R: Quasi-Poisson Family Function

quasipoissonff {VGAM} | R Documentation

## 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` | 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.

### 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).

### 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`.

### Note

This function will handle a matrix response automatically.

The call `poissonff(dispersion = 0, ...)` is equivalent to `quasipoissonff(...)`. The latter was written so that R users of `quasipoisson()` would only need to add a “`ff`” to the end of the family function name.

Regardless of whether the dispersion parameter is to be estimated or not, its value can be seen from the output from the `summary()` of the object.

### Author(s)

Thomas W. Yee

### References

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

### See Also

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

### Examples

    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

    ## End(Not run)

[Package VGAM version 1.0-3 Index]