pgam (version 0.3.3)

residuals.pgam: Residuals extraction

Description

Method for residuals extraction.

Usage

## 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

Value

• Vector of residuals of the model fitted.

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. adj_deviance These are the deviance residuals multiplied by the coefficient of skewness estimated from the distribution. So, considering the negative binomial predictive distribution, they take the form $r_{t}=sign\left(y_{t}-E\left(y_{t}|Y_{t-1}\right)\right)*sqrt\left(d_{t}\right)*K$, where $K$ is estimated by $K=\left(2-btt1\right)/sqrt\left(att1*\left(1-btt1\right)\right)$.

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

Campos, E. L., De Leon, A. C. M. P., Fernandes, C. A. C. (2003) Modelo Poisson-Gama para S�ries Temporais de Dados de Contagem - Teoria e Aplica��es. 10a ESTE - Escola de S�ries Temporais e Econometria

Junger, W. L. (2004) Modelo Poisson-Gama Semi-Param�trico: Uma Abordagem de Penaliza��o por Rugosidade. MSc Thesis. Rio de Janeiro, PUC-Rio, Departamento de Engenharia El�trica

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",partial.resid="response")

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