Fit Poisson-Gamma Additive Models using the roughness penalty approach
pgam(formula, dataset, omega = 0.8, beta = 0.1, offset = 1, digits = getOption("digits"),
na.action="na.exclude", maxit = 100, eps = 1e-06, lfn.scale=1, control = list(),
optim.method = "L-BFGS-B", bkf.eps = 0.001, bkf.maxit = 100, se.estimation = "numerical",
verbose = TRUE)List containing an object of class pgam.
a model formula. See formparser for details
a data set in the environment search path. Missing data is temporarily not handled
initial value for the discount factor
vector of initial values for covariates coefficients. If a sigle value is supplied it is replicated to fill in the whole vector
default is \(1\). Other value can be supplied here
number of decimal places for printing information out
action to be taken if missing values are found. Default is "na.exclude" and residuals and predictions are padded to fit the length of the data. If "na.fail" then the process will stop if missing values are found. If "na.omit" the process will continue without padding though. If "na.pass" the process will stop due to errors
convergence control iterations
convergence control criterion
scales the likelihood function and is passed to control in optim. Value must be positive to ensure maximization
convergence control of optim. See its help for details
optimization method passed to optim. Different methods can lead to different results, so the user must attempt to the trade off between speed and robustness. For example, BFGS is faster but sensitive to starting values and L-BFGS-B is more robust but slower. See its help for details.
convergence control criterion for the backfitting algorithm
convergence control iterations for the backfitting algorithm
if numerical numerical standard error of parameters are returned. If analytical then analytical extraction of the standard errors is performed. By setting it to none standard error estimation is avoided
if TRUE information during estimation process is printed out
Washington Leite Junger wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br
The formula is parsed by formparser in order to extract all the information necessary for model fit. Split the model into two parts regarding the parametric nature of the model.
A model can be specified as following:
$$Y~f\left(sf_{r}\right)+V1+V2+V3+g\left(V4,df_{4}\right)+g\left(V5,df_{5}\right)$$
where \(sf_{r}\) is a seasonal factor with period \(r\) and \(df_{i}\) is the degree of freedom of the smoother of the i-th covariate. Actually, two new formulae will be created:
$$~sf_{1}+\dots+sf_{r}+V1+V2+V3$$
and
$$~V4+V5$$
These two formulae will be used to build the necessary datasets for model estimation. Dummy variables reproducing the seasonal factors will be created also.
Models without explanatory variables must be specified as in the following formula $$Y~NULL$$
There are a lot of details to be written. It will be very soon.
Specific information can be obtained on functions help.
This algorithm fits fully parametric Poisson-Gamma model also.
Junger, W. L. (2004) Semiparametric Poisson-Gamma models: a roughness penalty approach. MSc Dissertation. Rio de Janeiro, PUC-Rio, Department of Electrical Engineering.
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
Green, P. J., Silverman, B. W. (1994) Nonparametric Regression and Generalized Linear Models: a roughness penalty approach. Chapman and Hall, London
predict.pgam, formparser, residuals.pgam, backfitting
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")
summary(m)
Run the code above in your browser using DataLab