AIC extraction

Description

Method for approximate Akaike Information Criterion extraction.

Usage

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

Arguments

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 wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

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

See Also

pgam, deviance.pgam, logLik.pgam

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)

Sample dataset

Description

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

Usage

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 wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

Source

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

Backfitting algorithm

Description

Fit the nonparametric part of the model via backfitting algorithm.

Usage

backfitting(y, x, df, smoother = "spline",
w = rep(1, length(y)), eps = 0.001, maxit = 100, info = TRUE)

Arguments

Details

Backfitting algorithm estimates the approximating regression surface, working around the "curse of dimentionality".

More details soon enough.

Value

Fitted smooth curves and partial residuals.

Note

This function is not intended to be called directly.

Author(s)

Washington Leite Junger wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

References

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

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

See Also

pgam, predict.pgam, bkfsmooth

Smoothing of nonparametric terms

Description

Interface for smoothing functions

Usage

bkfsmooth(y, x, df, smoother = "spline", w = rep(1, length(y)))

Arguments

Details

Although several smoothers can be used in semiparametric regression models, only natural cubic splines is intended to be used in Poisson-Gamma Additive Models due to its interesting mathematical properties.

Nowadays, this function interfaces the smooth.spline in stats library. It will become not dependent soon enough.

Value

Note

This function is not intended to be called directly.

Author(s)

Washington Leite Junger wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

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.

See Also

pgam, predict.pgam

Coefficients extraction

Description

Method for parametric coefficients extraction.

Usage

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

Arguments

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 wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

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.

See Also

pgam, pgam.fit, predict.pgam

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)

Deviance extraction

Description

Method for total deviance value extraction.

Usage

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

Arguments

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 wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

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.

See Also

pgam, pgam.fit, pgam.likelihood

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)

Utility function

Description

Gadget to compute the elapsed time of a process

Usage

elapsedtime(st, et)

Arguments

Details

Start and end times can be obtained with proc.time.

Value

String with the elapsed time in hh:mm:ss format.

Author(s)

Washington Leite Junger wjunger@ims.uerj.br

See Also

pgam

Generic function for simulated envelope generation.

Description

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

Usage

envelope(object, ...)

Arguments

Value

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

Author(s)

Washington Leite Junger wjunger@ims.uerj.br

References

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

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, ...)

Arguments

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

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 wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

References

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

See Also

pgam, predict.pgam, residuals.pgam

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)

Arguments

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 wjunger@ims.uerj.br

See Also

pgam, formparser

Fitted values extraction

Description

Method for fitted values extraction.

Usage

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

Arguments

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 wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

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.

See Also

pgam, pgam.fit, predict.pgam

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)

Utility function

Description

Return the index of first non-zero observation of a variable.

Usage

fnz(y)

Arguments

Value

The index of first non-zero value.

Note

This function is not intended to be called directly.

Author(s)

Washington Leite Junger wjunger@ims.uerj.br

See Also

pgam

Read the model formula and split it into the parametric and nonparametric partitions

Description

Read the model formula and split it into two new ones concerning the parametric and nonparametric partitions of the predictor.

Usage

formparser(formula, env=parent.frame())

Arguments

Details

This function extracts all the information in the model formula. Most important, 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

Value

List containing the information needed for model fitting.

Note

This function is not intended to be called directly.

Author(s)

Washington Leite Junger wjunger@ims.uerj.br

See Also

pgam, f, g

Utility function

Description

Generate a data frame given a formula and a dataset.

Usage

framebuilder(formula, dataset)

Arguments

Details

Actually, this function is a wrapper for model.frame.

Value

A data frame restricted to the model.

Note

This function is not intended to be called directly.

Author(s)

Washington Leite Junger wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

See Also

pgam, formparser

Utility function

Description

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

Usage

g(var, df = NULL)

Arguments

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 wjunger@ims.uerj.br

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.

See Also

pgam, formparser

Utility function

Description

Apply the link function or its inverse to the argument.

Usage

link(x, link = "log", inv = FALSE)

Arguments

Details

This function is intended to port other link functions than \log{\left(\right)} to Poisson-Gamma Additive Models. For now, the only allowed value is "log".

Value

Evaluated link function at x values.

Note

This function is not intended to be called directly.

Author(s)

Washington Leite Junger wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

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

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

See Also

pgam, formparser

Loglik extraction

Description

Method for loglik value extraction.

Usage

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

Arguments

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 wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

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.

See Also

pgam, pgam.fit, pgam.likelihood

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)

Utility function

Description

Compute the Lp-norm of two sequencies.

Usage

lpnorm(seq1, seq2 = 0, p = 0)

Arguments

Value

The computed norm value.

Author(s)

Washington Leite Junger wjunger@ims.uerj.br

See Also

pgam

Raw Periodogram

Description

A raw periodogram is returned and optionally plotted.

Usage

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

Arguments

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 wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

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.

See Also

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

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 wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

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)

Estimation of the conditional distributions parameters of the level

Description

The priori and posteriori conditional distributions of the level is gamma and their parameters are estimated through this recursive filter. See Details for a thorough description.

