#
#   Copyright 2007-2014 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: OneFactorModel_MatrixCov.R  
# Author: Ryne Estabrook
# Date: 2009.08.01 
#
# ModelType: Factor
# DataType: Continuous
# Field: None
#
# Purpose: 
#      One 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
# -----------------------------------------------------------------------------

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

myFADataCov<-matrix(
	c(0.997, 0.642, 0.611, 0.672, 0.637, 0.677,
	  0.642, 1.025, 0.608, 0.668, 0.643, 0.676,
	  0.611, 0.608, 0.984, 0.633, 0.657, 0.626,
	  0.672, 0.668, 0.633, 1.003, 0.676, 0.665,
	  0.637, 0.643, 0.657, 0.676, 1.028, 0.654,
	  0.677, 0.676, 0.626, 0.665, 0.654, 1.020),
	nrow=6,
	dimnames=list(
		c("x1","x2","x3","x4","x5","x6"),
		c("x1","x2","x3","x4","x5","x6"))
)

myFADataMeans <- c(2.988, 3.011, 2.986, 3.053, 3.016, 3.010)
names(myFADataMeans) <- c("x1","x2","x3","x4","x5","x6")
# Prepare Data
# -----------------------------------------------------------------------------

oneFactorModel <- mxModel("Common Factor Model Matrix Specification", 
	mxData(
		observed=myFADataCov, 
		type="cov", 
		numObs=500,
		mean=myFADataMeans
	),
	mxMatrix(
		type="Full", 
		nrow=7, 
		ncol=7,
		values=c(0,0,0,0,0,0,1,
		         0,0,0,0,0,0,1,
		         0,0,0,0,0,0,1,
		         0,0,0,0,0,0,1,
		         0,0,0,0,0,0,1,
		         0,0,0,0,0,0,1,
		         0,0,0,0,0,0,0),
		free=c(F, F, F, F, F, F, F,
		       F, F, F, F, F, F, T,
		       F, F, F, F, F, F, T,
		       F, F, F, F, F, F, T,
		       F, F, F, F, F, F, T,
		       F, F, F, F, F, F, T,
		       F, F, F, F, F, F, F),
		labels=c(NA,NA,NA,NA,NA,NA,"l1",
		         NA,NA,NA,NA,NA,NA,"l2",
		         NA,NA,NA,NA,NA,NA,"l3",
		         NA,NA,NA,NA,NA,NA,"l4",
		         NA,NA,NA,NA,NA,NA,"l5",
		         NA,NA,NA,NA,NA,NA,"l6",
		         NA,NA,NA,NA,NA,NA,NA),
		byrow=TRUE,
		name="A"
	),
	mxMatrix(
		type="Symm", 
		nrow=7, 
		ncol=7, 
		values=c(1,0,0,0,0,0,0,
		         0,1,0,0,0,0,0,
		         0,0,1,0,0,0,0,
		         0,0,0,1,0,0,0,
		         0,0,0,0,1,0,0,
		         0,0,0,0,0,1,0,
		         0,0,0,0,0,0,1),
		free=c(T, F, F, F, F, F, F,
		       F, T, F, F, F, F, F,
		       F, F, T, F, F, F, F,
		       F, F, F, T, F, F, F,
		       F, F, F, F, T, F, F,
		       F, F, F, F, F, T, F,
		       F, F, F, F, F, F, T),
		labels=c("e1", NA,   NA,   NA,   NA,   NA,   NA,
		         NA, "e2",   NA,   NA,   NA,   NA,   NA,
		         NA,   NA, "e3",   NA,   NA,   NA,   NA,
		         NA,   NA,   NA, "e4",   NA,   NA,   NA,
		         NA,   NA,   NA,   NA, "e5",   NA,   NA,
		         NA,   NA,   NA,   NA,   NA, "e6",   NA,
		         NA,   NA,   NA,   NA,   NA,   NA, "varF1"),
		byrow=TRUE,
		name="S"
	),
	mxMatrix(
		type="Full", 
		nrow=6, 
		ncol=7,
		free=FALSE,
		values=c(1,0,0,0,0,0,0,
		         0,1,0,0,0,0,0,
		         0,0,1,0,0,0,0,
		         0,0,0,1,0,0,0,
		         0,0,0,0,1,0,0,
		         0,0,0,0,0,1,0),
		byrow=TRUE,
		name="F"
	),
	mxMatrix(
		type="Full", 
		nrow=1, 
		ncol=7,
		values=c(1,1,1,1,1,1,0),
		free=c(T,T,T,T,T,T,F),
		labels=c("meanx1","meanx2","meanx3",
		         "meanx4","meanx5","meanx6",
		         NA),
		name="M"
	),
	mxFitFunctionML(),mxExpectationRAM("A","S","F","M",dimnames=c("x1","x2","x3","x4","x5","x6","F1"))
)
# Create an MxModel object
# -----------------------------------------------------------------------------
     
oneFactorFit <- mxRun(oneFactorModel)

summary(oneFactorFit)
oneFactorFit$output$estimate

omxCheckCloseEnough(oneFactorFit$output$estimate[["l2"]], 0.999, 0.01)
omxCheckCloseEnough(oneFactorFit$output$estimate[["l3"]], 0.959, 0.01)
omxCheckCloseEnough(oneFactorFit$output$estimate[["l4"]], 1.028, 0.01)
omxCheckCloseEnough(oneFactorFit$output$estimate[["l5"]], 1.008, 0.01)
omxCheckCloseEnough(oneFactorFit$output$estimate[["l6"]], 1.021, 0.01)
omxCheckCloseEnough(oneFactorFit$output$estimate[["varF1"]], 0.645, 0.01)
omxCheckCloseEnough(oneFactorFit$output$estimate[["e1"]], 0.350, 0.01)
omxCheckCloseEnough(oneFactorFit$output$estimate[["e2"]], 0.379, 0.01)
omxCheckCloseEnough(oneFactorFit$output$estimate[["e3"]], 0.389, 0.01)
omxCheckCloseEnough(oneFactorFit$output$estimate[["e4"]], 0.320, 0.01)
omxCheckCloseEnough(oneFactorFit$output$estimate[["e5"]], 0.370, 0.01)
omxCheckCloseEnough(oneFactorFit$output$estimate[["e6"]], 0.346, 0.01)
omxCheckCloseEnough(oneFactorFit$output$estimate[["meanx1"]], 2.988, 0.01)
omxCheckCloseEnough(oneFactorFit$output$estimate[["meanx2"]], 3.011, 0.01)
omxCheckCloseEnough(oneFactorFit$output$estimate[["meanx3"]], 2.986, 0.01)
omxCheckCloseEnough(oneFactorFit$output$estimate[["meanx4"]], 3.053, 0.01)
omxCheckCloseEnough(oneFactorFit$output$estimate[["meanx5"]], 3.016, 0.01)
omxCheckCloseEnough(oneFactorFit$output$estimate[["meanx6"]], 3.010, 0.01)
# Compare OpenMx results to Mx results 
# -----------------------------------------------------------------------------