Method for approximate Akaike Information Criterion extraction.
Usage
## S3 method for class 'pgam':
AIC(object, k = 2, ...)
Arguments
object
object of class pgam holding the fitted model
k
default is 2 for AIC. If $k=\log\left(n\right)$ then an approximation for BIC is obtained. Important to note that these are merely approximations.
...
further arguments passed to method
Value
The approximate AIC value of the fitted model.
Details
An approximate measure of parsimony of the Poisson-Gama Additive Models can be achieved by the expression
$$AIC=\left(D\left(y;\hat\mu\right)+2gle\right)/\left(n-\tau\right)$$
where $gle$ is the number of degrees of freedom of the fitted model and $\tau$ is the index of the first non-zero observation.
References
Harvey, A. C., Fernandes, C. (1989) Time series models for count data or qualitative observations. Journal of Business and Economic Statistics, 7(4):407--417
Junger, W. L. (2004) Semiparametric Poisson-Gamma models: a roughness penalty approach. MSc Dissertation. Rio de Janeiro, PUC-Rio, Department of Electrical Engineering.
Hastie, T. J., Tibshirani, R. J.(1990) Generalized Additive Models. Chapman and Hall, London
library(pgam)
data(aihrio)
attach(aihrio)
form <- ITRESP5~f(WEEK)+HOLIDAYS+rain+PM+g(tmpmax,7)+g(wet,3)
m <- pgam(form,aihrio,omega=.8,beta=.01,maxit=1e2,eps=1e-4,optim.method="BFGS")
AIC(m)