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#   Copyright 2007-2016 The OpenMx Project
#
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#        http://www.apache.org/licenses/LICENSE-2.0
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# -----------------------------------------------------------------------
# Program: TwoFactorModel_PathCov.R  
# Author: Ryne Estabrook
# Date: 2009.08.01 
#
# ModelType: Factor
# DataType: Continuous
# Field: None
#
# Purpose: 
# 	   Two Factor model to estimate factor loadings, residual variances and means
# 	   Path style model input - Covariance matrix data input
#
# RevisionHistory:
# 	   Hermine Maes -- 2009.10.08 updated & reformatted
# 	   Ross Gore -- 2011.06.06	added Model, Data & Field metadata
#      Hermine Maes -- 2014.11.02 piecewise specification
# -----------------------------------------------------------------------------

require(OpenMx)
# Load Library
# -----------------------------------------------------------------------------

myFADataCov <- matrix(
      c(0.997, 0.642, 0.611, 0.672, 0.637, 0.677, 0.342, 0.299, 0.337,
        0.642, 1.025, 0.608, 0.668, 0.643, 0.676, 0.273, 0.282, 0.287,
        0.611, 0.608, 0.984, 0.633, 0.657, 0.626, 0.286, 0.287, 0.264,
        0.672, 0.668, 0.633, 1.003, 0.676, 0.665, 0.330, 0.290, 0.274,
        0.637, 0.643, 0.657, 0.676, 1.028, 0.654, 0.328, 0.317, 0.331,
        0.677, 0.676, 0.626, 0.665, 0.654, 1.020, 0.323, 0.341, 0.349,
        0.342, 0.273, 0.286, 0.330, 0.328, 0.323, 0.993, 0.472, 0.467,
        0.299, 0.282, 0.287, 0.290, 0.317, 0.341, 0.472, 0.978, 0.507,
        0.337, 0.287, 0.264, 0.274, 0.331, 0.349, 0.467, 0.507, 1.059),
      nrow=9,
      dimnames=list(
          c("x1", "x2", "x3", "x4", "x5", "x6", "y1", "y2", "y3"),
          c("x1", "x2", "x3", "x4", "x5", "x6", "y1", "y2", "y3")),
)

twoFactorCov <- myFADataCov[c("x1","x2","x3","y1","y2","y3"),c("x1","x2","x3","y1","y2","y3")]
  
myFADataMeans <- c(2.988, 3.011, 2.986, 3.053, 3.016, 3.010, 2.955, 2.956, 2.967)
names(myFADataMeans) <- c("x1", "x2", "x3", "x4", "x5", "x6", "y1", "y2", "y3")
  
twoFactorMeans <- myFADataMeans[c(1:3,7:9)]
# Prepare Data
# -----------------------------------------------------------------------------

dataCov      <- mxData( observed=twoFactorCov, type="cov", numObs=500, means=twoFactorMeans )
# residual variances
resVars      <- mxPath( from=c("x1", "x2", "x3", "y1", "y2", "y3"), arrows=2,
                        free=TRUE, values=c(1,1,1,1,1,1),
                        labels=c("e1","e2","e3","e4","e5","e6") ) 
# latent variances and covariance
latVars      <- mxPath( from=c("F1","F2"), arrows=2, connect="unique.pairs",
                        free=TRUE, values=c(1,.5,1), labels=c("varF1","cov","varF2") )
# factor loadings for x variables	
facLoadsX    <- mxPath( from="F1", to=c("x1","x2","x3"), arrows=1,
                        free=c(F,T,T), values=c(1,1,1), labels=c("l1","l2","l3") )
# factor loadings for y variables
facLoadsY    <- mxPath( from="F2", to=c("y1","y2","y3"), arrows=1,
                        free=c(F,T,T), values=c(1,1,1), labels=c("l4","l5","l6") )
# means
means        <- mxPath( from="one", to=c("x1","x2","x3","y1","y2","y3","F1","F2"), 
                        arrows=1,
                        free=c(T,T,T,T,T,T,F,F), values=c(1,1,1,1,1,1,0,0),
                        labels=c("meanx1","meanx2","meanx3",
                                 "meany1","meany2","meany3",NA,NA) ) 

twoFactorModel <- mxModel("Two Factor Model Path Specification", type="RAM",
                        manifestVars=c("x1", "x2", "x3", "y1", "y2", "y3"), 
                        latentVars=c("F1","F2"),
                        dataCov, resVars, latVars, facLoadsX, facLoadsY, means)
# Create an MxModel object
# -----------------------------------------------------------------------------
      
twoFactorFit <- mxRun(twoFactorModel)

summary(twoFactorFit)
twoFactorFit$output$estimate

omxCheckCloseEnough(twoFactorFit$output$estimate[["l2"]], 0.9720, 0.01)
omxCheckCloseEnough(twoFactorFit$output$estimate[["l3"]], 0.9310, 0.01)
omxCheckCloseEnough(twoFactorFit$output$estimate[["l5"]], 1.0498, 0.01)
omxCheckCloseEnough(twoFactorFit$output$estimate[["l6"]], 1.0533, 0.01)
omxCheckCloseEnough(twoFactorFit$output$estimate[["varF1"]], 0.6622, 0.01)
omxCheckCloseEnough(twoFactorFit$output$estimate[["varF2"]], 0.4510, 0.01)
omxCheckCloseEnough(twoFactorFit$output$estimate[["cov"]], 0.2958, 0.01)
omxCheckCloseEnough(twoFactorFit$output$estimate[["e1"]], 0.3348, 0.01)
omxCheckCloseEnough(twoFactorFit$output$estimate[["e2"]], 0.3994, 0.01)
omxCheckCloseEnough(twoFactorFit$output$estimate[["e3"]], 0.4101, 0.01)
omxCheckCloseEnough(twoFactorFit$output$estimate[["e4"]], 0.5420, 0.01)
omxCheckCloseEnough(twoFactorFit$output$estimate[["e5"]], 0.4809, 0.01)
omxCheckCloseEnough(twoFactorFit$output$estimate[["e6"]], 0.5586, 0.01)
omxCheckCloseEnough(twoFactorFit$output$estimate[["meanx1"]], 2.988, 0.01)
omxCheckCloseEnough(twoFactorFit$output$estimate[["meanx2"]], 3.011, 0.01)
omxCheckCloseEnough(twoFactorFit$output$estimate[["meanx3"]], 2.986, 0.01)
omxCheckCloseEnough(twoFactorFit$output$estimate[["meany1"]], 2.955, 0.01)
omxCheckCloseEnough(twoFactorFit$output$estimate[["meany2"]], 2.956, 0.01)
omxCheckCloseEnough(twoFactorFit$output$estimate[["meany3"]], 2.967, 0.01)
# Compare OpenMx results to Mx results 
# -----------------------------------------------------------------------------