InfDiag {ARCensReg} R Documentation

## 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 perturbations schemes: response perturbation (y), scale matrix perturbation (Sigma) or explanatory variable perturbation (x). A benchmark value is calculated that depends on k.

### Usage

```InfDiag(theta,yest,yyest,x,k=3,plots=T,indpar=rep(1,length(theta)),
perturbation ='y',indcolx = rep(1,ncol(x)))
```

### Arguments

 `theta` Vector of estimated parameters. `yest` Vector of responses of length `n` with agmented data. Should be the value yest of the ARCensReg function in the case that at least one observation is censored. `yyest` Should be the value yyest of the ARCensReg function in the case that at least one observation is censored. Otherwise, must be `y%*%t(y)`. `x` Matrix of covariates of dimension `n x l`, where `l` is the number of fixed effects including the intercept, if considered (in models which include an intercept `x` should contain a column of ones). `k` Constant to be used in the benchmark calculation: `M0+k*sd(M0)`. `plots` TRUE or FALSE. Indicates if a graph should be plotted. `indpar` Vector of length equal to the number of parameters, with each element 0 or 1 indicating if the respective parameter should be taking into account in the influence calculation. `perturbation` Perturbation scheme. Possible values: "y" for response perturbation, "Sigma" for scale matrix perturbation or "x" for explanatory variable perturbation. `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.

### 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., 2016).

M0

### Author(s)

Fernanda L. Schumacher <fernandalschumacher@gmail.com>, Victor H. Lachos <hlachos@ime.unicamp.br> and Christian E. Galarza <cgalarza88@gmail.com>

Maintainer: Fernanda L. Schumacher <fernandalschumacher@gmail.com>

### References

Cook, R. D. (1986). Assessment of local influence. Journal of the Royal Statistical Society, Series B, 48, 133-169.

Schumacher, F. L., Lachos, V. H. & Vilca-Labra, F. E. (2016) Influence diagnostics for censored regression models with autoregressive errors. Submitted.

Zhu, H. & Lee, S. (2001). Local influence for incomplete-data models. Journal of the Royal Statistical Society, Series B, 63, 111-126.

`ARCensReg`

### Examples

```## Not run:
#generating the data
set.seed(12341)
x = cbind(1,runif(100))
dat = rARCens(n=100,beta = c(1,-1),pit = c(.4,-.2),sig2=.5,
x=x,cens='left',pcens=.05)
#creating an outlier
dat\$data\$y = 5
plot.ts(dat\$data\$y)

#fitting the model
fit = ARCensReg(cc=dat\$data\$cc,y=dat\$data\$y,x,p=2,cens='left',
tol=0.001,show_se=F)

#influence diagnostic
M0y = InfDiag(theta=fit\$res\$theta, yest=fit\$yest, yyest=fit\$yyest,
x=x, k = 3.5, perturbation = "y")
M0Sigma = InfDiag(theta=fit\$res\$theta, yest=fit\$yest, yyest=fit\$yyest,
x=x, k = 3.5, perturbation = "Sigma")
M0x = InfDiag(theta=fit\$res\$theta, yest=fit\$yest, yyest=fit\$yyest,
x=x, k = 3.5, perturbation = "x",indcolx =c(0,1))

#perturbation on a subset of parameters
M0y1 = InfDiag(theta=fit\$res\$theta, yest=fit\$yest, yyest=fit\$yyest,
x=x, k = 3.5, perturbation = "y",indpar=c(1,1,0,0,0))
M0y2 = InfDiag(theta=fit\$res\$theta, yest=fit\$yest, yyest=fit\$yyest,
x=x, k = 3.5, perturbation = "y",indpar=c(0,0,1,1,1))
plot(M0y1,M0y2)
abline(v = mean(M0y1)+3.5*sd(M0y1),h = mean(M0y2)+3.5*sd(M0y2),lty=2)

## End(Not run)
```

[Package ARCensReg version 2.1 Index]