R/simARCL_scaled_50.R
In jhorzek/OrzekMasterThesis: OrzekMasterThesis can be used to replicate the findings reportet in the master thesis "LASSO Regularization in Dynamic Panel Models"
Defines functions
simARCL_scaled_50
Documented in
simARCL_scaled_50
#' simARCL_scaled_50
#'
#'
#' simARCL_scaled_50 creates an ARCL(1)-SEM model with OpenMx with 5 latent variables and 1 manifest per latent and time point for data simulation. It returns the simulated data set and a covariance based and a raw data based model. 10 Timepoints are created of which the initial five are omitted (burned)
#' The model has 50% non-zero cross-lagged effects
#'
#'
#' @author Jannik Orzek
#' @import OpenMx
#'
#' @export
#'
#'
simARCL_scaled_50 <- function(sampleSize, autoEffect, crossEffect){
# t1
x1_t1 <-rnorm(n = sampleSize, mean = 0, sd = 1)
x2_t1 <-rnorm(n = sampleSize, mean = 0, sd = 1)
x3_t1 <-rnorm(n = sampleSize, mean = 0, sd = 1)
x4_t1 <-rnorm(n = sampleSize, mean = 0, sd = 1)
x5_t1 <-rnorm(n = sampleSize, mean = 0, sd = 1)
#t2
x1_t2 <- autoEffect*x1_t1 + crossEffect*x2_t1 + crossEffect*x3_t1 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x1_t1) +
crossEffect^2*var(x2_t1)+
crossEffect^2*var(x3_t1)+
2*autoEffect*crossEffect*cov(x1_t1,x2_t1)+
2*autoEffect*crossEffect*cov(x1_t1,x3_t1)+
2*crossEffect*crossEffect*cov(x2_t1,x3_t1))))
x2_t2 <- autoEffect*x2_t1 + crossEffect*x3_t1 + crossEffect*x4_t1 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x2_t1) +
crossEffect^2*var(x3_t1)+
crossEffect^2*var(x4_t1)+
2*autoEffect*crossEffect*cov(x2_t1,x3_t1)+
2*autoEffect*crossEffect*cov(x2_t1,x4_t1)+
2*crossEffect*crossEffect*cov(x3_t1,x4_t1))))
x3_t2 <- autoEffect*x3_t1 + crossEffect*x4_t1 + crossEffect*x5_t1 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x3_t1) +
crossEffect^2*var(x4_t1)+
crossEffect^2*var(x5_t1)+
2*autoEffect*crossEffect*cov(x3_t1,x4_t1)+
2*autoEffect*crossEffect*cov(x3_t1,x5_t1)+
2*crossEffect*crossEffect*cov(x4_t1,x5_t1))))
x4_t2 <- autoEffect*x4_t1 + crossEffect*x5_t1 + crossEffect*x1_t1 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x4_t1) +
crossEffect^2*var(x5_t1)+
crossEffect^2*var(x1_t1)+
2*autoEffect*crossEffect*cov(x4_t1,x5_t1)+
2*autoEffect*crossEffect*cov(x4_t1,x1_t1)+
2*crossEffect*crossEffect*cov(x5_t1,x1_t1))))
x5_t2 <- autoEffect*x5_t1 + crossEffect*x1_t1 + crossEffect*x2_t1 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x5_t1) +
crossEffect^2*var(x1_t1)+
crossEffect^2*var(x2_t1)+
2*autoEffect*crossEffect*cov(x5_t1,x1_t1)+
2*autoEffect*crossEffect*cov(x5_t1,x2_t1)+
2*crossEffect*crossEffect*cov(x1_t1,x2_t1))))
#t3
x1_t3 <- autoEffect*x1_t2 + crossEffect*x2_t2 + crossEffect*x3_t2 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x1_t2) +
crossEffect^2*var(x2_t2)+
crossEffect^2*var(x3_t2)+
2*autoEffect*crossEffect*cov(x1_t2,x2_t2)+
2*autoEffect*crossEffect*cov(x1_t2,x3_t2)+
2*crossEffect*crossEffect*cov(x2_t2,x3_t2))))
x2_t3 <- autoEffect*x2_t2 + crossEffect*x3_t2 + crossEffect*x4_t2 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x2_t2) +
crossEffect^2*var(x3_t2)+
crossEffect^2*var(x4_t2)+
2*autoEffect*crossEffect*cov(x2_t2,x3_t2)+
2*autoEffect*crossEffect*cov(x2_t2,x4_t2)+
2*crossEffect*crossEffect*cov(x3_t2,x4_t2))))
x3_t3 <- autoEffect*x3_t2 + crossEffect*x4_t2 + crossEffect*x5_t2 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x3_t2) +
crossEffect^2*var(x4_t2)+
crossEffect^2*var(x5_t2)+
2*autoEffect*crossEffect*cov(x3_t2,x4_t2)+
2*autoEffect*crossEffect*cov(x3_t2,x5_t2)+
2*crossEffect*crossEffect*cov(x4_t2,x5_t2))))
x4_t3 <- autoEffect*x4_t2 + crossEffect*x5_t2 + crossEffect*x1_t2 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x4_t2) +
crossEffect^2*var(x5_t2)+
crossEffect^2*var(x1_t2)+
2*autoEffect*crossEffect*cov(x4_t2,x5_t2)+
2*autoEffect*crossEffect*cov(x4_t2,x1_t2)+
2*crossEffect*crossEffect*cov(x5_t2,x1_t2))))
x5_t3 <- autoEffect*x5_t2 + crossEffect*x1_t2 + crossEffect*x2_t2 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x5_t2) +
crossEffect^2*var(x1_t2)+
crossEffect^2*var(x2_t2)+
2*autoEffect*crossEffect*cov(x5_t2,x1_t2)+
2*autoEffect*crossEffect*cov(x5_t2,x2_t2)+
2*crossEffect*crossEffect*cov(x1_t2,x2_t2))))
#t4
x1_t4 <- autoEffect*x1_t3 + crossEffect*x2_t3 + crossEffect*x3_t3 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x1_t3) +
