VGAM (version 0.8-3)

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

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

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.

Value

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

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.

See Also

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

Examples

quasipoissonff()

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