InfDiag: Influence diagnostic in censored linear regression model with...

In ARCensReg: Fitting Univariate Censored Linear Regression Model with Autoregressive Errors

Influence diagnostic in censored linear regression model with autoregressive errors

Description

It performs influence diagnostic by a local influence approach \insertCitecook1986assessmentARCensReg 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")

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.

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 \insertCiteschumacher2018influence;textualARCensReg.

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).

Author(s)

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

References

\insertRef

cook1986assessmentARCensReg

\insertRef

schumacher2018influenceARCensReg

\insertRef

zhu2001localARCensReg

See Also

ARCensReg

Examples

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()

ARCensReg documentation built on Aug. 30, 2023, 1:09 a.m.