Package 'pgam' reference manual

Title:	Poisson-Gamma Additive Models
Description:	This work is an extension of the state space model for Poisson count data, Poisson-Gamma model, towards a semiparametric specification. Just like the generalized additive models (GAM), cubic splines are used for covariate smoothing. The semiparametric models are fitted by an iterative process that combines maximization of likelihood and backfitting algorithm.
Authors:	Washington Junger <[email protected]>
Maintainer:	Washington Junger <[email protected]>
License:	GPL-3 \| file LICENSE
Version:	0.4.17
Built:	2025-01-22 05:11:24 UTC
Source:	https://github.com/wjunger/pgam

AIC extraction

Description

Method for approximate Akaike Information Criterion extraction.

Usage

## S3 method for class 'pgam'
AIC(object, k = 2, ...)
## 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

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.

Value

The approximate AIC value of the fitted model.

Author(s)

Washington Leite Junger [email protected] and Antonio Ponce de Leon [email protected]

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

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")

AIC(m)

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)

Sample dataset

Description

This is a dataset for Poisson-Gamma Additive Models functions testing.

Usage

data(aihrio)data(aihrio)

Format

A data frame with 365 observations on the following 33 variables.

DATE: a factor with levels
TIME: a numeric vector
ITRESP65: a numeric vector
ITCIRC65: a numeric vector
ITDPOC65: a numeric vector
ITPNM65: a numeric vector
ITAVC65: a numeric vector
ITIAM65: a numeric vector
ITDIC65: a numeric vector
ITTCA65: a numeric vector
ITRESP5: a numeric vector
ITPNEU5: a numeric vector
ITDPC5: a numeric vector
WEEK: a numeric vector
MON: a numeric vector
TUE: a numeric vector
WED: a numeric vector
THU: a numeric vector
FRI: a numeric vector
SAT: a numeric vector
SUN: a numeric vector
HOLIDAYS: a numeric vector
MONTH: a numeric vector
warm.season: a numeric vector
tmpmed: a numeric vector
tmpmin: a numeric vector
tmpmax: a numeric vector
wet: a numeric vector
rain: a numeric vector
rainy: a numeric vector
PM: a numeric vector
SO2: a numeric vector
CO: a numeric vector

Details

This is a reduced dataset of those used to estimate possible effects of air pollution on hospital admissions outcomes in Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brasil.

Author(s)

Washington Leite Junger [email protected] and Antonio Ponce de Leon [email protected]

Source

Secretary for the Environment of the Rio de Janeiro City, Brazilian Ministry of Defense and Brazilian Ministry of Health

Coefficients extraction

Description

Method for parametric coefficients extraction.

Usage

## S3 method for class 'pgam'
coef(object, ...)
## S3 method for class 'pgam'
coef(object, ...)

Arguments

`object`	object of class `pgam` holding the fitted model
`...`	further arguments passed to method

Details

This function only retrieves the estimated coefficients from the model object returned by pgam.

Value

Vector of coefficients estimates of the model fitted.

Author(s)

Washington Leite Junger [email protected] and Antonio Ponce de Leon [email protected]

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.

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")

coef(m)

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")

coef(m)

Deviance extraction

Description

Method for total deviance value extraction.

Usage

## S3 method for class 'pgam'
deviance(object, ...)
## S3 method for class 'pgam'
deviance(object, ...)

Arguments

`object`	object of class `pgam` holding the fitted model
`...`	further arguments passed to method

Details

See predict.pgam for further information on deviance extration in Poisson-Gamma models.

Value

The sum of deviance components.

Author(s)

Washington Leite Junger [email protected] and Antonio Ponce de Leon [email protected]

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.

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")

deviance(m)

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")

deviance(m)

Normal plot with simulated envelope of the residuals.

Description

A normal plot with simulated envelope of the residual is produced.

Usage

## S3 method for class 'pgam'
envelope(object, type = "deviance", size = 0.95, 
rep = 19, optim.method = NULL, epsilon = 0.001, maxit = 100, 
plot = TRUE, title="Simulated Envelope of Residuals", verbose = FALSE, ...)
## S3 method for class 'pgam'
envelope(object, type = "deviance", size = 0.95, 
rep = 19, optim.method = NULL, epsilon = 0.001, maxit = 100, 
plot = TRUE, title="Simulated Envelope of Residuals", verbose = FALSE, ...)

