#
#   Copyright 2007-2017 The OpenMx Project
#
#   Licensed under the Apache License, Version 2.0 (the "License");
#   you may not use this file except in compliance with the License.
#   You may obtain a copy of the License at
# 
#        http://www.apache.org/licenses/LICENSE-2.0
# 
#   Unless required by applicable law or agreed to in writing, software
#   distributed under the License is distributed on an "AS IS" BASIS,
#   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
#   See the License for the specific language governing permissions and
#   limitations under the License.


# -----------------------------------------------------------------------------
# Program: TwoFactorModel_MatrixCov.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
#      Matrix 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 -- 2014.11.04 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,
                        mean=twoFactorMeans )
dataRaw      <- mxData( observed=myFADataRaw, type="raw" )
matrA        <- mxMatrix( type="Full", nrow=8, ncol=8,
                          free=  c(F,F,F,F,F,F,F,F,
                                   F,F,F,F,F,F,T,F,
                                   F,F,F,F,F,F,T,F,
                                   F,F,F,F,F,F,F,F,
                                   F,F,F,F,F,F,F,T,
                                   F,F,F,F,F,F,F,T,
                                   F,F,F,F,F,F,F,F,
                                   F,F,F,F,F,F,F,F),
                          values=c(0,0,0,0,0,0,1,0,
                                   0,0,0,0,0,0,1,0,
                                   0,0,0,0,0,0,1,0,
                                   0,0,0,0,0,0,0,1,
                                   0,0,0,0,0,0,0,1,
                                   0,0,0,0,0,0,0,1,
                                   0,0,0,0,0,0,0,0,
                                   0,0,0,0,0,0,0,0),
                          labels=c(NA,NA,NA,NA,NA,NA,"l1",NA,
                                   NA,NA,NA,NA,NA,NA,"l2",NA,
                                   NA,NA,NA,NA,NA,NA,"l3",NA,
                                   NA,NA,NA,NA,NA,NA,NA,"l4",
                                   NA,NA,NA,NA,NA,NA,NA,"l5",
                                   NA,NA,NA,NA,NA,NA,NA,"l6",
                                   NA,NA,NA,NA,NA,NA,NA,NA,
                                   NA,NA,NA,NA,NA,NA,NA,NA),
                          byrow=TRUE, name="A" )
matrS        <- mxMatrix( type="Symm", nrow=8, ncol=8, 
                          free=  c(T,F,F,F,F,F,F,F,
                                   F,T,F,F,F,F,F,F,
                                   F,F,T,F,F,F,F,F,
                                   F,F,F,T,F,F,F,F,
                                   F,F,F,F,T,F,F,F,
                                   F,F,F,F,F,T,F,F,
                                   F,F,F,F,F,F,T,T,
                                   F,F,F,F,F,F,T,T),
                          values=c(1,0,0,0,0,0,0,0,
                                   0,1,0,0,0,0,0,0,
                                   0,0,1,0,0,0,0,0,
                                   0,0,0,1,0,0,0,0,
                                   0,0,0,0,1,0,0,0,
                                   0,0,0,0,0,1,0,0,
                                   0,0,0,0,0,0,1,.5,
                                   0,0,0,0,0,0,.5,1),
                          labels=c("e1",NA,  NA,  NA,  NA,  NA,  NA,  NA,
                                   NA, "e2", NA,  NA,  NA,  NA,  NA,  NA,
                                   NA,  NA, "e3", NA,  NA,  NA,  NA,  NA,
                                   NA,  NA,  NA, "e4", NA,  NA,  NA,  NA,
                                   NA,  NA,  NA,  NA, "e5", NA,  NA,  NA,
                                   NA,  NA,  NA,  NA,  NA, "e6", NA,  NA,
                                   NA,  NA,  NA,  NA,  NA,  NA,"varF1","cov",
                                   NA,  NA,  NA,  NA,  NA,  NA,"cov","varF2"),
                          byrow=TRUE, name="S" )
matrF        <- mxMatrix( type="Full", nrow=6, ncol=8,
                          free=FALSE,
                          values=c(1,0,0,0,0,0,0,0,
                                   0,1,0,0,0,0,0,0,
                                   0,0,1,0,0,0,0,0,
                                   0,0,0,1,0,0,0,0,
                                   0,0,0,0,1,0,0,0,
                                   0,0,0,0,0,1,0,0),
                          byrow=TRUE, name="F" )
matrM        <- mxMatrix( type="Full", nrow=1, ncol=8,
                          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",
                                   "meanx4","meanx5","meanx6",NA,NA),
                          name="M" )
exp          <- mxExpectationRAM("A","S","F","M", 
                                 dimnames=c("x1","x2","x3","y1","y2","y3","F1","F2"))
funML        <- mxFitFunctionML()
twoFactorModel <- mxModel("Two Factor Model Matrix Specification", 
                          dataCov, matrA, matrS, matrF, matrM, exp, funML)
# Create an MxModel object
# -----------------------------------------------------------------------------
      
twoFactorFit <- mxRun(twoFactorModel)

summary(twoFactorFit)
coef(twoFactorFit)

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[["meanx4"]], 2.955, 0.01)
omxCheckCloseEnough(twoFactorFit$output$estimate[["meanx5"]], 2.956, 0.01)
omxCheckCloseEnough(twoFactorFit$output$estimate[["meanx6"]], 2.967, 0.01)
# Compare OpenMx results to Mx results 
# -----------------------------------------------------------------------------