crossEffect^2*var(x2_t3)+
crossEffect^2*var(x3_t3)+
2*autoEffect*crossEffect*cov(x1_t3,x2_t3)+
2*autoEffect*crossEffect*cov(x1_t3,x3_t3)+
2*crossEffect*crossEffect*cov(x2_t3,x3_t3))))
x2_t4 <- autoEffect*x2_t3 + crossEffect*x3_t3 + crossEffect*x4_t3 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x2_t3) +
crossEffect^2*var(x3_t3)+
crossEffect^2*var(x4_t3)+
2*autoEffect*crossEffect*cov(x2_t3,x3_t3)+
2*autoEffect*crossEffect*cov(x2_t3,x4_t3)+
2*crossEffect*crossEffect*cov(x3_t3,x4_t3))))
x3_t4 <- autoEffect*x3_t3 + crossEffect*x4_t3 + crossEffect*x5_t3 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x3_t3) +
crossEffect^2*var(x4_t3)+
crossEffect^2*var(x5_t3)+
2*autoEffect*crossEffect*cov(x3_t3,x4_t3)+
2*autoEffect*crossEffect*cov(x3_t3,x5_t3)+
2*crossEffect*crossEffect*cov(x4_t3,x5_t3))))
x4_t4 <- autoEffect*x4_t3 + crossEffect*x5_t3 + crossEffect*x1_t3 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x4_t3) +
crossEffect^2*var(x5_t3)+
crossEffect^2*var(x1_t3)+
2*autoEffect*crossEffect*cov(x4_t3,x5_t3)+
2*autoEffect*crossEffect*cov(x4_t3,x1_t3)+
2*crossEffect*crossEffect*cov(x5_t3,x1_t3))))
x5_t4 <- autoEffect*x5_t3 + crossEffect*x1_t3 + crossEffect*x2_t3 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x5_t3) +
crossEffect^2*var(x1_t3)+
crossEffect^2*var(x2_t3)+
2*autoEffect*crossEffect*cov(x5_t3,x1_t3)+
2*autoEffect*crossEffect*cov(x5_t3,x2_t3)+
2*crossEffect*crossEffect*cov(x1_t3,x2_t3))))
#t5
x1_t5 <- autoEffect*x1_t4 + crossEffect*x2_t4 + crossEffect*x3_t4 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x1_t4) +
crossEffect^2*var(x2_t4)+
crossEffect^2*var(x3_t4)+
2*autoEffect*crossEffect*cov(x1_t4,x2_t4)+
2*autoEffect*crossEffect*cov(x1_t4,x3_t4)+
2*crossEffect*crossEffect*cov(x2_t4,x3_t4))))
x2_t5 <- autoEffect*x2_t4 + crossEffect*x3_t4 + crossEffect*x4_t4 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x2_t4) +
crossEffect^2*var(x3_t4)+
crossEffect^2*var(x4_t4)+
2*autoEffect*crossEffect*cov(x2_t4,x3_t4)+
2*autoEffect*crossEffect*cov(x2_t4,x4_t4)+
2*crossEffect*crossEffect*cov(x3_t4,x4_t4))))
x3_t5 <- autoEffect*x3_t4 + crossEffect*x4_t4 + crossEffect*x5_t4 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x3_t4) +
crossEffect^2*var(x4_t4)+
crossEffect^2*var(x5_t4)+
2*autoEffect*crossEffect*cov(x3_t4,x4_t4)+
2*autoEffect*crossEffect*cov(x3_t4,x5_t4)+
2*crossEffect*crossEffect*cov(x4_t4,x5_t4))))
x4_t5 <- autoEffect*x4_t4 + crossEffect*x5_t4 + crossEffect*x1_t4 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x4_t4) +
crossEffect^2*var(x5_t4)+
crossEffect^2*var(x1_t4)+
2*autoEffect*crossEffect*cov(x4_t4,x5_t4)+
2*autoEffect*crossEffect*cov(x4_t4,x1_t4)+
2*crossEffect*crossEffect*cov(x5_t4,x1_t4))))
x5_t5 <- autoEffect*x5_t4 + crossEffect*x1_t4 + crossEffect*x2_t4 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x5_t4) +
crossEffect^2*var(x1_t4)+
crossEffect^2*var(x2_t4)+
2*autoEffect*crossEffect*cov(x5_t4,x1_t4)+
2*autoEffect*crossEffect*cov(x5_t4,x2_t4)+
2*crossEffect*crossEffect*cov(x1_t4,x2_t4))))
#t6
x1_t6 <- autoEffect*x1_t5 + crossEffect*x2_t5 + crossEffect*x3_t5 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x1_t5) +
crossEffect^2*var(x2_t5)+
crossEffect^2*var(x3_t5)+
2*autoEffect*crossEffect*cov(x1_t5,x2_t5)+
2*autoEffect*crossEffect*cov(x1_t5,x3_t5)+
2*crossEffect*crossEffect*cov(x2_t5,x3_t5))))
x2_t6 <- autoEffect*x2_t5 + crossEffect*x3_t5 + crossEffect*x4_t5 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x2_t5) +
crossEffect^2*var(x3_t5)+
crossEffect^2*var(x4_t5)+
2*autoEffect*crossEffect*cov(x2_t5,x3_t5)+
2*autoEffect*crossEffect*cov(x2_t5,x4_t5)+
2*crossEffect*crossEffect*cov(x3_t5,x4_t5))))
x3_t6 <- autoEffect*x3_t5 + crossEffect*x4_t5 + crossEffect*x5_t5 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x3_t5) +
crossEffect^2*var(x4_t5)+
crossEffect^2*var(x5_t5)+
2*autoEffect*crossEffect*cov(x3_t5,x4_t5)+
2*autoEffect*crossEffect*cov(x3_t5,x5_t5)+
2*crossEffect*crossEffect*cov(x4_t5,x5_t5))))
x4_t6 <- autoEffect*x4_t5 + crossEffect*x5_t5 + crossEffect*x1_t5 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x4_t5) +
crossEffect^2*var(x5_t5)+
crossEffect^2*var(x1_t5)+
2*autoEffect*crossEffect*cov(x4_t5,x5_t5)+
2*autoEffect*crossEffect*cov(x4_t5,x1_t5)+
