gamma2 {VGAM} | R Documentation |
2-parameter Gamma Regression Family Function
Description
Estimates the 2-parameter gamma distribution by maximum likelihood estimation.
Usage
gamma2(lmu = "loglink", lshape = "loglink", imethod = 1, ishape = NULL,
parallel = FALSE, deviance.arg = FALSE, zero = "shape")
Arguments
lmu , lshape |
Link functions applied to the (positive) mu and shape
parameters (called |
ishape |
Optional initial value for shape.
A |
imethod |
An integer with value |
deviance.arg |
Logical. If |
zero |
See |
parallel |
Details at |
Details
This distribution can model continuous skewed responses. The density function is given by
for
,
and
.
Here,
is the gamma
function, as in
gamma
.
The mean of Y is (returned as the fitted
values) with variance
. If
then the density has a
pole at the origin and decreases monotonically as
increases.
If
then this corresponds to the exponential
distribution. If
then the density is zero at the
origin and is unimodal with mode at
; this can be achieved with
lshape="logloglink"
.
By default, the two linear/additive predictors are
and
.
This family function implements Fisher scoring and the working
weight matrices are diagonal.
This VGAM family function handles multivariate responses,
so that a matrix can be used as the response. The number of columns is
the number of species, say, and zero=-2
means that all
species have a shape parameter equalling a (different) intercept only.
Value
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
and vgam
.
Note
The response must be strictly positive. A moment estimator for the shape parameter may be implemented in the future.
If mu
and shape
are vectors, then rgamma(n = n,
shape = shape, scale = mu/shape)
will generate random gamma variates of this
parameterization, etc.;
see GammaDist
.
Author(s)
T. W. Yee
References
The parameterization of this VGAM family function is the 2-parameter gamma distribution described in the monograph
McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, 2nd ed. London: Chapman & Hall.
See Also
gamma1
for the 1-parameter gamma distribution,
gammaR
for another parameterization of
the 2-parameter gamma distribution that is directly matched
with rgamma
,
bigamma.mckay
for a bivariate gamma distribution,
gammaff.mm
for another,
expexpff
,
GammaDist
,
CommonVGAMffArguments
,
simulate.vlm
,
negloglink
.
Examples
# Essentially a 1-parameter gamma
gdata <- data.frame(y = rgamma(n = 100, shape = exp(1)))
fit1 <- vglm(y ~ 1, gamma1, data = gdata)
fit2 <- vglm(y ~ 1, gamma2, data = gdata, trace = TRUE, crit = "coef")
coef(fit2, matrix = TRUE)
c(Coef(fit2), colMeans(gdata))
# Essentially a 2-parameter gamma
gdata <- data.frame(y = rgamma(n = 500, rate = exp(-1), shape = exp(2)))
fit2 <- vglm(y ~ 1, gamma2, data = gdata, trace = TRUE, crit = "coef")
coef(fit2, matrix = TRUE)
c(Coef(fit2), colMeans(gdata))
summary(fit2)