# ARpMMEC.est: Censored Mixed-Effects Models with Autoregressive Correlation... In ARpLMEC: Censored Mixed-Effects Models with Different Correlation Structures

 ARpMMEC.est R Documentation

## Censored Mixed-Effects Models with Autoregressive Correlation Structure and DEC for Normal and t-Student Errors

### Description

This functino fits left, right or intervalar 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

ARpMMEC.est(
y,
x,
z,
tt,
cc,
nj,
struc = "UNC",
order = 1,
initial = NULL,
nu.fixed = TRUE,
typeModel = "Normal",
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 ordern x b, corresponding to vector of random effects. tt Vector 1 x n with the time the measurements were made, where n is the total number of measurements for all individuals. Default it's considered regular times. 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. struc UNC,ARp,DEC,SYM or DEC(AR) for uncorrelated ,autoregressive, DEC(phi1,phi2), DEC(phi1,phi2=1), DEC(DEC(phi1,phi2=1)) structure, respectively order Order of the autoregressive process. Must be a positive integer value. initial List with the initial values in the next orden: betas,sigma2,alphas,phi and nu. If it is not indicated it will be provided automatically. Default is NULL nu.fixed Logical. Should estimate the parameter "nu" for the t-student distribution?. If is False indicates the value in the list of initial values. Default is FALSE typeModel Normal for Normal distribution and Student for t-Student distribution. Default is Normal cens.type left for left censoring, right for right censoring and interval for intervalar 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. Available at the moment only for the typeModel=normal case. 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”:

 FixEffect Data frame with: estimate, standar errors and confidence intervals of the fixed effects. Sigma2 Data frame with: estimate, standar errors and confidence intervals of the variance of the white noise process. Phi Data frame with: estimate, standar errors and confidence intervals of the autoregressive parameters. RandEffect Data frame with: estimate, standar errors and confidence intervals of the random effects. nu the parameter "nu" for the t-student distribution Est Vector of parameters estimate (fixed Effects, sigma2, phi, random effects). SE Vector of the standard errors of (fixed Effects, sigma2, phi, random effects). Residual Vector of the marginal residuals. loglik Log-likelihood value. AIC Akaike information criterion. BIC Bayesian information criterion. AICc Corrected Akaike information criterion. iter Number of iterations until convergence. Yfit Vector "y" fitted MI Information matrix Prev Predicted values (if xpre and zpre is not NULL). time Processing time. others The first and second moments of the random effect and vector Y

### References

Olivari, R. C., Garay, A. M., Lachos, V. H., & Matos, L. A. (2021). Mixed-effects models for censored data with autoregressive errors. Journal of Biopharmaceutical Statistics, 31(3), 273-294. doi: 10.1080/10543406.2020.1852246

### Examples

## 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    = 0.6
beta   = c(1,2,1)
nj=rep(4,10)
tt=rep(1:4,length(nj))
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=ARpMMEC.sim(m,x,z,tt,nj,beta,sigma2,D,phi,struc="ARp",typeModel="Normal",p.cens=p.cens)

teste1=ARpMMEC.est(data\$y_cc,x,z,tt,data\$cc,nj,struc="ARp",order=1,typeModel="Normal",MaxIter = 2)
teste2=ARpMMEC.est(data\$y_cc,x,z,tt,data\$cc,nj,struc="ARp",order=1,typeModel="Student",MaxIter = 2)

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)
teste3=ARpMMEC.est(data\$y_cc,x,z,tt,data\$cc,nj,struc="ARp",order=1,typeModel="Normal",
MaxIter = 2,Prev=TRUE,step=2,isubj=isubj,xpre=xx,zpre=zz)
teste3\$Prev

## End(Not run)

ARpLMEC documentation built on June 27, 2022, 1:06 a.m.