pgam (version 0.4.17)

residuals.pgam: Residuals extraction

Description

Method for residuals extraction.

Usage

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

Value

Vector of residuals of the model fitted.

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

Author

Washington Leite Junger and Antonio Ponce de Leon

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.

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)