2*crossEffect*crossEffect*cov(x5_t5,x1_t5))))
x5_t6 <- autoEffect*x5_t5 + crossEffect*x1_t5 + crossEffect*x2_t5 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x5_t5) +
crossEffect^2*var(x1_t5)+
crossEffect^2*var(x2_t5)+
2*autoEffect*crossEffect*cov(x5_t5,x1_t5)+
2*autoEffect*crossEffect*cov(x5_t5,x2_t5)+
2*crossEffect*crossEffect*cov(x1_t5,x2_t5))))
#t7
x1_t7 <- autoEffect*x1_t6 + crossEffect*x2_t6 + crossEffect*x3_t6 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x1_t6) +
crossEffect^2*var(x2_t6)+
crossEffect^2*var(x3_t6)+
2*autoEffect*crossEffect*cov(x1_t6,x2_t6)+
2*autoEffect*crossEffect*cov(x1_t6,x3_t6)+
2*crossEffect*crossEffect*cov(x2_t6,x3_t6))))
x2_t7 <- autoEffect*x2_t6 + crossEffect*x3_t6 + crossEffect*x4_t6 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x2_t6) +
crossEffect^2*var(x3_t6)+
crossEffect^2*var(x4_t6)+
2*autoEffect*crossEffect*cov(x2_t6,x3_t6)+
2*autoEffect*crossEffect*cov(x2_t6,x4_t6)+
2*crossEffect*crossEffect*cov(x3_t6,x4_t6))))
x3_t7 <- autoEffect*x3_t6 + crossEffect*x4_t6 + crossEffect*x5_t6 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x3_t6) +
crossEffect^2*var(x4_t6)+
crossEffect^2*var(x5_t6)+
2*autoEffect*crossEffect*cov(x3_t6,x4_t6)+
2*autoEffect*crossEffect*cov(x3_t6,x5_t6)+
2*crossEffect*crossEffect*cov(x4_t6,x5_t6))))
x4_t7 <- autoEffect*x4_t6 + crossEffect*x5_t6 + crossEffect*x1_t6 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x4_t6) +
crossEffect^2*var(x5_t6)+
crossEffect^2*var(x1_t6)+
2*autoEffect*crossEffect*cov(x4_t6,x5_t6)+
2*autoEffect*crossEffect*cov(x4_t6,x1_t6)+
2*crossEffect*crossEffect*cov(x5_t6,x1_t6))))
x5_t7 <- autoEffect*x5_t6 + crossEffect*x1_t6 + crossEffect*x2_t6 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x5_t6) +
crossEffect^2*var(x1_t6)+
crossEffect^2*var(x2_t6)+
2*autoEffect*crossEffect*cov(x5_t6,x1_t6)+
2*autoEffect*crossEffect*cov(x5_t6,x2_t6)+
2*crossEffect*crossEffect*cov(x1_t6,x2_t6))))
#t8
x1_t8 <- autoEffect*x1_t7 + crossEffect*x2_t7 + crossEffect*x3_t7 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x1_t7) +
crossEffect^2*var(x2_t7)+
crossEffect^2*var(x3_t7)+
2*autoEffect*crossEffect*cov(x1_t7,x2_t7)+
2*autoEffect*crossEffect*cov(x1_t7,x3_t7)+
2*crossEffect*crossEffect*cov(x2_t7,x3_t7))))
x2_t8 <- autoEffect*x2_t7 + crossEffect*x3_t7 + crossEffect*x4_t7 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x2_t7) +
crossEffect^2*var(x3_t7)+
crossEffect^2*var(x4_t7)+
2*autoEffect*crossEffect*cov(x2_t7,x3_t7)+
2*autoEffect*crossEffect*cov(x2_t7,x4_t7)+
2*crossEffect*crossEffect*cov(x3_t7,x4_t7))))
x3_t8 <- autoEffect*x3_t7 + crossEffect*x4_t7 + crossEffect*x5_t7 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x3_t7) +
crossEffect^2*var(x4_t7)+
crossEffect^2*var(x5_t7)+
2*autoEffect*crossEffect*cov(x3_t7,x4_t7)+
2*autoEffect*crossEffect*cov(x3_t7,x5_t7)+
2*crossEffect*crossEffect*cov(x4_t7,x5_t7))))
x4_t8 <- autoEffect*x4_t7 + crossEffect*x5_t7 + crossEffect*x1_t7 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x4_t7) +
crossEffect^2*var(x5_t7)+
crossEffect^2*var(x1_t7)+
2*autoEffect*crossEffect*cov(x4_t7,x5_t7)+
2*autoEffect*crossEffect*cov(x4_t7,x1_t7)+
2*crossEffect*crossEffect*cov(x5_t7,x1_t7))))
x5_t8 <- autoEffect*x5_t7 + crossEffect*x1_t7 + crossEffect*x2_t7 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x5_t7) +
crossEffect^2*var(x1_t7)+
crossEffect^2*var(x2_t7)+
2*autoEffect*crossEffect*cov(x5_t7,x1_t7)+
2*autoEffect*crossEffect*cov(x5_t7,x2_t7)+
2*crossEffect*crossEffect*cov(x1_t7,x2_t7))))
#t9
x1_t9 <- autoEffect*x1_t8 + crossEffect*x2_t8 + crossEffect*x3_t8 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x1_t8) +
crossEffect^2*var(x2_t8)+
crossEffect^2*var(x3_t8)+
2*autoEffect*crossEffect*cov(x1_t8,x2_t8)+
2*autoEffect*crossEffect*cov(x1_t8,x3_t8)+
2*crossEffect*crossEffect*cov(x2_t8,x3_t8))))
x2_t9 <- autoEffect*x2_t8 + crossEffect*x3_t8 + crossEffect*x4_t8 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x2_t8) +
crossEffect^2*var(x3_t8)+
crossEffect^2*var(x4_t8)+
2*autoEffect*crossEffect*cov(x2_t8,x3_t8)+
2*autoEffect*crossEffect*cov(x2_t8,x4_t8)+
2*crossEffect*crossEffect*cov(x3_t8,x4_t8))))
x3_t9 <- autoEffect*x3_t8 + crossEffect*x4_t8 + crossEffect*x5_t8 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x3_t8) +
crossEffect^2*var(x4_t8)+
