each response (column), by default. Setting `onedpar=TRUE` will pool them so that there is only one dispersion parameter to be estimated.

parallel

A logical or formula. Used only if the response is a matrix.

zero

Can be an integer-valued vector specifying which linear/additive predictors are modelled as intercepts only. The values must be from the set {1,2,…,\(M\)}, where \(M\) is the number of columns of the matrix response. See `CommonVGAMffArguments` for more information.

## Value

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

## Warning

See the warning in `quasibinomialff`.

## Details

\(M\) defined above is the number of linear/additive predictors.

If the dispersion parameter is unknown, then the resulting estimate is not fully a maximum likelihood estimate.

A dispersion parameter that is less/greater than unity corresponds to under-/over-dispersion relative to the Poisson model. Over-dispersion is more common in practice.

When fitting a Quadratic RR-VGLM, the response is a matrix of \(M\), say, columns (e.g., one column per species). Then there will be \(M\) dispersion parameters (one per column of the response matrix).

## References

McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models, 2nd ed. London: Chapman & Hall.

`poissonff`, `negbinomial`, `loge`, `rrvglm`, `cqo`, `cao`, `binomialff`, `quasibinomialff`, `quasipoisson`.

## Examples

Run this code
``````# NOT RUN {
quasipoissonff()

# }
# NOT RUN {
n <- 200; p <- 5; S <- 5
mydata <- rcqo(n, p, S, fam = "poisson", eq.tol = FALSE)
myform <- attr(mydata, "formula")
p1 <- cqo(myform, fam = quasipoissonff, eq.tol = FALSE, data = mydata)
sort(deviance(p1, history = TRUE))  # A history of all the iterations
lvplot(p1, y = TRUE, lcol = 1:S, pch = 1:S, pcol = 1:S)
summary(p1)  # The dispersion parameters are estimated
# }
``````

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