SimulatedDataGenerator.CumulativeProbit {BayesRGMM}

Simulating a longitudinal ordinal data with HSD correlation structures.

Description

This function is used to simulate data for the cumulative probit mixed-effects model with HSD correlation structures.

Usage

SimulatedDataGenerator.CumulativeProbit(
  Num.of.Obs,
  Num.of.TimePoints,
  Num.of.Cats,
  Fixed.Effs,
  Random.Effs,
  DesignMat,
  Missing,
  HSD.DesignMat.para
)

Arguments

Num.of.Obs

the number of subjects will be simulated.

Num.of.TimePoints

the maximum number of time points among all subjects.

Num.of.Cats

the number of categories.

Fixed.Effs

a vector of regression coefficients.

Random.Effs

a list of covariance matrix and the degree of freedom,
e.g., list(Sigma = 0.5*diag(1), df=3).

DesignMat

a design matrix.

Missing

a list of the missing mechanism of observations, 0: data is complete, 1: missing complete at random, 2: missing at random related to responses , and 3: 2: missing at random related to covariates and the corresponding regression coefficients (weights) on the previous observed values either responses or covariates, e.g., Missing = list(Missing.Mechanism = 3, RegCoefs = c(0.4, 1.2, -2.1)).

HSD.DesignMat.para

the list of parameters in HSD correlation structure,
e.g., HSD.DesignMat.para = list(HSD.para = HSD.para, DesignMat = w).

Value

a list containing the following components:

sim.data

The simulated response variables y, covariates x's, and subject identifcation ‘⁠id⁠’.

beta.true

The given values of fixed effects.

classes

The intervals of classes.

HSD.para

The given values of parameters in HSD model.

Examples

## Not run: 
library(BayesRGMM)
rm(list=ls(all=TRUE))

Fixed.Effs = c(-0.1, 0.1, -0.1)  
P = length(Fixed.Effs) 
q = 1 #number of random effects
T = 7 #time points
N = 100 #number of subjects
Num.of.Cats = 3 #number of categories 
num.of.iter = 1000 #number of iterations

HSD.para = c(-0.9, -0.6) #the parameters in HSD model
a = length(HSD.para)
w = array(runif(T*T*a), c(T, T, a)) #design matrix in HSD model
 
for(time.diff in 1:a)
w[, , time.diff] = 1*(as.matrix(dist(1:T, 1:T, method="manhattan")) 
==time.diff)


x = array(0, c(T, P, N))
for(i in 1:N){
    x[, 1, i] = 1:T
    x[, 2, i] = rbinom(1, 1, 0.5)
    x[, 3, i] = x[, 1, i]*x[, 2, i]
}

DesignMat = x

#MAR
CPREM.sim.data = SimulatedDataGenerator.CumulativeProbit(
 Num.of.Obs = N, Num.of.TimePoints = T, Num.of.Cats = Num.of.Cats, 
 Fixed.Effs = Fixed.Effs, Random.Effs = list(Sigma = 0.5*diag(1), df=3), 
 DesignMat = DesignMat, Missing = list(Missing.Mechanism = 2, 
 MissingRegCoefs=c(-0.7, -0.2, -0.1)), 
 HSD.DesignMat.para = list(HSD.para = HSD.para, DesignMat = w))


print(table(CPREM.sim.data$sim.data$y))
print(CPREM.sim.data$classes)

## End(Not run)