Usage

pgam.filter(w, y, eta)

Arguments

Details

Consider Y_{t-1} a vector of observed values of a Poisson process untill the instant t-1. Conditional on that, \mu_{t} has gamma distribution with parameters given by

a_{t|t-1}=\omega a_{t-1}

b_{t|t-1}=\omega b_{t-1}\exp\left(-\eta_{t}\right)

Once y_{t} is known, the posteriori distribution of \mu_{t}|Y_{t} is also gamma with parameters given by

a_{t}=\omega a_{t-1}+y_{t}

b_{t}=\omega b_{t-1}+\exp\left(\eta_{t}\right)

with t=\tau,\ldots,n, where \tau is the index of the first non-zero observation of y.

Diffuse initialization of the filter is applied by setting a_{0}=0 and b_{0}=0. A proper distribution of \mu_{t} is obtained at t=\tau, where \tau is the fisrt non-zero observation of the time series.

Value

A list containing the time varying parmeters of the priori and posteriori conditional distribution is returned.

Note

This function is not intended to be called directly.

Author(s)

Washington Leite Junger wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

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

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

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

See Also

pgam, pgam.likelihood, pgam.fit, predict.pgam

One-step ahead prediction and variance

Description

Estimate one-step ahead expectation and variance of y_{t} conditional on observed time series until the instant t-1.

Usage

pgam.fit(w, y, eta, partial.resid)

Arguments

Details

Partial residuals for semiparametric estimation is extracted. Those are regarded to the parametric partition fit of the model. Available types are raw, pearson and deviance. The type raw is prefered. Properties of other form of residuals not fully tested. Must be careful on choosing it. See details in predict.pgam and residuals.pgam.

Value

Note

This function is not intended to be called directly.

Author(s)

Washington Leite Junger wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

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

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

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

See Also

pgam, residuals.pgam, predict.pgam

Utility function

Description

Put hyperparameters hessian matrix in the form of omega and beta standard error.

Usage

pgam.hes2se(hes, fperiod, se.estimation="numerical")

Arguments

Value

List containing the hyperparameters omega and beta standard errors.

Note

This function is not intended to be called directly.

Author(s)

Washington Leite Junger wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

See Also

pgam, formparser

Likelihood function to be maximized

Description

This is the log-likelihood function that is passed to optim for likelihood maximization.

Usage

pgam.likelihood(par, y, x, offset, fperiod, env = parent.frame())

Arguments

Details

Log-likelihood function of hyperparameters \omega and \beta is given by

\log L\left(\omega,\beta\right)=\sum_{t=\tau+1}^{n}{\log \Gamma\left(a_{t|t-1}+y_{t}\right)-\log y_{t}!-\log \Gamma\left(a_{t|t-1}\right)+a_{t|t-1}\log b_{t|t-1}-\left(a_{t|t-1}+y_{t}\right)\log \left(1+b_{t|t-1}\right)}

where a_{t|t-1} and b_{t|t-1} are estimated as it is shown in pgam.filter.

Value

List containing log-likelihood value, optimum linear predictor and the gamma parameters vectors.

Note

This function is not intended to be called directly.

Author(s)

Washington Leite Junger wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

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

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

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

See Also

pgam, pgam.filter, pgam.fit

Utility function

Description

Put unconstrained optimized parameters back into omega and beta form.

Usage

pgam.par2psi(par, fperiod)

Arguments

Value

List containing the hyperparameters omega and beta.

Note

This function is not intended to be called directly.

Author(s)

Washington Leite Junger wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

See Also

pgam, formparser

Utility function

Description

Put hyperparameters into unconstrained form for optimization.

Usage

pgam.psi2par(w, beta, fperiod)

Arguments

Value

Vector of unconstrained parameters.

Note

This function is not intended to be called directly.

Author(s)

Washington Leite Junger wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

See Also

pgam, formparser

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, ...)

Arguments

Details

Error band of smooth terms is approximated.

Value

No value returned.

Author(s)

Washington Leite Junger wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

See Also

pgam, pgam.fit, pgam.likelihood

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)

Prediction

Description

Prediction and forecasting of the fitted model.

Usage

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

Arguments

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 wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

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

See Also

pgam, residuals.pgam

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)

Model output

Description

Print model information

Usage

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

Arguments

Details

This function only prints out the information.

Value

No value is returned.

Author(s)

Washington Leite Junger wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

See Also

pgam, predict.pgam

Summary output

Description

Print output of model information

Usage

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

Arguments

Details

This function actually only prints out the information.

Value

No value is returned.

Author(s)

Washington Leite Junger wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

See Also

pgam, predict.pgam

Residuals extraction

Description

Method for residuals extraction.

Usage

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

Arguments

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 wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

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

See Also

pgam, pgam.fit, predict.pgam

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)

Summary output

Description

Output of model information

Usage

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

Arguments

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 wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

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

See Also

pgam, predict.pgam

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)

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 = "   ")

Arguments

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 wjunger@ims.uerj.br

See Also

pgam

Examples

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