View source: R/family.univariate.R
genpoisson1 | R Documentation |
Estimation of the two-parameter generalized Poisson distribution (GP-1 parameterization) which has the variance as a linear function of the mean.
genpoisson1(lmeanpar = "loglink", ldispind = "logloglink",
imeanpar = NULL, idispind = NULL, imethod = c(1, 1),
ishrinkage = 0.95, gdispind = exp(1:5),
parallel = FALSE, zero = "dispind")
lmeanpar, ldispind |
Parameter link functions for |
imeanpar, idispind |
Optional initial values for |
imethod |
See |
ishrinkage, zero |
See |
gdispind, parallel |
See |
This is a variant of the generalized Poisson distribution (GPD)
and is similar to the
GP-1 referred to by some writers such as Yang, et al. (2009).
Compared to the original GP-0 (see genpoisson0
)
the GP-1 has
\theta = \mu / \sqrt{\varphi}
and
\lambda = 1 - 1 / \sqrt{\varphi}
so that
the variance is \mu \varphi
.
The first linear predictor by default is
\eta_1 = \log \mu
so that the GP-1
is more suitable for regression than the GP-1.
This family function can handle
only overdispersion relative to the Poisson.
An ordinary Poisson distribution corresponds
to \varphi = 1
.
The mean (returned as the fitted values) is E(Y) = \mu
.
For overdispersed data,
this GP parameterization is a direct competitor of the NB-1 and
quasi-Poisson.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
,
and vgam
.
See genpoisson0
for warnings relevant here,
e.g., it is a good idea to monitor convergence because of
equidispersion and underdispersion.
T. W. Yee.
Genpois1
,
genpoisson0
,
genpoisson2
,
poissonff
,
negbinomial
,
Poisson
,
quasipoisson
.
gdata <- data.frame(x2 = runif(nn <- 500))
gdata <- transform(gdata, y1 = rgenpois1(nn, mean = exp(2 + x2),
logloglink(-1, inverse = TRUE)))
gfit1 <- vglm(y1 ~ x2, genpoisson1, data = gdata, trace = TRUE)
coef(gfit1, matrix = TRUE)
summary(gfit1)
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