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# ---------------------------------------------------------------------
# Program: LDE_2ndOrder_OneIndicator_5D.R
# Author: Steven Boker and Pascal Deboeck
# Date: Sat Sep 5 12:23:32 EDT 2009
#
# This program runs an example single indicator 2nd order LDE model
# with 5 time-delay columns in the embedded state space matrix
#
#
# ---------------------------------------------------------------------
# Revision History
# -- Sat Sep 5 12:23:32 EDT 2009
# Created untitled.
#
# ---------------------------------------------------------------------
# ---------------------------------------------------------------------
# Variables
# ---------------------------------------------------------------------
#
# ---------------------------------------------------------------------
# ----------------------------------
# Read libraries and set options.
require(OpenMx)
# ----------------------------------
# Read demo data.
data(Oscillator)
plot(Oscillator[,1], type='l')
# ----------------------------------
# Set constants.
tau <- 1 # The lag between subsequent columns in the embedded matrix
deltaT <- .3 # The amount of time elapsed between subsequent observations
embedD <- 7 # The number of columns in the time-delay embedded matrix
# ----------------------------------
# Time delay embed the demo data.
Embed <- function(x, E, tau) { # create a time delay matrix from x with embedding dimension E and lag tau
len <- length(x)
out <- x[1:(len-(E*tau)+tau)]
for(i in 2:E) { out <- cbind(out,x[(1+((i-1)*tau)):(len-(E*tau)+(i*tau))]) }
return(out)
}
embeddedOscillator <- Embed(Oscillator$x, embedD, tau)
dimnames(embeddedOscillator) <- list(NULL, paste("x", 1:embedD, sep=""))
# ----------------------------------
# Create the fixed LDE loading matrix.
L1 <- rep(1,embedD)
L2 <- c(1:embedD)*tau*deltaT-mean(c(1:embedD)*tau*deltaT)
L3 <- (L2^2)/2
LDE.Original <- cbind(L1,L2,L3)
# ----------------------------------
# Create 2nd order LDE model.
manifestVars <- dimnames(embeddedOscillator)[[2]]
latentVars <- paste0('d', 0:(ncol(LDE.Original)-1), 'y')
ldeModel1 <- mxModel("LDE_Model_1",
mxMatrix("Full",
values=LDE.Original,
free=FALSE,
name="L",
byrow=TRUE,
dimnames=list(manifestVars, latentVars)
),
mxMatrix("Full", 3, 3,
values=c( 0, 0, 0,
0, 0, 0,
-.2,-.2, 0),
free=c(FALSE,FALSE,FALSE,
FALSE,FALSE,FALSE,
TRUE, TRUE,FALSE),
lbound=-2,
ubound=2,
name="A",
byrow=TRUE,
dimnames=list(latentVars, latentVars)
),
mxMatrix("Symm", 3, 3,
values=c(.8, -.1, 0,
-.1,.8, 0,
0, 0,.8),
free=c( TRUE, TRUE, FALSE,
TRUE, TRUE,FALSE,
FALSE,FALSE, TRUE),
name="S",
byrow=TRUE,
lbound=c(0.000001, -10000, 0.000001,
-10000, 0.000001, 0.000001,
0.000001, 0.000001, 0.000001),
dimnames=list(latentVars, latentVars)
),
mxMatrix("Diag", embedD, embedD,
values=.2,
free=TRUE,
name="U",
lbound=0.000001,
dimnames=list(manifestVars, manifestVars)
),
#mxExpectationNormal(cov="R"),
mxExpectationLISREL(LY='L', BE='A', PS='S', TE='U'),
mxFitFunctionML(),
mxData(cov(embeddedOscillator),
type="cov",
numObs=dim(embeddedOscillator)[1]
)
)
# ----------------------------------
# Fit the LDE model and examine the summary results.
ldeModel1Fit <- mxRun(ldeModel1)
summary(ldeModel1Fit)
# ----------------------------------
# Specify the same model, but add means
# and use raw data
ldeModel2 <- mxModel(ldeModel1,
mxMatrix('Full', name='M', nrow=nrow(LDE.Original), ncol=1, dimnames=list(manifestVars, 'one'), free=TRUE),
mxMatrix('Full', name='N', nrow=ncol(LDE.Original), ncol=1, dimnames=list(latentVars, 'one')),
mxExpectationLISREL(LY='L', BE='A', PS='S', TE='U', TY='M', AL='N'),
mxData(embeddedOscillator, 'raw')
)
# ----------------------------------
# Fit the raw data model with means
ldeModel2Fit <- mxRun(ldeModel2)
summary(ldeModel2Fit)
# ----------------------------------
# Check that parameter estimates are good
a <- c(-0.292118167, -0.108630533, 0.142931593, -0.012848260, 0.044742836,
0.011126886, 0.007458037, 0.008658088, 0.008505263, 0.008332743,
0.008255869, 0.008158013, 0.007594966)
b <- c(-0.292118480, -0.108629216, 0.142931822, -0.012848367, 0.044742889,
0.011126912, 0.007458019, 0.008658099, 0.008505253, 0.008332736,
0.008255873, 0.008158008, 0.007594939, 0.023681632, 0.011287883,
-0.002021944, -0.012821669, -0.026326066, -0.035579923, -0.040730626)
omxCheckCloseEnough(coef(ldeModel1Fit), a, 0.001)
omxCheckCloseEnough(coef(ldeModel2Fit), b, 0.001)
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