ARCensReg (version 3.0.1)

InfDiag: Influence diagnostic in censored linear regression model with autoregressive errors

Description

It performs influence diagnostic by a local influence approach cook1986assessmentARCensReg with three possible perturbation schemes: response perturbation (y), scale matrix perturbation (Sigma), or explanatory variable perturbation (x). A benchmark value is calculated that depends on k.

Usage

InfDiag(object, k = 3, indpar = rep(1, length(object$theta)), 
  indcolx = rep(1, ncol(object$x)), perturbation = "y")

Value

An object of class "DiagARpCRM" with the following components is returned:

M0

Vector of length \(n\) with the aggregated contribution of all eigenvectors of the matrix associated with the normal curvature.

perturbation

Perturbation scheme.

benchmark

M0 + k*sd(M0).

Arguments

object

Object of class 'ARpCRM' given as an output of function ARCensReg.

k

Constant to be used in the benchmark calculation: M0+k*sd(M0).

indpar

Vector of length equal to the number of parameters, with each element 0 or 1 indicating if the respective parameter should be considered in the influence calculation.

indcolx

If perturbation="x", indcolx must be a vector of length equal to the number of columns of x, with each element 0 or 1 indicating if the respective column of x should be perturbed. All columns are perturbed by default.

perturbation

Perturbation scheme. Possible values: "y" for response perturbation, "Sigma" for scale matrix perturbation, or "x" for explanatory variable perturbation.

Author

Fernanda L. Schumacher, Katherine L. Valeriano, Victor H. Lachos, Christian E. Galarza, and Larissa A. Matos

Details

The function returns a vector of length n with the aggregated contribution (M0) of all eigenvectors of the matrix associated with the normal curvature. For details see schumacher2018influence;textualARCensReg.

References

cook1986assessmentARCensReg

schumacher2018influenceARCensReg

zhu2001localARCensReg

See Also

ARCensReg

Examples

# \donttest{
library(ggplot2)

# Generating the data
set.seed(12341)
x = cbind(1,runif(100))
dat = rARCens(n=100, beta=c(1,-1), phi=c(.48,-.2), sig2=.5, x=x, 
              cens='left', pcens=.05)
              
# Creating an outlier
dat$data$y[40] = 5
ggplot(dat$data) + geom_line(aes(x=1:100, y=y)) + theme_bw() +
  labs(x="Time")

# Fitting the model
fit = ARCensReg(dat$data$cc, dat$data$lcl, dat$data$ucl, dat$data$y, x, 
                p=2, tol=0.001, show_se=FALSE)

# Influence diagnostic
M0y = InfDiag(fit, k=3.5, perturbation="y")
plot(M0y)
M0Sigma = InfDiag(fit, k=3.5, perturbation="Sigma")
plot(M0Sigma)
M0x = InfDiag(fit, k=3.5, indcolx=c(0,1), perturbation="x")
plot(M0x)

# Perturbation on a subset of parameters
M0y1 = InfDiag(fit, k=3.5, indpar=c(1,1,0,0,0), perturbation="y")$M0
M0y2 = InfDiag(fit, k=3.5, indpar=c(0,0,1,1,1), perturbation="y")$M0
#
ggplot(data.frame(M0y1,M0y2)) + geom_point(aes(x=M0y1, y=M0y2)) +
  geom_hline(yintercept=mean(M0y2)+3.5*sd(M0y2), linetype="dashed") +
  geom_vline(xintercept=mean(M0y1)+3.5*sd(M0y1), linetype="dashed") +
  theme_bw()
# }