lsmm {FlexVarJM}

lsmm : Estimation of location scale mixed model

Description

This function fits complex mixed effects model with a time and covariate dependent variance. We suppose that the variance of the residual error is time-dependent and subject-specific. Parameters are estimated simultaneously through a maximum likelihood method, using a Marquardt-Levenberg algorithm.

Usage

lsmm(
  formFixed,
  formRandom,
  formGroup,
  timeVar,
  data.long,
  variability_hetero = TRUE,
  formFixedVar,
  formRandomVar,
  correlated_re = FALSE,
  S1 = 1000,
  S2 = 5000,
  nproc = 1,
  clustertype = "SOCK",
  maxiter = 100,
  print.info = FALSE,
  file = NULL,
  epsa = 0.001,
  epsb = 0.001,
  epsd = 0.001,
  binit = NULL
)

Arguments

formFixed

A formula for the fixed effects of the longitudinal submodel

formRandom

A formula for the random effects of the longitudinal submodel

formGroup

A formula which indicates the group variable

timeVar

The name of the column of time in data.long. This variable must appears in data.long

data.long

A dataframe with the longitudinal data

variability_hetero

A logical to indicate if we suppose a subject_specific variability

formFixedVar

A formula for the fixed effects of the variance predictor

formRandomVar

A formula for the random effects of the variance predictor

correlated_re

A logical to indicate if the random effects of the marker and the variance predictors are correlated (By default there are supposed to be independent)

S1

An integer : the number of QMC draws for the first step

S2

An integer : the number of QMC draws for the second step

nproc

An integer : the number of processors for parallel computing

clustertype

one of the supported types from makeCluster function

maxiter

optional maximum number of iterations for the marqLevAlg iterative algorithm.

print.info

logical indicating if the outputs of each iteration should be written

file

optional character giving the name of the file where the outputs of each iteration should be written (if print.info=TRUE)

epsa

optional threshold for the convergence criterion based on the parameter stability.

epsb

optional threshold for the convergence criterion based on the objective function stability.

epsd

optional threshold for the relative distance to maximum. This criterion has the nice interpretation of estimating the ratio of the approximation error over the statistical error, thus it can be used for stopping the iterative process whatever the problem.

binit

optional initials parameters.

Details

The model is defined by : #' \quad\left\{\begin{array}{ll} Y_{ij} = Y_{i}(t_{ij}) = \widetilde{Y}_i(t_{ij}) + \epsilon_{ij} = X_{ij}^{\top} \beta+Z_{ij}^{\top} b_{i}+\epsilon_{ij}, \\ \epsilon_{ij}(t_{ij}) \sim \mathcal{N}(0,\sigma_i^2(t_{ij})) \hspace{3mm} \text{with} \hspace{3mm} \log(\sigma_i(t_{ij})) = O_{ij}^{\top} \mu+M_{ij}^{\top} \tau_{i} \end{array} \right.

with X_{ij}, O_{ij}, Z_{ij} and M_{ij} four vectors of explanatory variables for subject i at visit j, respectively associated with the fixed-effect vectors \beta and \mu, and the subject-specific random-effect vector b_i and \tau_i, such as \quad\left(\begin{array}{c} b_{i} \\ \tau_i \end{array}\right) \sim N\left(\left(\begin{array}{c} 0 \\ 0 \end{array}\right),\left(\begin{array}{cc} \Sigma_{b} & \Sigma_{\tau b} \\ \Sigma_{\tau b}' & \Sigma_{\tau} \end{array}\right)\right)

Y_{i}(t_{ij}) = \tilde{Y}_i(t_{ij}) + \epsilon_{ij} = X_{ij}^{\top} \beta+Z_{ij}^{\top} b_{i}+\epsilon_{ij}

with X_{ij} and Z_{ij} two covariate vectors for subject i at visit j, respectively associated with the vector of fixed effects \beta and the vector of subject-specific individual random effects b_i. The vector b_i is assumed to be normally distributed and a specific-subject random effect on the variance of the measure error can be added: \epsilon_{ij} \sim \mathcal{N}(0,\sigma_i^2) and

\quad\left(\begin{array}{c} b_{i} \\ \log \sigma_{i} \end{array}\right) \sim \mathcal{N}\left(\left(\begin{array}{c} 0 \\ \mu_{\sigma} \end{array}\right),\left(\begin{array}{cc} \Sigma_{b} & 0 \\ 0 & \tau_{\sigma}^{2} \end{array}\right)\right)

Value

A FlexVarJoint object which contains the following elements :

result

A marqLevAlg object with the results of the estimation.

table.res

The table of results : Estimation and SE

time.compute

Computation time

control

A list of control elements

Examples

#fit a joint model with competing risks and subject-specific variability
example <- lsmm(formFixed = y~visit,
formRandom = ~ visit,
formGroup = ~ID,
timeVar = "visit",
data.long = Data_toy,
variability_hetero = TRUE,
formFixedVar =~visit,
formRandomVar =~visit,
correlated_re = TRUE,
S1 = 100,
S2 = 1000,
nproc = 1,
maxiter = 100
)

summary(example)