InfDiag {ARCensReg}

Influence diagnostic in censored linear regression model with autoregressive errors

Description

It performs influence diagnostic by a local influence approach (Cook 1986) 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 Schumacher et al. (2018).

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

Cook RD (1986). “Assessment of local influence.” Journal of the Royal Statistical Society: Series B (Methodological), 48(2), 133–155.

Schumacher FL, Lachos VH, Vilca-Labra FE, Castro LM (2018). “Influence diagnostics for censored regression models with autoregressive errors.” Australian & New Zealand Journal of Statistics, 60(2), 209–229.

Zhu H, Lee S (2001). “Local influence for incomplete data models.” Journal of the Royal Statistical Society: Series B (Statistical Methodology), 63(1), 111–126.

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()