ARCensReg {ARCensReg}R Documentation

Censored Linear Regression Model with Autoregressive Errors

Description

It fits an univariate left or right censored linear regression model with autoregressive errors under the normal distribution using the SAEM algorithm. It provides estimates and standard errors of the parameters, prediction of future observations and it supports missing values on the dependent variable. It also provides convergence plots when exists at least one censored observation.

Usage

ARCensReg(cc,y,x,p=1,cens='left',x_pred=NULL,miss=NULL,
  tol=0.0001,show.convergence=TRUE,M=10,perc=0.25,MaxIter=400,
  pc=0.18,show_se=TRUE)

Arguments

cc

Vector of censoring indicators of length n, where n is the total of observations. For each observation: 0 if non-censored, 1 if censored.

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).

y

Vector of responses of length n.

p

Order of the autoregressive process. Must be a positive integer value. For p equal to 0 we suggest to use the function CensReg.SMN from SMNCensReg package.

cens

"left" for left censoring, "right" for right censoring.

x_pred

Matrix of covariates for responses to be predicted. If x_pred = NULL no responses are predicted.

miss

Vector containing the index of missing observations. miss = NULL indicates that no observations are missing.

tol

The convergence maximum error permitted.

show.convergence

TRUE or FALSE. Indicates if convergence graphs should be built for the parameters estimates (for the case with at least one censored observation). The dashed line indicates the iteration of the SAEM algorithm that simulations start being smoothed. Default=TRUE.

M

Size of the Monte Carlo sample generated in each step of the SAEM algorithm. Default=10.

perc

Percentage of burn-in on the Monte Carlo sample. Default=0.25.

MaxIter

The maximum number of iterations of the SAEM algorithm. Default=400.

pc

Percentage of initial iterations of the SAEM algorithm. It is recommended that 50<MaxIter*pc<100. Default=0.18.

show_se

TRUE or FALSE. Indicates if the standard errors should be estimated. Default=TRUE.

Details

The initial values are obtained by ignoring censoring and applying maximum likelihood estimation with the censored data simply replaced by their censoring limits. If you want to fit a regression model with autoregressive errors for non-censored data, just set "cc" as a vector of zeros and "cens" as either "right" or "left".

Value

beta

Estimate of the regression parameters.

sigma2

Estimated variance of the white noise process.

phi

Estimate of the autoregressive parameters.

pi1

Estimate of the first p partial autocorrelations.

theta

Vector of parameters estimate (beta, sigma2, phi).

SE

Vector of the standard errors of (beta, sigma2, phi).

loglik

Log-likelihood value.

AIC

Akaike information criterion.

BIC

Bayesian information criterion.

AICcorr

Corrected Akaike information criterion.

time

Processing time.

pred

Predicted values (if x_pred is not NULL).

criteria

Attained criteria value.

yest

Augmented response variable based on the fitted model.

yyest

Final estimative of E(Y%*%t(Y)).

iter

Number of iterations until convergence.

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

Delyon, B., Lavielle, M. & Moulines, E. (1999) Convergence of a stochastic approximation version of the EM algorithm. Journal of the Royal Statistical Society, Series B, 39, 1-38.

Schumacher, F. L., Lachos, V. H. & Dey, D. K. (2016) Censored regression models with autoregressive errors: A likelihood-based perspective. Submitted.

See Also

arima, CensReg.SMN, InfDiag

Examples

##simple example (p = l = 1)
#generating a sample
set.seed(23451)
n=50
x=rep(1,n)
dat = rARCens(n=n,beta=2,pit=.5,sig2=.3,x=x,
                cens='left',pcens=.1)

#fitting the model (quick convergence)
fit0 = ARCensReg(dat$data$cc,dat$data$y,x,tol=0.001,
                  pc=.12,M=5,show_se=FALSE)

## Not run: 

##another example (p = l = 2)
#generating a sample
n=100
x=cbind(1,runif(n))
dat = rARCens(n=n,beta=c(2,1),pit=c(.4,-.2),sig2=.5,
                    x=x,cens='left',pcens=.05)

#fitting the model
fit1 = ARCensReg(dat$data$cc,dat$data$y,x,p=2,
                      cens="left",tol=0.0001)

#plotting the augmented variable
par(mfrow=c(1,1))
plot.ts(fit1$yest,lty='dashed',col=4)
lines(dat$data$y)

#simulating missing values
miss = sample(1:n,3)
yMISS = dat$data$y
yMISS[miss] = NA
fit2 = ARCensReg(dat$data$cc,yMISS,x,p=2,miss=miss,
                cens="left",tol=0.0001)


## End(Not run)

[Package ARCensReg version 2.1 Index]