DataLongGenerator {LongituRF}

Longitudinal data generator

Description

Simulate longitudinal data according to the semi-parametric stochastic mixed-effects model given by:

Y_i(t)=f(X_i(t))+Z_i(t)\beta_i + \omega_i(t)+\epsilon_i

with Y_i(t) the output at time t for the ith individual; X_i(t) the input predictors (fixed effects) at time t for the ith individual; Z_i(t) are the random effects at time t for the ith individual; \omega_i(t) is a Brownian motion with volatility \gamma^2=0.8 at time t for the ith individual; \epsilon_i is the residual error with variance \sigma^2=0.5. The data are simulated according to the simulations in low dimensional in the low dimensional scheme of the paper <doi:10.1177/0962280220946080>

Usage

DataLongGenerator(n = 50, p = 6, G = 6)

Arguments

n

[numeric]: Number of individuals. The default value is n=50.

p

[numeric]: Number of predictors. The default value is p=6.

G

[numeric]: Number of groups of predictors with temporal behavior, generates p-G input variables with no temporal behavior.

Value

a list of the following elements:

• Y: vector of the output trajectories.

• X : matrix of the fixed-effects predictors.

• Z: matrix of the random-effects predictors.

• id: vector of the identifiers for each individual.

• time: vector the the time measurements for each individual.

Examples

oldpar <- par()
oldopt <- options()
data <- DataLongGenerator(n=17, p=6,G=6) # Generate the data
# Let's see the output :
w <- which(data$id==1)
plot(data$time[w],data$Y[w],type="l",ylim=c(min(data$Y),max(data$Y)), col="grey")
for (i in unique(data$id)){
  w <- which(data$id==i)
  lines(data$time[w],data$Y[w], col='grey')
}
# Let's see the fixed effects predictors:
par(mfrow=c(2,3), mar=c(2,3,3,2))
for (i in 1:ncol(data$X)){
  w <- which(data$id==1)
  plot(data$time[w],data$X[w,i], col="grey",ylim=c(min(data$X[,i]),
  max(data$X[,i])),xlim=c(1,max(data$time)),main=latex2exp::TeX(paste0("$X^{(",i,")}$")))
  for (k in unique(data$id)){
    w <- which(data$id==k)
    lines(data$time[w],data$X[w,i], col="grey")
  }
}
par(oldpar)
options(oldopt)