pgam {pgam}

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\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.

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)