VGAM: genpoisson2 – R documentation

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genpoisson2

Generalized Poisson Regression (GP-2 Parameterization)

Description

Estimation of the two-parameter generalized Poisson distribution (GP-2 parameterization) which has the variance as a cubic function of the mean.

Usage

genpoisson2(lmeanpar = "loglink", ldisppar = "loglink",
           imeanpar = NULL, idisppar = NULL, imethod = c(1, 1),
           ishrinkage = 0.95, gdisppar = exp(1:5),
           parallel = FALSE, zero = "disppar")

Arguments

`lmeanpar, ldisppar`	Parameter link functions for μ and α. They are called the mean and dispersion parameters respectively. See `Links` for more choices. In theory the α parameter might be allowed to be negative to handle underdispersion but this is not supported. All parameters are positive, therefore the defaults are the log link.
`imeanpar, idisppar`	Optional initial values for μ and α. The default is to choose values internally.
`imethod`	See `CommonVGAMffArguments` for information. The argument is recycled to length 2, and the first value corresponds to μ, etc.
`ishrinkage, zero`	See `CommonVGAMffArguments` for information.
`gdisppar, parallel`	See `CommonVGAMffArguments` for information. Argument `gdisppar` is similar to `gsigma` there and is currently used only if `imethod[2] = 2`.

Details

This is a variant of the generalized Poisson distribution (GPD) and called GP-2 by some writers such as Yang, et al. (2009). Compared to the original GP-0 (see genpoisson0 the GP-2 has θ = μ / (1 + α μ) and λ = α μ / (1 + α μ) so that the variance is μ (1 + α μ)^2. The first linear predictor by default is eta1 = log mu so that the GP-2 is more suitable for regression than the GP-0.

This family function can handle only overdispersion relative to the Poisson. An ordinary Poisson distribution corresponds to α = 0. The mean (returned as the fitted values) is E(Y) = μ.

Value

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

Warning

See genpoisson0 for warnings relevant here, e.g., it is a good idea to monitor convergence because of equidispersion and underdispersion.

Author(s)

T. W. Yee.

References

Letac, G. and Mora, M. (1990). Natural real exponential familes with cubic variance functions. Annals of Statistics 18, 1–37.

Examples

gdata <- data.frame(x2 = runif(nn <- 500))
gdata <- transform(gdata, y1 = rgenpois2(nn, mean = exp(2 + x2),
                                         loglink(-1, inverse = TRUE)))
gfit2 <- vglm(y1 ~ x2, genpoisson2, data = gdata, trace = TRUE)
coef(gfit2, matrix = TRUE)
summary(gfit2)

VGAM

Vector Generalized Linear and Additive Models

v1.1-5

GPL-3

Authors

Thomas Yee [aut, cre], Cleve Moler [ctb] (author of several LINPACK routines)

Initial release

2021-01-13