Tweedie Distributions
The AIC for Tweedie glms
AICtweedie( glm.obj, dispersion=NULL, k = 2, verbose=TRUE)
glm.obj |
a fitted Tweedie |
dispersion |
the dispersion parameter phi; the default is |
k |
numeric: the penalty per parameter to be used; the default is k=2 |
verbose |
if |
Returns a numeric value with the corresponding AIC (or BIC, depending on k)
Computing the AIC may take a long time.
Tweedie distributions with the index parameter as 1
correspond to Poisson distributions when phi=1.
However,
in general a Tweedie distribution with an index parameter equal to one
may not be referring to a Poisson distribution with phi=1,
so we cannot assume that phi=1 just because the index parameter is set to one.
If the Poisson distribution is intended,
then dispersion=1 should be specified.
The same argument applies for similar situations.
Peter Dunn (pdunn2@usc.edu.au)
Dunn, P. K. and Smyth, G. K. (2008). Evaluation of Tweedie exponential dispersion model densities by Fourier inversion. Statistics and Computing, 18, 73–86. doi: 10.1007/s11222-007-9039-6
Dunn, Peter K and Smyth, Gordon K (2005). Series evaluation of Tweedie exponential dispersion model densities Statistics and Computing, 15(4). 267–280. doi: 10.1007/s11222-005-4070-y
Jorgensen, B. (1997). Theory of Dispersion Models. Chapman and Hall, London.
Sakamoto, Y., Ishiguro, M., and Kitagawa G. (1986). Akaike Information Criterion Statistics. D. Reidel Publishing Company.
library(statmod) # Needed to use tweedie family object ### Generate some fictitious data test.data <- rgamma(n = 200, scale = 1, shape = 1) ### Fit a Tweedie glm and find the AIC m1 <- glm( test.data ~ 1, family = tweedie(link.power = 0, var.power = 2) ) ### A Tweedie glm with p=2 is equivalent to a gamma glm: m2 <- glm( test.data ~ 1, family = Gamma(link = log)) ### The models are equivalent, so the AIC shoud be the same: AICtweedie(m1) AIC(m2)
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