residuals.pgam {pgam} | R Documentation |
Method for residuals extraction.
## S3 method for class 'pgam': residuals(object, type = "deviance", ...)
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 |
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(y_{t}|Y_{t-1}).
pearson
Pearson residuals are quite known and for this model they take the form r_{t}=(y_{t}-E(y_{t}|Y_{t-1}))/Var(y_{t}|Y_{t-1}).
deviance
Deviance residuals are estimated by r_{t}=sign(y_{t}-E(y_{t}|Y_{t-1}))*sqrt(d_{t}), 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(y_{t}-E(y_{t}|Y_{t-1}))*sqrt(d_{t}/(1-h_{t})).
The element h_{t} has the form h_{t}=omegaexp(eta_{t+1})/sum_{j=0}^{t-1}omega^{j}exp(eta_{t-j}), 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(y_{t}-E(y_{t}|Y_{t-1}))*sqrt(d_{t}/phi*(1-h_{t})), where phi is the estimated dispersion parameter of the model. See summary.pgam
for phi estimation.
Vector of residuals of the model fitted.
Washington Leite Junger wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br
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) Modelo Poisson-Gama Semi-Parametrico: Uma Abordagem de Penalizacao por Rugosidade. MSc Thesis. Rio de Janeiro, PUC-Rio, Departamento de Engenharia Eletrica
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
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)