smn.clmm: ML estimation of scale mixture of normal linear mixed models...

In skewlmm: Scale Mixture of Skew-Normal Linear Mixed Models

ML estimation of scale mixture of normal linear mixed models with censored responses

Description

It fits left, right, or interval censored scale mixture of normal linear mixed model with possible within-subject dependence structure, using the EM algorithm. It provides estimates and standard errors of parameters.

Usage

smn.clmm(data, formFixed, groupVar, formRandom = ~1, depStruct = "UNC",
         ci, lcl, ucl, timeVar = NULL, distr = "norm",
         nufix = FALSE, pAR = 1, control = lmmControl())

Arguments

data	A data frame containing the variables named in formFixed, formRandom, groupVar, timeVar, ci, lcl, and ucl.
formFixed	A two-sided linear formula object describing the fixed effects part of the model, with the response on the left of a ~ operator and the covariates, separated by + operators, on the right.
groupVar	A character containing the name of the variable which represents the subjects or groups in data.
formRandom	A one-sided linear formula object describing the random effects part of the model, with the covariates, separated by + operators, on the right of a ~ operator. By default, a model with random intercept is considered.
depStruct	A character indicating which dependence structure should be used. "UNC" for conditionally uncorrelated ("CI" is also accepted), "ARp" for AR(p) – p is length(phi)–, "CS" for compound symmetry, "DEC" for DEC, "CAR1" for continuous-time AR(1), and "MA1" for moving average of order 1.
ci	A character containing the name of the censoring indicator variable in data, which should be 1 if the respective observation is censored or missing, and 1 otherwise. If missing, it is assumed that none of the observations is censored.
lcl	A character containing the name of the lower censoring limit in data. If missing, it is assumed lcl=-Inf, i.e., no left limit.
ucl	A character containing the name of the upper censoring limit in data. If missing, it is assumed ucl=Inf, i.e., no right limit.
timeVar	A character containing the name of the variable which represents the time in data. Meaningless if depStruct="UNC" or depStruct="CS". For other structures, if is.null(timeVar) the observations are considered equally spaced and ordered. If depStruct="ARp", timeVar must be an index, preferably starting at 1.
distr	A character indicating which distribution should be used. "norm" for normal and "t" for Student-t.
nufix	TRUE or FALSE indicating if nu should be estimated for t distribution. If nufix=TRUE, nu must be especified through lmmControl().
pAR	If depStruct="ARp", pAR indicates the order of the autoregressive process that should be used (1 by default). Otherwise, it is meaningless.
control	An object resulting from the function lmmControl(), containing additional options for the estimation algorithm.

Details

It fits the model Y_i = X_i \beta + Z_i b_i + \epsilon_i, for i=1,\dots,n, where Y_i is a vector with n_i observed continuous responses, b_i ~ SMN(0, D; H) and \epsilon_i ~ SMN(0, \Sigma_i; H), indexed by the same mixing distribution.

For details see Matos et al. (2013) and Lachos et al. (2019).

Value

An object of class "SMNclmm" representing the SMN-CLMM fit. Generic functions such as print and summary have methods to show the results of the fit. The functions fitted and ranef can be used to extract some of its components.

Specifically, the following components are returned:

theta	Named vector with parameter estimates.
iter	Number of iterations runned.
estimates	A named list containing parameter estimates.
yest	Imputed values in the response variable.
uhat	Estimated weights.
loglik.track	Vector containing the log-likelihood value from each iteration of the estimation procedure.
random.effects	Estimated random effects.
std.error	A vector with standard errors.
loglik	Value of the log-likelihood at last iteration.
elapsedTime	Time elapsed in processing, in seconds.
error	Convergence criterion at last iteration.
criteria	A list with AIC, BIC, and SIC criterion.
call	The smn.clmm call that produced the object.
data	The data frame used on smn.clmm call.
formula	A list containing the formulas used on smn.clmm call.
depStruct	A character indicating which dependence structure was used.
covRandom	A character indicating which structure was used for the random effects scale matrix.
distr	A character indicating which distribution was used.
N	The number of observations used.
n	The number of individuals/groups used.
groupVar	A character indicating the name of the grouping variable.
timeVar	A character indicating the name of the time variable, if any.
fitted	A vector of fitted values.

Author(s)

Larissa A. Matos, Victor H. Lachos, Katherine L. Valeriano and Fernanda L. Schumacher

References

Henderson, N. C. and R. Varadhan (2019). Damped anderson acceleration with restarts and monotonicity control for accelerating EM and EM-like algorithms. Journal of Computational and Graphical Statistics 28(4), 834-846.

Matos, L. A., Prates, M. O., Chen, M. H., and Lachos, V. H. (2013). Likelihood-based inference for mixed-effects models with censored response using the multivariate-t distribution. Statistica Sinica 23(3), 1323-1345.

Lachos, V. H., A. Matos, L., Castro, L. M., and Chen, M. H. (2019). Flexible longitudinal linear mixed models for multiple censored responses data. Statistics in medicine, 38(6), 1074-1102.

See Also

lmmControl, update, predict.SMNclmm, residuals.SMNclmm, plot.SMNclmm, smn.lmm, smsn.lmm

Examples

# Generating a sample for m=30 individuals with 5 times
# Considering 10% of left censoring responses
# AR(1) and normal distribution
nj1 = 5
m = 30
time = rep(1:nj1, times=m)
groups = as.factor(rep(1:m, each=nj1))
dat1 = rsmsn.clmm(time = time, ind = groups, x = cbind(1,time), z = rep(1,m*nj1),
                  sigma2=0.6, D=0.5*diag(1), beta=c(1,2), depStruct="ARp",
                  phi=0.4, pcens = .1, type = "left")

# Estimation using UNC
fm0 = smn.clmm(dat1, formFixed=y~x, groupVar="ind", ci="ci", ucl="ucl")
summary(fm0)

# Estimation using AR(1)
fm1 = update(fm0, depStruct="ARp")

# Estimation using AR(1) and t distribution
fm2 = update(fm1, distr="t")

# Comparing fitted models
criteria(list(fm0= fm0, fm1=fm1, fm2=fm2))

skewlmm documentation built on July 9, 2023, 7:29 p.m.