crossEffect^2*var(x5_t8)+
2*autoEffect*crossEffect*cov(x3_t8,x4_t8)+
2*autoEffect*crossEffect*cov(x3_t8,x5_t8)+
2*crossEffect*crossEffect*cov(x4_t8,x5_t8))))
x4_t9 <- autoEffect*x4_t8 + crossEffect*x5_t8 + crossEffect*x1_t8 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x4_t8) +
crossEffect^2*var(x5_t8)+
crossEffect^2*var(x1_t8)+
2*autoEffect*crossEffect*cov(x4_t8,x5_t8)+
2*autoEffect*crossEffect*cov(x4_t8,x1_t8)+
2*crossEffect*crossEffect*cov(x5_t8,x1_t8))))
x5_t9 <- autoEffect*x5_t8 + crossEffect*x1_t8 + crossEffect*x2_t8 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x5_t8) +
crossEffect^2*var(x1_t8)+
crossEffect^2*var(x2_t8)+
2*autoEffect*crossEffect*cov(x5_t8,x1_t8)+
2*autoEffect*crossEffect*cov(x5_t8,x2_t8)+
2*crossEffect*crossEffect*cov(x1_t8,x2_t8))))
#t10
x1_t10 <- autoEffect*x1_t9 + crossEffect*x2_t9 + crossEffect*x3_t9 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x1_t9) +
crossEffect^2*var(x2_t9)+
crossEffect^2*var(x3_t9)+
2*autoEffect*crossEffect*cov(x1_t9,x2_t9)+
2*autoEffect*crossEffect*cov(x1_t9,x3_t9)+
2*crossEffect*crossEffect*cov(x2_t9,x3_t9))))
x2_t10 <- autoEffect*x2_t9 + crossEffect*x3_t9 + crossEffect*x4_t9 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x2_t9) +
crossEffect^2*var(x3_t9)+
crossEffect^2*var(x4_t9)+
2*autoEffect*crossEffect*cov(x2_t9,x3_t9)+
2*autoEffect*crossEffect*cov(x2_t9,x4_t9)+
2*crossEffect*crossEffect*cov(x3_t9,x4_t9))))
x3_t10 <- autoEffect*x3_t9 + crossEffect*x4_t9 + crossEffect*x5_t9 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x3_t9) +
crossEffect^2*var(x4_t9)+
crossEffect^2*var(x5_t9)+
2*autoEffect*crossEffect*cov(x3_t9,x4_t9)+
2*autoEffect*crossEffect*cov(x3_t9,x5_t9)+
2*crossEffect*crossEffect*cov(x4_t9,x5_t9))))
x4_t10 <- autoEffect*x4_t9 + crossEffect*x5_t9 + crossEffect*x1_t9 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x4_t9) +
crossEffect^2*var(x5_t9)+
crossEffect^2*var(x1_t9)+
2*autoEffect*crossEffect*cov(x4_t9,x5_t9)+
2*autoEffect*crossEffect*cov(x4_t9,x1_t9)+
2*crossEffect*crossEffect*cov(x5_t9,x1_t9))))
x5_t10 <- autoEffect*x5_t9 + crossEffect*x1_t9 + crossEffect*x2_t9 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x5_t9) +
crossEffect^2*var(x1_t9)+
crossEffect^2*var(x2_t9)+
2*autoEffect*crossEffect*cov(x5_t9,x1_t9)+
2*autoEffect*crossEffect*cov(x5_t9,x2_t9)+
2*crossEffect*crossEffect*cov(x1_t9,x2_t9))))
SimulatedDataSet <- cbind(x1_t1, x2_t1, x3_t1, x4_t1, x5_t1,
x1_t2, x2_t2, x3_t2, x4_t2, x5_t2,
x1_t3, x2_t3, x3_t3, x4_t3, x5_t3,
x1_t4, x2_t4, x3_t4, x4_t4, x5_t4,
x1_t5, x2_t5, x3_t5, x4_t5, x5_t5,
x1_t6, x2_t6, x3_t6, x4_t6, x5_t6,
x1_t7, x2_t7, x3_t7, x4_t7, x5_t7,
x1_t8, x2_t8, x3_t8, x4_t8, x5_t8,
x1_t9, x2_t9, x3_t9, x4_t9, x5_t9,
x1_t10, x2_t10, x3_t10, x4_t10, x5_t10)
Avalues <- diag(.5,nrow=5,ncol = 5)
Avalues[1,2] <-crossEffect
Avalues[1,3] <-crossEffect
Avalues[2,3] <-crossEffect
Avalues[2,4] <-crossEffect
Avalues[3,4] <-crossEffect
Avalues[3,5] <-crossEffect
Avalues[4,5] <-crossEffect
Avalues[4,1] <-crossEffect
Avalues[5,1] <-crossEffect
Avalues[5,2] <-crossEffect
Afree <- matrix(TRUE, 5,5)
Alabel <- matrix(c("a11", "a12", "a13", "a14", "a15", "a21", "a22", "a23", "a24", "a25", "a31", "a32", "a33", "a34", "a35", "a41", "a42", "a43", "a44", "a45", "a51", "a52", "a53", "a54", "a55"), nrow = 5, byrow = T)
Svalues <- diag(1-.5^2,nrow=5,ncol = 5)
Svalues[1,1] <- 1-.5^2 -crossEffect^2-crossEffect^2
Svalues[2,2] <- 1-.5^2 -crossEffect^2-crossEffect^2
Svalues[3,3] <- 1-.5^2 -crossEffect^2-crossEffect^2
Svalues[4,4] <- 1-.5^2 -crossEffect^2-crossEffect^2
Svalues[5,5] <- 1-.5^2 -crossEffect^2-crossEffect^2
Sfree <- diag(TRUE, 5,5)
Slabel <- matrix(c("s11", NA, NA, NA, NA,
NA, "s22", NA, NA, NA,
NA, NA, "s33", NA, NA,
NA, NA, NA, "s44", NA,
NA, NA, NA, NA, "s55"), nrow = 5, byrow = T)
AnalysisModels <- createARCLModel(numLatent = 5, Timepoints = 5, burning = 5,
Avalues = Avalues, Afree = Afree, Alabel = Alabel,
Svalues = Svalues, Sfree = Sfree, Slabel = Slabel,
S_firstObsAllFree = T, SimulatedDataSet = SimulatedDataSet, sampleSize = sampleSize
)
ret = list("mxARCL_cov" = AnalysisModels$mxARCL_cov, "mxARCL_FIML" = AnalysisModels$mxARCL_FIML, "SimulatedDataSet" = SimulatedDataSet)
return(ret)
}
jhorzek/OrzekMasterThesis documentation built on Aug. 7, 2019, 8:20 a.m.