Arguments

`object`	object of class `pgam` holding the fitted model
`type`	type of residuals to be extracted. Default is `deviance`. Options are described in `residuals.pgam`
`size`	value giving the size of the envelope. Default is `.95` which is equivalent to a 95% band
`rep`	number of replications for envelope construction. Default is `19`

, that is the smallest 95% band that can be build

`optim.method`	optimization method to be passed to `pgam` and therefore to `optim`
`epsilon`	convergence control to be passed to `pgam`
`maxit`	convergence control to be passed to `pgam`
`plot`	if `TRUE` a plot of the envelope is produced
`title`	title for the plot
`verbose`	if `TRUE` a sort of information is printed during the running time
`...`	further arguments to `plot` function

Details

Method for the generic function envelope.

Sometimes the usual Q-Q plot shows an unsatisfactory pattern of the residuals of a model fitted and we are led to think that the model is badly specificated. The normal plot with simulated envelope indicates that under the distribution of the response variable the model is OK if only a few points fall off the envelope.

If object is of class pgam the envelope is estimated and optionally plotted, else if is of class envelope then it is only plotted.

Value

An object of class envelope holding the information needed to plot the envelope.

Author(s)

Washington Leite Junger [email protected] and Antonio Ponce de Leon [email protected]

References

Atkinson, A. C. (1985) Plots, transformations and regression : an introduction to graphical methods of diagnostic regression analysis. Oxford Science Publications, Oxford.

Utility function

Description

Generate the partition of design matrix regarded to the seasonal factor in its argument. Used in the model formula.

Usage

f(factorvar)
f(factorvar)

Arguments

factorvar

variable with the seasonal levels

Value

List containing data matrix of dummy variables, level names and seasonal periods.

Note

This function is intended to be called from within a model formula.

Author(s)

Washington Leite Junger [email protected]

Fitted values extraction

Description

Method for fitted values extraction.

Usage

## S3 method for class 'pgam'
fitted(object, ...)
## S3 method for class 'pgam'
fitted(object, ...)

Arguments

`object`	object of class `pgam` holding the fitted model
`...`	further arguments passed to method

Details

Actually, the fitted values are worked out by the function predict.pgam. Thus, this method is supposed to turn fitted values extraction easier. See predict.pgam for details on one-step ahead prediction.

Value

Vector of predicted values of the model fitted.

Author(s)

Washington Leite Junger [email protected] and Antonio Ponce de Leon [email protected]

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.

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")

f <- fitted(m)

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")

f <- fitted(m)

Utility function

Description

Collect information to smooth the term in its argument. Used in the model formula.

Usage

g(var, df = NULL)
g(var, df = NULL)

Arguments

`var`	variable to be smoothed
`df`	equivalent degrees of freedom to be passed to the smoother. If `NULL`, smoothing parameter is selected by cross-validation

Details

This function only sets things up for model fitting. The smooth terms are actually fitted by bkfsmooth.

Value

List containing the same elements of its argument.

Note

This function is intended to be called from within a model formula.

Author(s)

Washington Leite Junger [email protected]

References

Green, P. J., Silverman, B. W. (1994) Nonparametric Regression and Generalized Linear Models: a roughness penalty approach. Chapman and Hall, London

Hastie, T. J., Tibshirani, R. J.(1990) Generalized Additive Models. Chapman and Hall, London

Junger, W. L. (2004) Semiparametric Poisson-Gamma models: a roughness penalty approach. MSc Dissertation. Rio de Janeiro, PUC-Rio, Department of Electrical Engineering.

Loglik extraction

Description

Method for loglik value extraction.

Usage

## S3 method for class 'pgam'
logLik(object, ...)
## S3 method for class 'pgam'
logLik(object, ...)

Arguments

`object`	object of class `pgam` holding the fitted model
`...`	further arguments passed to method

Details

See pgam.likelihood for more information on log-likelihood evaluation in Poisson-Gamma models.

Value

The maximum value achieved by the likelihood optimization process.

