ARtCensReg {ARCensReg}  R Documentation 
It fits a univariate left, right, or interval censored linear regression model with autoregressive errors considering Studentt innovations, through the SAEM algorithm. It provides estimates and standard errors of the parameters, supporting missing values on the dependent variable.
ARtCensReg(cc, lcl = NULL, ucl = NULL, y, x, p = 1, M = 10,
perc = 0.25, MaxIter = 400, pc = 0.18, nufix = NULL, 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

nufix 
If the degrees of freedom ( 
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
, x_t = (x_{t1},..., x_{tl})^T
is a vector of nonstochastic regressor variables values, and \xi_t
is the AR
error with \eta_t
being a shock of disturbance following the Studentt distribution
with \nu
degrees of freedom, \phi = (\phi_1,..., \phi_p)^T
being the vector of AR
coefficients, and n
denoting 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. Moreover,
just set cc
as a vector of zeros to fit a regression model with autoregressive
errors for noncensored data.
An object of class "ARtpCRM" representing the AR(p) censored regression Studentt 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 parameter estimates.
Specifically, the following components are returned:
beta 
Estimate of the regression parameters. 
sigma2 
Estimated scale parameter of the innovation. 
phi 
Estimate of the autoregressive parameters. 
nu 
Estimated degrees of freedom. 
theta 
Vector of parameters estimate ( 
SE 
Vector of the standard errors of ( 
yest 
Augmented response variable based on the fitted model. 
uest 
Final estimated weight variables. 
x 
Matrix of covariates of dimension 
iter 
Number of iterations until convergence. 
criteria 
Attained criteria value. 
call 
The 
tab 
Table of estimates. 
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. 
This algorithm assumes that the first p
values in the response vector are completely observed.
Katherine L. Valeriano, Fernanda L. Schumacher, 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.
Valeriano KL, Schumacher FL, Galarza CE, Matos LA (2021).
“Censored autoregressive regression models with Student t
innovations.”
arXiv preprint arXiv:2110.00224.
## Example 1: (p = l = 1)
# Generating a sample
set.seed(1234)
n = 80
x = rep(1, n)
dat = rARCens(n=n, beta=2, phi=.6, sig2=.3, x=x, cens='right', pcens=.05,
innov='t', nu=4)
# Fitting the model (quick convergence)
fit0 = ARtCensReg(dat$data$cc, dat$data$lcl, dat$data$ucl, dat$data$y, x,
M=5, pc=.12, tol=0.001)
fit0
## Example 2: (p = l = 2)
# Generating a sample
set.seed(783796)
n = 200
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, innov='t', nu=5)
# Fitting the model with nu known
fit1 = ARtCensReg(dat$data$cc, dat$data$lcl, dat$data$ucl, dat$data$y, x,
p=2, M=15, pc=.20, nufix=5)
summary(fit1)
plot(fit1)
# Fitting the model with nu unknown
fit2 = ARtCensReg(dat$data$cc, dat$data$lcl, dat$data$ucl, dat$data$y, x,
p=2, M=15, pc=.20)
summary(fit2)
plot(fit2)