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Defines functions simARCL_scaled_50
Documented in simARCL_scaled_50
#' simARCL_scaled_50
#'
#'
#' simARCL_scaled_50 creates an ARCL(1)-SEM model with OpenMx with 5 latent variables and 1 manifest per latent and time point for data simulation. It returns the simulated data set and a covariance based and a raw data based model. 10 Timepoints are created of which the initial five are omitted (burned)
#' The model has 50% non-zero cross-lagged effects
#'
#'
#' @author Jannik Orzek
#' @import OpenMx
#'
#' @export
#'
#'
simARCL_scaled_50 <- function(sampleSize, autoEffect, crossEffect){
# t1
x1_t1 <-rnorm(n = sampleSize, mean = 0, sd = 1)
x2_t1 <-rnorm(n = sampleSize, mean = 0, sd = 1)
x3_t1 <-rnorm(n = sampleSize, mean = 0, sd = 1)
x4_t1 <-rnorm(n = sampleSize, mean = 0, sd = 1)
x5_t1 <-rnorm(n = sampleSize, mean = 0, sd = 1)
#t2
x1_t2 <- autoEffect*x1_t1 + crossEffect*x2_t1 + crossEffect*x3_t1 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x1_t1) +
crossEffect^2*var(x2_t1)+
crossEffect^2*var(x3_t1)+
2*autoEffect*crossEffect*cov(x1_t1,x2_t1)+
2*autoEffect*crossEffect*cov(x1_t1,x3_t1)+
2*crossEffect*crossEffect*cov(x2_t1,x3_t1))))
x2_t2 <- autoEffect*x2_t1 + crossEffect*x3_t1 + crossEffect*x4_t1 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x2_t1) +
crossEffect^2*var(x3_t1)+
crossEffect^2*var(x4_t1)+
2*autoEffect*crossEffect*cov(x2_t1,x3_t1)+
2*autoEffect*crossEffect*cov(x2_t1,x4_t1)+
2*crossEffect*crossEffect*cov(x3_t1,x4_t1))))
x3_t2 <- autoEffect*x3_t1 + crossEffect*x4_t1 + crossEffect*x5_t1 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x3_t1) +
crossEffect^2*var(x4_t1)+
crossEffect^2*var(x5_t1)+
2*autoEffect*crossEffect*cov(x3_t1,x4_t1)+
2*autoEffect*crossEffect*cov(x3_t1,x5_t1)+
2*crossEffect*crossEffect*cov(x4_t1,x5_t1))))
x4_t2 <- autoEffect*x4_t1 + crossEffect*x5_t1 + crossEffect*x1_t1 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x4_t1) +
crossEffect^2*var(x5_t1)+
crossEffect^2*var(x1_t1)+
2*autoEffect*crossEffect*cov(x4_t1,x5_t1)+
2*autoEffect*crossEffect*cov(x4_t1,x1_t1)+
2*crossEffect*crossEffect*cov(x5_t1,x1_t1))))
x5_t2 <- autoEffect*x5_t1 + crossEffect*x1_t1 + crossEffect*x2_t1 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x5_t1) +
crossEffect^2*var(x1_t1)+
crossEffect^2*var(x2_t1)+
2*autoEffect*crossEffect*cov(x5_t1,x1_t1)+
2*autoEffect*crossEffect*cov(x5_t1,x2_t1)+
2*crossEffect*crossEffect*cov(x1_t1,x2_t1))))
#t3
x1_t3 <- autoEffect*x1_t2 + crossEffect*x2_t2 + crossEffect*x3_t2 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x1_t2) +
crossEffect^2*var(x2_t2)+
crossEffect^2*var(x3_t2)+
2*autoEffect*crossEffect*cov(x1_t2,x2_t2)+
2*autoEffect*crossEffect*cov(x1_t2,x3_t2)+
2*crossEffect*crossEffect*cov(x2_t2,x3_t2))))
x2_t3 <- autoEffect*x2_t2 + crossEffect*x3_t2 + crossEffect*x4_t2 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x2_t2) +
crossEffect^2*var(x3_t2)+
crossEffect^2*var(x4_t2)+
2*autoEffect*crossEffect*cov(x2_t2,x3_t2)+
2*autoEffect*crossEffect*cov(x2_t2,x4_t2)+
2*crossEffect*crossEffect*cov(x3_t2,x4_t2))))
x3_t3 <- autoEffect*x3_t2 + crossEffect*x4_t2 + crossEffect*x5_t2 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x3_t2) +
crossEffect^2*var(x4_t2)+
crossEffect^2*var(x5_t2)+
2*autoEffect*crossEffect*cov(x3_t2,x4_t2)+
2*autoEffect*crossEffect*cov(x3_t2,x5_t2)+
2*crossEffect*crossEffect*cov(x4_t2,x5_t2))))
x4_t3 <- autoEffect*x4_t2 + crossEffect*x5_t2 + crossEffect*x1_t2 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x4_t2) +
crossEffect^2*var(x5_t2)+
crossEffect^2*var(x1_t2)+
2*autoEffect*crossEffect*cov(x4_t2,x5_t2)+
2*autoEffect*crossEffect*cov(x4_t2,x1_t2)+
2*crossEffect*crossEffect*cov(x5_t2,x1_t2))))
x5_t3 <- autoEffect*x5_t2 + crossEffect*x1_t2 + crossEffect*x2_t2 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x5_t2) +
crossEffect^2*var(x1_t2)+
crossEffect^2*var(x2_t2)+
2*autoEffect*crossEffect*cov(x5_t2,x1_t2)+
2*autoEffect*crossEffect*cov(x5_t2,x2_t2)+
2*crossEffect*crossEffect*cov(x1_t2,x2_t2))))
#t4
x1_t4 <- autoEffect*x1_t3 + crossEffect*x2_t3 + crossEffect*x3_t3 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x1_t3) +
crossEffect^2*var(x2_t3)+
crossEffect^2*var(x3_t3)+
