genpoisson2 {VGAM} | R Documentation |
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",
parallel = FALSE, zero = "disppar",
vfl = FALSE, oparallel = FALSE,
imeanpar = NULL, idisppar = NULL, imethod = c(1, 1),
ishrinkage = 0.95, gdisppar = exp(1:5))
Arguments
lmeanpar , ldisppar |
Parameter link functions for |
imeanpar , idisppar |
Optional initial values for |
vfl , oparallel |
Argument |
imethod |
See |
ishrinkage , zero |
See |
gdisppar , parallel |
See |
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
\theta = \mu / (1 + \alpha \mu)
and
\lambda = \alpha \mu / (1 + \alpha \mu)
so that the variance is \mu (1 +
\alpha \mu)^2
. The first linear predictor
by default is \eta_1 = \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 \alpha = 0
. The mean (returned as
the fitted values) is E(Y) = \mu
.
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.
See Also
Genpois2
,
genpoisson0
,
genpoisson1
,
poissonff
,
negbinomial
,
Poisson
,
quasipoisson
.
Examples
gdata <- data.frame(x2 = runif(nn <- 500))
gdata <- transform(gdata, y1 = rgenpois2(nn, exp(2 + x2),
loglink(-1, inverse = TRUE)))
gfit2 <- vglm(y1 ~ x2, genpoisson2, gdata, trace = TRUE)
coef(gfit2, matrix = TRUE)
summary(gfit2)