ARCensReg {ARCensReg}  R Documentation 
It fits a univariate left, right, or interval censored linear regression model with autoregressive errors under the normal distribution, using the SAEM algorithm. It provides estimates and standard errors of the parameters, supporting missing values on the dependent variable.
ARCensReg(cc, lcl = NULL, ucl = NULL, y, x, p = 1, M = 10,
perc = 0.25, MaxIter = 400, pc = 0.18, tol = 1e04,
show_se = TRUE, quiet = FALSE)
cc 
Vector of censoring indicators of length 
lcl , ucl 
Vectors of length 
y 
Vector of responses of length 
x 
Matrix of covariates of dimension 
p 
Order of the autoregressive process. It must be a positive integer value. 
M 
Size of the Monte Carlo sample generated in each step of the SAEM algorithm. Default=10. 
perc 
Percentage of burnin 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 with no memory. It is recommended that

tol 
The convergence maximum error permitted. 
show_se 

quiet 

The linear regression model with autocorrelated errors, defined as a discretetime autoregressive (AR) process of order p
, at time t
is given by
Y_t = x_t^T \beta + \xi_t,
\xi_t = \phi_1 \xi_{t1} + ... + \phi_p \xi_{tp} + \eta_t, t=1, ..., n,
where Y_t
is the response variable, \beta = (\beta_1, ..., \beta_l)^T
is a vector
of regression parameters of dimension l
, and x_t = (x_{t1}, ..., x_{tl})^T
is a
vector of nonstochastic regressor variables values; \xi_t
is the AR error with Gaussian
disturbance \eta_t
, \phi = (\phi_1, ..., \phi_p)^T
is the vector of AR coefficients,
and n
is the sample size.
It is assumed that Y_t
is not fully observed for all t
.
For left censored observations, we have lcl=Inf
and ucl=
V_t
,
such that the true value Y_t \leq V_t
. For right censoring, lcl=
V_t
and ucl=Inf
, such that Y_t \geq V_t
. For interval censoring, lcl
and ucl
must be finite values, such that V_{1t} \leq Y_t \leq V_{2t}
. Missing data can be defined by setting lcl=Inf
and ucl=Inf
.
The initial values are obtained by ignoring censoring and applying maximum likelihood
estimation with the censored data replaced by their censoring limits. Furthermore, just set cc
as a vector of zeros to fit a regression model with autoregressive errors for noncensored data.
An object of class "ARpCRM", representing the AR(p) censored regression normal fit. Generic functions such as print and summary have methods to show the results of the fit. The function plot provides convergence graphics for the parameters when at least one censored observation exists.
Specifically, the following components are returned:
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 
theta 
Vector of parameters estimate ( 
SE 
Vector of the standard errors of ( 
loglik 
Loglikelihood value. 
AIC 
Akaike information criterion. 
BIC 
Bayesian information criterion. 
AICcorr 
Corrected Akaike information criterion. 
yest 
Augmented response variable based on the fitted model. 
yyest 
Final estimative of 
x 
Matrix of covariates of dimension 
iter 
Number of iterations until convergence. 
criteria 
Attained criteria value. 
call 
The 
tab 
Table of estimates. 
critFin 
Selection criteria. 
cens 
"left", "right", or "interval" for left, right, or interval censoring, respectively. 
nmiss 
Number of missing observations. 
ncens 
Number of censored observations. 
converge 
Logical indicating convergence of the estimation algorithm. 
MaxIter 
The maximum number of iterations used for the SAEM algorithm. 
M 
Size of the Monte Carlo sample generated in each step of the SAEM algorithm. 
pc 
Percentage of initial iterations of the SAEM algorithm with no memory. 
time 
Time elapsed in processing. 
plot 
A list containing convergence information. 
Fernanda L. Schumacher, Katherine L. Valeriano, Victor H. Lachos, Christian E. Galarza, and Larissa A. Matos
Delyon B, Lavielle M, Moulines E (1999). “Convergence of a stochastic approximation version of the EM algorithm.” Annals of statistics, 94–128.
Schumacher FL, Lachos VH, Dey DK (2017). “Censored regression models with autoregressive errors: A likelihoodbased perspective.” Canadian Journal of Statistics, 45(4), 375–392.
## Example 1: (p = l = 1)
# Generating a sample
set.seed(23451)
n = 50
x = rep(1, n)
dat = rARCens(n=n, beta=2, phi=.5, sig2=.3, x=x, cens='left', pcens=.1)
# Fitting the model (quick convergence)
fit0 = ARCensReg(dat$data$cc, dat$data$lcl, dat$data$ucl, dat$data$y, x,
M=5, pc=.12, tol=0.001, show_se=FALSE)
fit0
## Example 2: (p = l = 2)
# Generating a sample
n = 100
x = cbind(1, runif(n))
dat = rARCens(n=n, beta=c(2,1), phi=c(.48,.2), sig2=.5, x=x, cens='left',
pcens=.05)
# Fitting the model
fit1 = ARCensReg(dat$data$cc, dat$data$lcl, dat$data$ucl, dat$data$y, x,
p=2, tol=0.0001)
summary(fit1)
plot(fit1)
# Plotting the augmented variable
library(ggplot2)
data.plot = data.frame(yobs=dat$data$y, yest=fit1$yest)
ggplot(data.plot) + theme_bw() +
geom_line(aes(x=1:nrow(data.plot), y=yest), color=4, linetype="dashed") +
geom_line(aes(x=1:nrow(data.plot), y=yobs)) + labs(x="Time", y="y")
## Example 3: Simulating missing values
miss = sample(1:n, 3)
yMISS = dat$data$y
yMISS[miss] = NA
cc = dat$data$cc
cc[miss] = 1
lcl = dat$data$lcl
ucl = dat$data$ucl
ucl[miss] = Inf
fit2 = ARCensReg(cc, lcl, ucl, yMISS, x, p=2)
plot(fit2)
# Imputed missing values
data.frame(yobs=dat$data$y[miss], yest=fit2$yest[miss])