gammaRff  R Documentation 
Estimates the 2–parameter gamma distribution by maximum likelihood. One linear predictor models the mean.
gammaRff(zero = "shape", lmu = "gammaRMlink",
lrate = NULL, lshape = "loglink",
irate = NULL, ishape = NULL, lss = TRUE)
zero 
Specifies the parameters to be modelled as intercept–only. See 
lmu 
The link function applied to the gamma distribution mean, i.e.,

lrate, lshape, irate, ishape, lss 
Same as 
This family function slightly enlarges the functionalities of
gammaR
by directly modelling the mean
of the gamma distribution. It performs very much like
gamma2
, but involves the ordinary
(not reparametrized) density, given by
f(y; \alpha, \beta) = \frac{ \beta^\alpha }{ \Gamma(\alpha) }
e^{\beta y} y^{\alpha  1},
Here, \alpha
and \beta
are positive shape
and rate parameters as in gammaR
.
The default linear predictors are
\eta1 = {\tt{gammaRMlink}}(\alpha; \beta) = \log \mu =
\log (\alpha / \beta)
, and
\eta2 = \log \alpha
,
unlike \eta1 = \log \beta
and
\eta2 = \log \alpha
from gammaR
.
lmu
overrides lrate
and no link other than
gammaRMlink
is a valid entry
(lmu
). To
mimic gammaR
simply
set lmu = NULL
and lrate = "loglink"
.
The mean (\mu
) is returned as the fitted values.
gammaRff
differs from
gamma2
. The latter estimates a
reparametrization
of the gamma distribution in terms \mu
and
\alpha
.
This VGAM family function does not handle censored data.
An object of class "vglm"
.
See vglmclass
for full details.
The parameters \alpha
and \beta
match the arguments shape
and rate
of
rgamma
.
Multiple responses are handled.
V. Miranda and Thomas W. Yee.
Yee, T. W. (2015) Vector Generalized Linear and Additive Models: With an Implementation in R. Springer, New York, USA.
gammaRMlink
,
CommonVGAMffArguments
,
gammaR
,
gamma2
,
Links
.
### Modelling the mean in terms of x2, two responses.
set.seed(2017022101)
nn < 80
x2 < runif(nn)
mu < exp(2 + 0.5 * x2)
# Shape and rate parameters in terms of 'mu'
shape < rep(exp(1), nn)
rate < gammaRMlink(theta = log(mu), shape = shape,
inverse = TRUE, deriv = 0)
# Generating some random data
y1 < rgamma(n = nn, shape = shape, rate = rate)
gdata < data.frame(x2 = x2, y1 = y1)
rm(y1)
# lmu = "gammaRMlink" replaces lshape, whilst lrate = "loglink"
fit1 < vglm(cbind(y1, y1) ~ x2,
gammaRff(lmu = "gammaRMlink", lss = TRUE, zero = "shape"),
data = gdata, trace = TRUE, crit = "log")
coef(fit1, matrix = TRUE)
summary(fit1)
# Comparing fitted values with true values.
compare1 < cbind(fitted.values(fit1)[, 1, drop = FALSE], mu)
colnames(compare1) < c("Fitted.vM1", "mu")
head(compare1)
### Mimicking gammaR. Note that lmu = NULL.
fit2 < vglm(y1 ~ x2, gammaRff(lmu = NULL, lrate = "loglink",
lshape = "loglink", lss = FALSE, zero = "shape"),
data = gdata, trace = TRUE, crit = "log")
# Compare fitted values with true values.
compare2 < with(gdata, cbind(fitted.values(fit2), y1, mu))
colnames(compare2) < c("Fitted.vM2", "y", "mu")
head(compare2)
### Fitted values  Model1 vs Fitted values  Model2
fit1vsfit2 < cbind(fitted.values(fit1)[, 1, drop = FALSE],
fitted.values(fit2))
colnames(fit1vsfit2) < c("Fitted.vM1", "Fitted.vM2")
head(fit1vsfit2)
### Use gamma2()
fit3 < vglm(y1 ~ x2, gamma2,
data = gdata, trace = TRUE, crit = "log")
fit1.fit3 < cbind(fitted.values(fit1)[, 1, drop = FALSE],
fitted.values(fit2), fitted.values(fit3))
colnames(fit1.fit3) < c("Fitted.vM1", "Fitted.vM2", "Fitted.vM3")
head(fit1.fit3)
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