# ARpLMEC.est

##### Autoregressive Censored Linear Mixed Effects Models

This function fits left, right or interval censored mixed-effects linear model, with autoregressive errors of order `p`

, using the EM algorithm. It returns estimates, standard errors and prediction of future observations.

##### Usage

```
ARpLMEC.est(y, x, z, cc, nj, Arp = 1, beta0 = NULL, sigma0 = NULL,
D0 = NULL, pi0 = NULL, cens.type = "left", LI = NULL,
LS = NULL, MaxIter = 200, error = 1e-04, Prev = FALSE,
step = NULL, isubj = NULL, xpre = NULL, zpre = NULL)
```

##### Arguments

- y
Vector

`1 x n`

of censored responses, where`n`

is the sum of the number of observations of each individual.- x
Design matrix of the fixed effects of order

`n x s`

, corresponding to vector of fixed effects.- z
Design matrix of the random effects of order

`n x b`

, corresponding to vector of random effects.- 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.- nj
Vector

`1 x m`

with the number of observations for each subject, where`m`

is the total number of individuals.- Arp
Order of the autoregressive process. Must be a positive integer value. To consider a model uncorrelated use

`UNC`

.- beta0
Initial values for the vector of fixed effects. If it is not indicated it will be provided automatically. Default is

`NULL`

.- sigma0
Initial values for sigma. If it is not indicated it will be provided automatically. Default is

`NULL`

.- D0
Initial values for the covariance matrix for the random effects. If it is not indicated it will be provided automatically. Default is

`NULL`

.- pi0
Initial values for the vector for autoregressive coefficients pi's. If it is not indicated it will be provided automatically. Default is

`NULL`

.- cens.type
`left`

for left censoring,`right`

for right censoring and`interval`

for interval censoring. Default is`left`

.- LI
Vector censoring lower limit indicator of length

`n`

. For each observation:`0`

if non-censored,`-inf`

if censored. It is only indicated for when`cens.type`

is`both`

. Default is`NULL`

.- LS
Vector censoring upper limit indicator of length

`n`

. For each observation:`0`

if non-censored,`inf`

if censored.It is only indicated for when`cens.type`

is`both`

. Default is`NULL`

.- MaxIter
The maximum number of iterations of the EM algorithm. Default is

`200`

.- error
The convergence maximum error. Default is

`0.0001`

.- Prev
Indicator of the prediction process. Default is

`FALSE`

.- step
Number of steps for prediction. Default is

`NULL`

.- isubj
Vector indicator of subject included in the prediction process. Default is

`NULL`

.- xpre
Design matrix of the fixed effects to be predicted. Default is

`NULL`

.- zpre
Design matrix of the random effects to be predicted. Default is

`NULL`

.

##### Value

returns list of class “ARpMMEC”:

Data frame with: estimate, standars erros and confidence intervals of the fixed effects.

Data frame with: estimate, standars erros and confidence intervals of the variance of the white noise process.

Data frame with: estimate, standars erros and confidence intervals of the autoregressive parameters.

Data frame with: estimate, standars erros and confidence intervals of the random effects.

Vector of parameters estimate (fixed Effects, sigma2, phi, random effects).

Vector of the standard errors of (fixed Effects, sigma2, phi, random effects).

Log-likelihood value.

Akaike information criterion.

Bayesian information criterion.

Corrected Akaike information criterion.

Number of iterations until convergence.

Information matrix

Predicted values (if xpre and zpre is not `NULL`

).

Processing time.

##### References

Vaida F, Liu L (2009). Fast implementation for normal mixed Effects models with censored response. Journal of Computational and Graphical Statistics; https://doi.org/10.1198/jcgs.2009.07130

Matos LA, Lachos V, Balakrishnan N, Labra F (2013). Influence diagnostics in linear and nonlinear mixed-effects models with censored data. Computational Statistics & Data Analysis; https://doi.org/10.1016/j.csda.2012.06.021

Schumacher FL, Lachos VH, Dey DK (2017). Censored regression models with autoregressive errors: A likelihood-based perspective. Canadian Journal of Statistics. https://doi.org/10.1002/cjs.11338

##### Examples

```
# NOT RUN {
# }
# NOT RUN {
p.cens = 0.1
m = 10
D = matrix(c(0.049,0.001,0.001,0.002),2,2)
sigma2 = 0.30
phi = c(0.48,-0.2)
beta = c(1,2,1)
nj=c(6,5,6,8,5,7,8,6,5,4)
x<-matrix(runif(sum(nj)*length(beta),-1,1),sum(nj),length(beta))
z<-matrix(runif(sum(nj)*dim(D)[1],-1,1),sum(nj),dim(D)[1])
data=ARpLMEC.sim(m,x,z,nj,beta,sigma2,D,phi,p.cens)
attach(data)
Arp = 2
##Estimacao sem Previcao
teste1=ARpLMEC.est(y_cc,x,z,cc,nj,Arp,MaxIter = 10)
##Estimacao com Previcao
xx=matrix(runif(6*length(beta),-1,1),6,length(beta))
zz=matrix(runif(6*dim(D)[1],-1,1),6,dim(D)[1])
isubj=c(1,4,5)
teste2=ARpLMEC.est(y_cc,x,z,cc,nj,Arp,MaxIter=10,Prev=TRUE,step=2,isubj=isubj,xpre=xx,zpre=zz)
teste2$Prev
# }
# NOT RUN {
# }
```

*Documentation reproduced from package ARpLMEC, version 1.0, License: GPL (>= 2)*