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 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.

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.

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, loge, rrvglm, cqo, cao, binomialff, quasibinomialff, quasipoisson.

Examples

quasipoissonff()

## Not run: 
n = 200; p = 5; S = 5
mydata = rcqo(n, p, S, fam="poisson", EqualTol=FALSE)
myform = attr(mydata, "formula")
p1 = cqo(myform, fam=quasipoissonff, EqualTol=FALSE, data=mydata)
sort(p1@misc$deviance.Bestof) # 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 0.7-7 Index]