pgam: Poisson-Gamma Additive Models

In pgam: Poisson-Gamma Additive Models

Poisson-Gamma Additive Models

Description

Fit Poisson-Gamma Additive Models using the roughness penalty approach

Usage

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)

Arguments

formula	a model formula. See formparser for details
dataset	a data set in the environment search path. Missing data is temporarily not handled
omega	initial value for the discount factor
beta	vector of initial values for covariates coefficients. If a sigle value is supplied it is replicated to fill in the whole vector
offset	default is 1. Other value can be supplied here
digits	number of decimal places for printing information out
na.action	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
maxit	convergence control iterations
eps	convergence control criterion
lfn.scale	scales the likelihood function and is passed to control in optim. Value must be positive to ensure maximization
control	convergence control of optim. See its help for details
optim.method	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.

bkf.eps	convergence control criterion for the backfitting algorithm
bkf.maxit	convergence control iterations for the backfitting algorithm
se.estimation	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
verbose	if TRUE information during estimation process is printed out

Details

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≤ft(sf_{r}\right)+V1+V2+V3+g≤ft(V4,df_{4}\right)+g≤ft(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}+…+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.

Value

List containing an object of class pgam.

Author(s)

Washington Leite Junger [e-mail] and Antonio Ponce de Leon [e-mail]

References

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

See Also

predict.pgam, formparser, residuals.pgam, backfitting

Examples

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)

pgam documentation built on Aug. 20, 2022, 1:06 a.m.