2*autoEffect*crossEffect*cov(x1_t3,x2_t3)+
2*autoEffect*crossEffect*cov(x1_t3,x3_t3)+
2*crossEffect*crossEffect*cov(x2_t3,x3_t3))))
x2_t4 <- autoEffect*x2_t3 + crossEffect*x3_t3 + crossEffect*x4_t3 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x2_t3) +
crossEffect^2*var(x3_t3)+
crossEffect^2*var(x4_t3)+
2*autoEffect*crossEffect*cov(x2_t3,x3_t3)+
2*autoEffect*crossEffect*cov(x2_t3,x4_t3)+
2*crossEffect*crossEffect*cov(x3_t3,x4_t3))))
x3_t4 <- autoEffect*x3_t3 + crossEffect*x4_t3 + crossEffect*x5_t3 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x3_t3) +
crossEffect^2*var(x4_t3)+
crossEffect^2*var(x5_t3)+
2*autoEffect*crossEffect*cov(x3_t3,x4_t3)+
2*autoEffect*crossEffect*cov(x3_t3,x5_t3)+
2*crossEffect*crossEffect*cov(x4_t3,x5_t3))))
x4_t4 <- autoEffect*x4_t3 + crossEffect*x5_t3 + crossEffect*x1_t3 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x4_t3) +
crossEffect^2*var(x5_t3)+
crossEffect^2*var(x1_t3)+
2*autoEffect*crossEffect*cov(x4_t3,x5_t3)+
2*autoEffect*crossEffect*cov(x4_t3,x1_t3)+
2*crossEffect*crossEffect*cov(x5_t3,x1_t3))))
x5_t4 <- autoEffect*x5_t3 + crossEffect*x1_t3 + crossEffect*x2_t3 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x5_t3) +
crossEffect^2*var(x1_t3)+
crossEffect^2*var(x2_t3)+
2*autoEffect*crossEffect*cov(x5_t3,x1_t3)+
2*autoEffect*crossEffect*cov(x5_t3,x2_t3)+
2*crossEffect*crossEffect*cov(x1_t3,x2_t3))))
#t5
x1_t5 <- autoEffect*x1_t4 + crossEffect*x2_t4 + crossEffect*x3_t4 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x1_t4) +
crossEffect^2*var(x2_t4)+
crossEffect^2*var(x3_t4)+
2*autoEffect*crossEffect*cov(x1_t4,x2_t4)+
2*autoEffect*crossEffect*cov(x1_t4,x3_t4)+
2*crossEffect*crossEffect*cov(x2_t4,x3_t4))))
x2_t5 <- autoEffect*x2_t4 + crossEffect*x3_t4 + crossEffect*x4_t4 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x2_t4) +
crossEffect^2*var(x3_t4)+
crossEffect^2*var(x4_t4)+
2*autoEffect*crossEffect*cov(x2_t4,x3_t4)+
2*autoEffect*crossEffect*cov(x2_t4,x4_t4)+
2*crossEffect*crossEffect*cov(x3_t4,x4_t4))))
x3_t5 <- autoEffect*x3_t4 + crossEffect*x4_t4 + crossEffect*x5_t4 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x3_t4) +
crossEffect^2*var(x4_t4)+
crossEffect^2*var(x5_t4)+
2*autoEffect*crossEffect*cov(x3_t4,x4_t4)+
2*autoEffect*crossEffect*cov(x3_t4,x5_t4)+
2*crossEffect*crossEffect*cov(x4_t4,x5_t4))))
x4_t5 <- autoEffect*x4_t4 + crossEffect*x5_t4 + crossEffect*x1_t4 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x4_t4) +
crossEffect^2*var(x5_t4)+
crossEffect^2*var(x1_t4)+
2*autoEffect*crossEffect*cov(x4_t4,x5_t4)+
2*autoEffect*crossEffect*cov(x4_t4,x1_t4)+
2*crossEffect*crossEffect*cov(x5_t4,x1_t4))))
x5_t5 <- autoEffect*x5_t4 + crossEffect*x1_t4 + crossEffect*x2_t4 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x5_t4) +
crossEffect^2*var(x1_t4)+
crossEffect^2*var(x2_t4)+
2*autoEffect*crossEffect*cov(x5_t4,x1_t4)+
2*autoEffect*crossEffect*cov(x5_t4,x2_t4)+
2*crossEffect*crossEffect*cov(x1_t4,x2_t4))))
#t6
x1_t6 <- autoEffect*x1_t5 + crossEffect*x2_t5 + crossEffect*x3_t5 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x1_t5) +
crossEffect^2*var(x2_t5)+
crossEffect^2*var(x3_t5)+
2*autoEffect*crossEffect*cov(x1_t5,x2_t5)+
2*autoEffect*crossEffect*cov(x1_t5,x3_t5)+
2*crossEffect*crossEffect*cov(x2_t5,x3_t5))))
x2_t6 <- autoEffect*x2_t5 + crossEffect*x3_t5 + crossEffect*x4_t5 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x2_t5) +
crossEffect^2*var(x3_t5)+
crossEffect^2*var(x4_t5)+
2*autoEffect*crossEffect*cov(x2_t5,x3_t5)+
2*autoEffect*crossEffect*cov(x2_t5,x4_t5)+
2*crossEffect*crossEffect*cov(x3_t5,x4_t5))))
x3_t6 <- autoEffect*x3_t5 + crossEffect*x4_t5 + crossEffect*x5_t5 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x3_t5) +
crossEffect^2*var(x4_t5)+
crossEffect^2*var(x5_t5)+
2*autoEffect*crossEffect*cov(x3_t5,x4_t5)+
2*autoEffect*crossEffect*cov(x3_t5,x5_t5)+
2*crossEffect*crossEffect*cov(x4_t5,x5_t5))))
x4_t6 <- autoEffect*x4_t5 + crossEffect*x5_t5 + crossEffect*x1_t5 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x4_t5) +
crossEffect^2*var(x5_t5)+
crossEffect^2*var(x1_t5)+
2*autoEffect*crossEffect*cov(x4_t5,x5_t5)+
2*autoEffect*crossEffect*cov(x4_t5,x1_t5)+
2*crossEffect*crossEffect*cov(x5_t5,x1_t5))))