Author(s)

Washington Leite Junger [email protected] and Antonio Ponce de Leon [email protected]

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.

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")

logLik(m)

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")

logLik(m)

Raw Periodogram

Description

A raw periodogram is returned and optionally plotted.

Usage

periodogram(y, rows = trunc(length(na.omit(y))/2-1), plot = TRUE, ...)
periodogram(y, rows = trunc(length(na.omit(y))/2-1), plot = TRUE, ...)

Arguments

`y`	time series
`rows`	number of rows to be returned. Default and largest is $n/2-1$ , where $n$ is the number of valid observations of the time series $y$
`plot`	if `TRUE` a raw periodogram is plotted
`...`	further arguments to `plot` function

Details

The raw periodogram is an estimator of the spectrum of a time series, it still is a good indicator of unresolved seasonality patterns in residuals of the fitted model. Check the function intensity for frequencies extraction.

This function plots a fancy periodogram where the intensities of the angular frequencies are plotted resembling tiny lollipops.

Value

Periodogram ordered by intensity.

Author(s)

Washington Leite Junger [email protected] and Antonio Ponce de Leon [email protected]

References

Box, G., Jenkins, G., Reinsel, G. (1994) Time Series Analysis : Forecasting and Control. 3rd edition, Prentice Hall, New Jersey.

Diggle, P. J. (1989) Time Series : A Biostatistical Introduction. Oxford University Press, Oxford.

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)
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 [email protected] and Antonio Ponce de Leon [email protected]

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

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)

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)

Plot of estimated curves

Description

Plot of the local level and, when semiparametric model is fitted, the estimated smooth terms.

Usage

## S3 method for class 'pgam'
plot(x, rug = TRUE, se = TRUE, at.once = FALSE, scaled = FALSE, ...)
## S3 method for class 'pgam'
plot(x, rug = TRUE, se = TRUE, at.once = FALSE, scaled = FALSE, ...)

Arguments

`x`	object of class `pgam` holding the fitted model
`rug`	if `TRUE` a density rug is drawn on the bottom of the graphic
`se`	if `TRUE` error band is drawn around the fitted values
`at.once`	if `TRUE` each plot goes to a separate window, else the user is prompted to continue
`scaled`	if `TRUE` the same scale will be used for plots of smoothed functions
`...`	further arguments passed to method

Details

Error band of smooth terms is approximated.

Value

No value returned.

Author(s)

Washington Leite Junger [email protected] and Antonio Ponce de Leon [email protected]

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")

plot(m,at.once=TRUE)

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")

plot(m,at.once=TRUE)

Prediction

Description

Prediction and forecasting of the fitted model.

Usage

## S3 method for class 'pgam'
predict(object, forecast = FALSE, k = 1, x = NULL, ...)
## S3 method for class 'pgam'
predict(object, forecast = FALSE, k = 1, x = NULL, ...)

Arguments

`object`	object of class `pgam` holding the fitted model
`forecast`	if `TRUE` the function tries to forecast
`k`	steps for forecasting
`x`	covariate values for forecasting if the model has covariates. Must have the $k$ rows and $p$ columns
`...`	further arguments passed to method

Details

It estimates predicted values, their variances, deviance components, generalized Pearson statistics components, local level, smoothed prediction and forecast.

Considering a Poisson process and a gamma priori, the predictive distribution of the model is negative binomial with parameters $a_{t|t-1}$ and $b_{t|t-1}$ . So, the conditional mean and variance are given by

$E\left(y_{t}|Y_{t-1}\right)=a_{t|t-1}/b_{t|t-1}$

and

$Var\left(y_{t}|Y_{t-1}\right)=a_{t|t-1}\left(1+b_{t|t-1}\right)/b_{t|t-1}^{2}$

Deviance components are estimated as follow

$D\left(y;\hat\mu\right)=2\sum_{t=\tau+1}^{n}{a_{t|t-1}\log \left(\frac{a_{t|t-1}}{y_{t}b_{t|t-1}}\right)-\left(a_{t|t-1}+y_{t}\right)\log \frac{\left(y_{t}+a_{t|t-1}\right)}{\left(1+b_{t|t-1}\right)y_{t}}}$

Generalized Pearson statistics has the form

$X^{2}=\sum_{t=\tau+1}^{n}\frac{\left(y_{t}b_{t|t-1}-a_{t|t-1}\right)^{2}} {a_{t|t-1}\left(1+b_{t|t-1}\right)}$

Approximate scale parameter is given by the expression

$\hat\phi=frac{X^{2}}{edf}$

where $edf$ is the number o degrees of reedom of the fitted model.

