| Tweedie {mgcv} | R Documentation |
A Tweedie family, designed for use with gam from the mgcv library.
Restricted to variance function powers between 1 and 2. A useful alternative to quasi when a
full likelihood is desirable.
Tweedie(p=1, link = power(0))
p |
the variance of an observation is proportional to its mean to the power p. p must
be greater than 1 and less than or equal to 2. 1 would be Poisson, 2 is gamma. |
link |
The link function: one of "log", "identity", "inverse", "sqrt", or a
power link. |
A Tweedie random variable with 1<p<2 is a sum of N gamma random variables
where N has a Poisson distribution. The p=1 case is a generalization of a Poisson distribution and is a discrete
distribution supported on integer multiples of the scale parameter. For 1<p<2 the distribution is supported on the
positive reals with a point mass at zero. p=2 is a gamma distribution. As p gets very close to 1 the continuous
distribution begins to converge on the discretely supported limit at p=1, and is therefore highly multimodal.
See ldTweedie for more on this behaviour.
Tweedie is based partly on the poisson family, and partly on tweedie from the
statmod package. It includes extra components to work with all mgcv GAM fitting methods as well as
an aic function. The required log density evaluation (+ derivatives w.r.t. scale) is based on the series
evaluation method of Dunn and Smyth (2005).
Without the restriction on p the calculation of Tweedie densities is less straightforward, and there does not
currently seem to be an implementation which offers any benefit over quasi. If you really need to this
case then the tweedie package is the place to start.
An object inheriting from class family, with additional elements
dvar |
the function giving the first derivative of the variance function w.r.t. mu. |
d2var |
the function giving the second derivative of the variance function w.r.t. mu. |
ls |
A function returning a 3 element array: the saturated log likelihood followed by its first 2 derivatives w.r.t. the scale parameter. |
Simon N. Wood simon.wood@r-project.org
modified from Venables and Ripley's negative.binomial family.
Dunn, P.K. and G.K. Smith (2005) Series evaluation of Tweedie exponential dispersion model densities. Statistics and Computing 15:267-280
Tweedie, M. C. K. (1984). An index which distinguishes between some important exponential families. Statistics: Applications and New Directions. Proceedings of the Indian Statistical Institute Golden Jubilee International Conference (Eds. J. K. Ghosh and J. Roy), pp. 579-604. Calcutta: Indian Statistical Institute.
library(mgcv)
set.seed(3)
n<-400
## Simulate data (really Poisson with log-link)
dat <- gamSim(1,n=n,dist="poisson",scale=.2)
## Fit a `nearby' Tweedie...
b <- gam(y~s(x0)+s(x1)+s(x2)+s(x3),family=Tweedie(1.1,power(.1)),
data=dat)
plot(b,pages=1)
print(b)
## Same by approximate REML...
b1 <- gam(y~s(x0)+s(x1)+s(x2)+s(x3),family=Tweedie(1.1,power(.1)),
data=dat,method="REML")
plot(b1,pages=1)
print(b1)
rm(dat)