x5_t6 <- autoEffect*x5_t5 + crossEffect*x1_t5 + crossEffect*x2_t5 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x5_t5) +
crossEffect^2*var(x1_t5)+
crossEffect^2*var(x2_t5)+
2*autoEffect*crossEffect*cov(x5_t5,x1_t5)+
2*autoEffect*crossEffect*cov(x5_t5,x2_t5)+
2*crossEffect*crossEffect*cov(x1_t5,x2_t5))))
#t7
x1_t7 <- autoEffect*x1_t6 + crossEffect*x2_t6 + crossEffect*x3_t6 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x1_t6) +
crossEffect^2*var(x2_t6)+
crossEffect^2*var(x3_t6)+
2*autoEffect*crossEffect*cov(x1_t6,x2_t6)+
2*autoEffect*crossEffect*cov(x1_t6,x3_t6)+
2*crossEffect*crossEffect*cov(x2_t6,x3_t6))))
x2_t7 <- autoEffect*x2_t6 + crossEffect*x3_t6 + crossEffect*x4_t6 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x2_t6) +
crossEffect^2*var(x3_t6)+
crossEffect^2*var(x4_t6)+
2*autoEffect*crossEffect*cov(x2_t6,x3_t6)+
2*autoEffect*crossEffect*cov(x2_t6,x4_t6)+
2*crossEffect*crossEffect*cov(x3_t6,x4_t6))))
x3_t7 <- autoEffect*x3_t6 + crossEffect*x4_t6 + crossEffect*x5_t6 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x3_t6) +
crossEffect^2*var(x4_t6)+
crossEffect^2*var(x5_t6)+
2*autoEffect*crossEffect*cov(x3_t6,x4_t6)+
2*autoEffect*crossEffect*cov(x3_t6,x5_t6)+
2*crossEffect*crossEffect*cov(x4_t6,x5_t6))))
x4_t7 <- autoEffect*x4_t6 + crossEffect*x5_t6 + crossEffect*x1_t6 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x4_t6) +
crossEffect^2*var(x5_t6)+
crossEffect^2*var(x1_t6)+
2*autoEffect*crossEffect*cov(x4_t6,x5_t6)+
2*autoEffect*crossEffect*cov(x4_t6,x1_t6)+
2*crossEffect*crossEffect*cov(x5_t6,x1_t6))))
x5_t7 <- autoEffect*x5_t6 + crossEffect*x1_t6 + crossEffect*x2_t6 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x5_t6) +
crossEffect^2*var(x1_t6)+
crossEffect^2*var(x2_t6)+
2*autoEffect*crossEffect*cov(x5_t6,x1_t6)+
2*autoEffect*crossEffect*cov(x5_t6,x2_t6)+
2*crossEffect*crossEffect*cov(x1_t6,x2_t6))))
#t8
x1_t8 <- autoEffect*x1_t7 + crossEffect*x2_t7 + crossEffect*x3_t7 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x1_t7) +
crossEffect^2*var(x2_t7)+
crossEffect^2*var(x3_t7)+
2*autoEffect*crossEffect*cov(x1_t7,x2_t7)+
2*autoEffect*crossEffect*cov(x1_t7,x3_t7)+
2*crossEffect*crossEffect*cov(x2_t7,x3_t7))))
x2_t8 <- autoEffect*x2_t7 + crossEffect*x3_t7 + crossEffect*x4_t7 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x2_t7) +
crossEffect^2*var(x3_t7)+
crossEffect^2*var(x4_t7)+
2*autoEffect*crossEffect*cov(x2_t7,x3_t7)+
2*autoEffect*crossEffect*cov(x2_t7,x4_t7)+
2*crossEffect*crossEffect*cov(x3_t7,x4_t7))))
x3_t8 <- autoEffect*x3_t7 + crossEffect*x4_t7 + crossEffect*x5_t7 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x3_t7) +
crossEffect^2*var(x4_t7)+
crossEffect^2*var(x5_t7)+
2*autoEffect*crossEffect*cov(x3_t7,x4_t7)+
2*autoEffect*crossEffect*cov(x3_t7,x5_t7)+
2*crossEffect*crossEffect*cov(x4_t7,x5_t7))))
x4_t8 <- autoEffect*x4_t7 + crossEffect*x5_t7 + crossEffect*x1_t7 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x4_t7) +
crossEffect^2*var(x5_t7)+
crossEffect^2*var(x1_t7)+
2*autoEffect*crossEffect*cov(x4_t7,x5_t7)+
2*autoEffect*crossEffect*cov(x4_t7,x1_t7)+
2*crossEffect*crossEffect*cov(x5_t7,x1_t7))))
x5_t8 <- autoEffect*x5_t7 + crossEffect*x1_t7 + crossEffect*x2_t7 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x5_t7) +
crossEffect^2*var(x1_t7)+
crossEffect^2*var(x2_t7)+
2*autoEffect*crossEffect*cov(x5_t7,x1_t7)+
2*autoEffect*crossEffect*cov(x5_t7,x2_t7)+
2*crossEffect*crossEffect*cov(x1_t7,x2_t7))))
#t9
x1_t9 <- autoEffect*x1_t8 + crossEffect*x2_t8 + crossEffect*x3_t8 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x1_t8) +
crossEffect^2*var(x2_t8)+
crossEffect^2*var(x3_t8)+
2*autoEffect*crossEffect*cov(x1_t8,x2_t8)+
2*autoEffect*crossEffect*cov(x1_t8,x3_t8)+
2*crossEffect*crossEffect*cov(x2_t8,x3_t8))))
x2_t9 <- autoEffect*x2_t8 + crossEffect*x3_t8 + crossEffect*x4_t8 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x2_t8) +
crossEffect^2*var(x3_t8)+
crossEffect^2*var(x4_t8)+
2*autoEffect*crossEffect*cov(x2_t8,x3_t8)+
2*autoEffect*crossEffect*cov(x2_t8,x4_t8)+
2*crossEffect*crossEffect*cov(x3_t8,x4_t8))))
x3_t9 <- autoEffect*x3_t8 + crossEffect*x4_t8 + crossEffect*x5_t8 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x3_t8) +
crossEffect^2*var(x4_t8)+
crossEffect^2*var(x5_t8)+