Value

List with those described in Details

Author(s)

Washington Leite Junger [email protected] and Antonio Ponce de Leon [email protected]

References

Green, P. J., Silverman, B. W. (1994) Nonparametric Regression and Generalized Linear Models: a roughness penalty approach. Chapman and Hall, London

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.

Harvey, A. C. (1990) Forecasting, structural time series models and the Kalman Filter. Cambridge, New York

Hastie, T. J., Tibshirani, R. J.(1990) Generalized Additive Models. Chapman and Hall, London

McCullagh, P., Nelder, J. A. (1989). Generalized Linear Models. Chapman and Hall, 2nd edition, London

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")

p <- predict(m)$yhat
plot(ITRESP5)
lines(p)

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")

p <- predict(m)$yhat
plot(ITRESP5)
lines(p)

Model output

Description

Print model information

Usage

## S3 method for class 'pgam'
print(x, digits, ...)
## S3 method for class 'pgam'
print(x, digits, ...)

Arguments

`x`	object of class `summary.pgam` holding the fitted model information
`digits`	number of decimal places for output
`...`	further arguments passed to method

Details

This function only prints out the information.

Value

No value is returned.

Author(s)

Washington Leite Junger [email protected] and Antonio Ponce de Leon [email protected]

Summary output

Description

Print output of model information

Usage

## S3 method for class 'pgam'
print.summary(x, digits, ...)
## S3 method for class 'pgam'
print.summary(x, digits, ...)

Arguments

`x`	object of class `summary.pgam` holding the fitted model information
`digits`	number of decimal places for output
`...`	further arguments passed to method

Details

This function actually only prints out the information.

Value

No value is returned.

Author(s)

Washington Leite Junger [email protected] and Antonio Ponce de Leon [email protected]

Residuals extraction

Description

Method for residuals extraction.

Usage

## S3 method for class 'pgam'
residuals(object, type = "deviance", ...)
## S3 method for class 'pgam'
residuals(object, type = "deviance", ...)

Arguments

`object`	object of class `pgam` holding the fitted model
`type`	type of residuals to be extracted. Default is `deviance`. Options are described in Details
`...`	further arguments passed to method

Details

The types of residuals available and a brief description are the following:

response
These are raw residuals of the form $r_{t}=y_{t}-E\left(y_{t}|Y_{t-1}\right)$ .

pearson
Pearson residuals are quite known and for this model they take the form $r_{t}=\left(y_{t}-E\left(y_{t}|Y_{t-1}\right)\right)/Var\left(y_{t}|Y_{t-1}\right)$ .

deviance
Deviance residuals are estimated by $r_{t}=sign\left(y_{t}-E\left(y_{t}|Y_{t-1}\right)\right)*sqrt\left(d_{t}\right)$ , where $d_{t}$ is the deviance contribution of the t-th observation. See deviance.pgam for details on deviance component estimation.

std_deviance
Same as deviance, but the deviance component is divided by $(1-h_{t})$ , where $h_{t}$ is the t-th element of the diagonal of the pseudo hat matrix of the approximating linear model. So they turn into $r_{t}=sign\left(y_{t}-E\left(y_{t}|Y_{t-1}\right)\right)*sqrt\left(d_{t}/\left(1-h_{t}\right)\right)$ .
The element $h_{t}$ has the form $h_{t}=\omega\exp\left(\eta_{t+1}\right)/\sum_{j=0}^{t-1}\omega^{j}\exp\left(\eta_{t-j}\right)$ , where $\eta$ is the predictor of the approximating linear model.

std_scl_deviance
Just like the last one except for the dispersion parameter in its expression, so they have the form $r_{t}=sign\left(y_{t}-E\left(y_{t}|Y_{t-1}\right)\right)*sqrt\left(d_{t}/\phi*\left(1-h_{t}\right)\right)$ , where $\phi$ is the estimated dispersion parameter of the model. See summary.pgam for $\phi$ estimation.