2*autoEffect*crossEffect*cov(x3_t8,x4_t8)+
2*autoEffect*crossEffect*cov(x3_t8,x5_t8)+
2*crossEffect*crossEffect*cov(x4_t8,x5_t8))))
x4_t9 <- autoEffect*x4_t8 + crossEffect*x5_t8 + crossEffect*x1_t8 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x4_t8) +
crossEffect^2*var(x5_t8)+
crossEffect^2*var(x1_t8)+
2*autoEffect*crossEffect*cov(x4_t8,x5_t8)+
2*autoEffect*crossEffect*cov(x4_t8,x1_t8)+
2*crossEffect*crossEffect*cov(x5_t8,x1_t8))))
x5_t9 <- autoEffect*x5_t8 + crossEffect*x1_t8 + crossEffect*x2_t8 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x5_t8) +
crossEffect^2*var(x1_t8)+
crossEffect^2*var(x2_t8)+
2*autoEffect*crossEffect*cov(x5_t8,x1_t8)+
2*autoEffect*crossEffect*cov(x5_t8,x2_t8)+
2*crossEffect*crossEffect*cov(x1_t8,x2_t8))))
#t10
x1_t10 <- autoEffect*x1_t9 + crossEffect*x2_t9 + crossEffect*x3_t9 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x1_t9) +
crossEffect^2*var(x2_t9)+
crossEffect^2*var(x3_t9)+
2*autoEffect*crossEffect*cov(x1_t9,x2_t9)+
2*autoEffect*crossEffect*cov(x1_t9,x3_t9)+
2*crossEffect*crossEffect*cov(x2_t9,x3_t9))))
x2_t10 <- autoEffect*x2_t9 + crossEffect*x3_t9 + crossEffect*x4_t9 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x2_t9) +
crossEffect^2*var(x3_t9)+
crossEffect^2*var(x4_t9)+
2*autoEffect*crossEffect*cov(x2_t9,x3_t9)+
2*autoEffect*crossEffect*cov(x2_t9,x4_t9)+
2*crossEffect*crossEffect*cov(x3_t9,x4_t9))))
x3_t10 <- autoEffect*x3_t9 + crossEffect*x4_t9 + crossEffect*x5_t9 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x3_t9) +
crossEffect^2*var(x4_t9)+
crossEffect^2*var(x5_t9)+
2*autoEffect*crossEffect*cov(x3_t9,x4_t9)+
2*autoEffect*crossEffect*cov(x3_t9,x5_t9)+
2*crossEffect*crossEffect*cov(x4_t9,x5_t9))))
x4_t10 <- autoEffect*x4_t9 + crossEffect*x5_t9 + crossEffect*x1_t9 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x4_t9) +
crossEffect^2*var(x5_t9)+
crossEffect^2*var(x1_t9)+
2*autoEffect*crossEffect*cov(x4_t9,x5_t9)+
2*autoEffect*crossEffect*cov(x4_t9,x1_t9)+
2*crossEffect*crossEffect*cov(x5_t9,x1_t9))))
x5_t10 <- autoEffect*x5_t9 + crossEffect*x1_t9 + crossEffect*x2_t9 + rnorm(n = sampleSize, 0, sd = sqrt(1-(autoEffect^2*var(x5_t9) +
crossEffect^2*var(x1_t9)+
crossEffect^2*var(x2_t9)+
2*autoEffect*crossEffect*cov(x5_t9,x1_t9)+
2*autoEffect*crossEffect*cov(x5_t9,x2_t9)+
2*crossEffect*crossEffect*cov(x1_t9,x2_t9))))
SimulatedDataSet <- cbind(x1_t1, x2_t1, x3_t1, x4_t1, x5_t1,
x1_t2, x2_t2, x3_t2, x4_t2, x5_t2,
x1_t3, x2_t3, x3_t3, x4_t3, x5_t3,
x1_t4, x2_t4, x3_t4, x4_t4, x5_t4,
x1_t5, x2_t5, x3_t5, x4_t5, x5_t5,
x1_t6, x2_t6, x3_t6, x4_t6, x5_t6,
x1_t7, x2_t7, x3_t7, x4_t7, x5_t7,
x1_t8, x2_t8, x3_t8, x4_t8, x5_t8,
x1_t9, x2_t9, x3_t9, x4_t9, x5_t9,
x1_t10, x2_t10, x3_t10, x4_t10, x5_t10)
Avalues <- diag(.5,nrow=5,ncol = 5)
Avalues[1,2] <-crossEffect
Avalues[1,3] <-crossEffect
Avalues[2,3] <-crossEffect
Avalues[2,4] <-crossEffect
Avalues[3,4] <-crossEffect
Avalues[3,5] <-crossEffect
Avalues[4,5] <-crossEffect
Avalues[4,1] <-crossEffect
Avalues[5,1] <-crossEffect
Avalues[5,2] <-crossEffect
Afree <- matrix(TRUE, 5,5)
Alabel <- matrix(c("a11", "a12", "a13", "a14", "a15", "a21", "a22", "a23", "a24", "a25", "a31", "a32", "a33", "a34", "a35", "a41", "a42", "a43", "a44", "a45", "a51", "a52", "a53", "a54", "a55"), nrow = 5, byrow = T)
Svalues <- diag(1-.5^2,nrow=5,ncol = 5)
Svalues[1,1] <- 1-.5^2 -crossEffect^2-crossEffect^2
Svalues[2,2] <- 1-.5^2 -crossEffect^2-crossEffect^2
Svalues[3,3] <- 1-.5^2 -crossEffect^2-crossEffect^2
Svalues[4,4] <- 1-.5^2 -crossEffect^2-crossEffect^2
Svalues[5,5] <- 1-.5^2 -crossEffect^2-crossEffect^2
Sfree <- diag(TRUE, 5,5)
Slabel <- matrix(c("s11", NA, NA, NA, NA,
NA, "s22", NA, NA, NA,
NA, NA, "s33", NA, NA,
NA, NA, NA, "s44", NA,
NA, NA, NA, NA, "s55"), nrow = 5, byrow = T)
AnalysisModels <- createARCLModel(numLatent = 5, Timepoints = 5, burning = 5,
Avalues = Avalues, Afree = Afree, Alabel = Alabel,
Svalues = Svalues, Sfree = Sfree, Slabel = Slabel,
S_firstObsAllFree = T, SimulatedDataSet = SimulatedDataSet, sampleSize = sampleSize
)
ret = list("mxARCL_cov" = AnalysisModels$mxARCL_cov, "mxARCL_FIML" = AnalysisModels$mxARCL_FIML, "SimulatedDataSet" = SimulatedDataSet)
return(ret)
}
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