Value

Vector of residuals of the model fitted.

Author(s)

Washington Leite Junger [email protected] and Antonio Ponce de Leon [email protected]

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.

McCullagh, P., Nelder, J. A. (1989). Generalized Linear Models. Chapman and Hall, 2nd edition, London

Pierce, D. A., Schafer, D. W. (1986) Residuals in generalized linear models. Journal of the American Statistical Association, 81(396),977-986

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")

r <- resid(m,"pearson")
plot(r)

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")

r <- resid(m,"pearson")
plot(r)

Summary output

Description

Output of model information

Usage

## S3 method for class 'pgam'
summary(object, smo.test = FALSE, ...)
## S3 method for class 'pgam'
summary(object, smo.test = FALSE, ...)

Arguments

`object`	object of class `pgam` holding the fitted model
`smo.test`	Approximate significance test of smoothing terms. It can take long, so default is `FALSE`
`...`	further arguments passed to method

Details

Hypothesis tests of coefficients are based o t distribution. Significance tests of smooth terms are approximate for model selection purpose only. Be very careful about the later.

Value

List containing all the information about the model fitted.

Author(s)

Washington Leite Junger [email protected] and Antonio Ponce de Leon [email protected]

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.

Green, P. J., Silverman, B. W. (1994) Nonparametric Regression and Generalized Linear Models: a roughness penalty approach. Chapman and Hall, London

Hastie, T. J., Tibshirani, R. J.(1990) Generalized Additive Models. Chapman and Hall, London

McCullagh, P., Nelder, J. A. (1989). Generalized Linear Models. Chapman and Hall, 2nd edition, London

Pierce, D. A., Schafer, D. W. (1986) Residuals in generalized linear models. Journal of the American Statistical Association, 81(396),977-986

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)

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)

LaTeX table exporter

Description

Export a data frame to a fancy LaTeX table environment.

Usage

tbl2tex(tbl, label = "tbl:label(must_be_changed!)", 
caption = "Table generated with tbl2tex.", centered = TRUE, 
alignment = "center", digits = getOption("digits"), hline = TRUE, 
vline = TRUE, file = "", topleftcell = "   ")
tbl2tex(tbl, label = "tbl:label(must_be_changed!)", 
caption = "Table generated with tbl2tex.", centered = TRUE, 
alignment = "center", digits = getOption("digits"), hline = TRUE, 
vline = TRUE, file = "", topleftcell = "   ")

Arguments

`tbl`	object of type data frame or matrix
`label`	label for LaTeX cross reference
`caption`	caption for LaTeX tabular environment
`centered`	logical. `TRUE` for centered cells
`alignment`	alignment of the object on the page
`digits`	decimal digits after decimal point
`hline`	logical. `TRUE` for horizontal borders
`vline`	logical. `TRUE` for vertical borders
`file`	filename for outputting. If none is provided, LaTeX code is routed through the console
`topleftcell`	text for the top-left cell of the table

Details

This is a utility function intended to ease convertion of R objects to LaTeX format. It only exports data frame or data matrix nonetheless.

Value

LaTeX code is routed through file or console for copying and pasting.

Note

For now, it handles only numerical data.

Author(s)

Washington Leite Junger [email protected]

Examples

library(pgam)
data(aihrio)
m <- aihrio[1:10,4:10]
tbl2tex(m,label="tbl:r_example",caption="R example of tbl2tex",digits=4)
library(pgam)
data(aihrio)
m <- aihrio[1:10,4:10]
tbl2tex(m,label="tbl:r_example",caption="R example of tbl2tex",digits=4)

Package 'pgam'

Help Index

AIC extraction

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Sample dataset

Description

Usage

Format

Details

Author(s)

Source

Coefficients extraction

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Deviance extraction

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Normal plot with simulated envelope of the residuals.

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Utility function

Description

Usage

Arguments

Value

Note

Author(s)

See Also

Fitted values extraction

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Utility function

Description

Usage

Arguments

Details

Value

Note

Author(s)

References

See Also

Loglik extraction

Description

Usage

Arguments