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#   Copyright 2007-2018 by the individuals mentioned in the source code history
#
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# -----------------------------------------------------------------------
# Program: UnivariateTwinAnalysis_MatrixRaw.R  
#  Author: Hermine Maes
#    Date: 08 01 2009 
#
# Univariate Twin Analysis model to estimate causes of variation (ACE)
# Matrix style model input - Raw data input
#
# Revision History
#   Hermine Maes -- 10 08 2009 updated & reformatted
# -----------------------------------------------------------------------

require(OpenMx)

#Prepare Data
# -----------------------------------------------------------------------
data(twinData)
summary(twinData)
selVars <- c('bmi1','bmi2')
mzfData <- as.matrix(subset(twinData, zyg==1, c(bmi1,bmi2)))
dzfData <- as.matrix(subset(twinData, zyg==3, c(bmi1,bmi2)))
colMeans(mzfData,na.rm=TRUE)
colMeans(dzfData,na.rm=TRUE)
cov(mzfData,use="complete")
cov(dzfData,use="complete")

#Fit ACE Model with RawData and Matrices Input
# -----------------------------------------------------------------------
twinACEModel <- mxModel("twinACE",
	# Matrices X, Y, and Z to store a, c, and e path coefficients
	mxMatrix(
		type="Full", 
		nrow=1, 
		ncol=1, 
		free=TRUE,  
		values=.6,  
		label="a", 
		name="X"
	), 
	mxMatrix(
		type="Full", 
		nrow=1, 
		ncol=1, 
		free=TRUE,  
		values=.6,  
		label="c", 
		name="Y"
	),
	mxMatrix(
		type="Full", 
		nrow=1, 
		ncol=1, 
		free=TRUE,  
		values=.6,  
		label="e", 
		name="Z"
	),
	# Matrices A, C, and E compute variance components
	mxAlgebra(
		expression=X %*% t(X), 
		name="A"
	), 
	mxAlgebra(
		expression=Y %*% t(Y), 
		name="C"
	), 
	mxAlgebra(
		expression=Z %*% t(Z), 
		name="E"
	),
	mxMatrix(
		type="Full", 
		nrow=1, 
		ncol=2, 
		free=TRUE, 
		values= 20,
		label="mean", 
		name="expMean"
	),
    # Algebra for expected variance/covariance matrix in MZ
    mxAlgebra(
		expression= rbind  (cbind(A+C+E , A+C),
							cbind(A+C   , A+C+E)), 
		name="expCovMZ"
	),
    # Algebra for expected variance/covariance matrix in DZ
    # note use of 0.5, converted to 1*1 matrix
    mxAlgebra(
		expression= rbind  (cbind(A+C+E     , 0.5%x%A+C),
							cbind(0.5%x%A+C , A+C+E)), 
		name="expCovDZ"
	),
	mxModel("MZ",
	    mxData(
			observed=mzfData, 
			type="raw"
		), 
		mxExpectationNormal(
			covariance="twinACE.expCovMZ", 
			means="twinACE.expMean", 
			dimnames=selVars
		),
		mxFitFunctionML(vector=TRUE)
	),
	mxModel("DZ",
	    mxData(
			observed=dzfData, 
			type="raw"
		), 
		mxFitFunctionML(),mxExpectationNormal(
			covariance="twinACE.expCovDZ", 
			means="twinACE.expMean", 
			dimnames=selVars
		),
		mxFitFunctionML(vector=TRUE)
	),
    mxAlgebra(
		expression=-2.0 *sum(log(MZ.objective), log(DZ.objective)), 
		name="twin"
	), 
	mxFitFunctionAlgebra("twin")
)

#Run ACE model
# -----------------------------------------------------------------------
twinACEFit <- mxRun(twinACEModel)

MZc <- mxEval(expCovMZ, twinACEFit)  			# expected covariance matrix for MZ's
DZc <- mxEval(expCovDZ, twinACEFit)  			# expected covariance matrix for DZ's
M <- mxEval(expMean, twinACEFit)				# expected mean
A <- mxEval(a*a, twinACEFit)					# additive genetic variance, a^2
C <- mxEval(c*c, twinACEFit)					# shared environmental variance, c^2
E <- mxEval(e*e, twinACEFit)					# unique environmental variance, e^2
V <- (A+C+E)									# total variance
a2 <- A/V										# standardized additive genetic variance
c2 <- C/V										# standardized shared environmental variance
e2 <- E/V										# standardized unique environmental variance
ACEest <- rbind(cbind(A,C,E),cbind(a2,c2,e2)) 	# table of estimates
LL_ACE <- mxEval(objective, twinACEFit)			# likelihood of ACE model


#Mx answers hard-coded
# -----------------------------------------------------------------------
#1: Heterogeneity Model
Mx.A <- 0.6173023
Mx.C <- 5.595822e-14
Mx.E <- 0.1730462
Mx.M <- matrix(c(21.39293, 21.39293),1,2)
Mx.LL_ACE <- 4067.663

#Compare OpenMx results to Mx results (LL: likelihood; EC: expected covariance, EM: expected means)
# -----------------------------------------------------------------------
omxCheckCloseEnough(LL_ACE,Mx.LL_ACE,.001)
omxCheckCloseEnough(A,Mx.A,.001)
omxCheckCloseEnough(C,Mx.C,.001)
omxCheckCloseEnough(E,Mx.E,.001)
omxCheckCloseEnough(M,Mx.M,.001)


#Run AE model
# -----------------------------------------------------------------------
twinAEModel <- mxModel(twinACEModel, #name = "twinAE",
	# drop c at 0
	mxMatrix(
		type="Full", 
		nrow=1, 
		ncol=1, 
		free=FALSE, 
		values=0, 
		label="c", 
		name="Y"
	)	
)

twinAEFit <- mxRun(twinAEModel)

MZc <- mxEval(expCovMZ, twinAEFit)
DZc <- mxEval(expCovDZ, twinAEFit)
M <- mxEval(expMean, twinAEFit)
A <- mxEval(a*a, twinAEFit)
C <- mxEval(c*c, twinAEFit)
E <- mxEval(e*e, twinAEFit)
V <- (A+C+E)
a2 <- A/V
c2 <- C/V
e2 <- E/V
AEest <- rbind(cbind(A,C,E),cbind(a2,c2,e2))
LL_AE <- mxEval(objective, twinAEFit)

#Mx answers hard-coded
# -----------------------------------------------------------------------
#1: Homogeneity Model
Mx.A <- 0.6173023
Mx.C <- 0
Mx.E <- 0.1730462
Mx.M <- matrix(c(21.39293, 21.39293),1,2)
Mx.LL_AE <- 4067.663

#Compare OpenMx results to Mx results 
# -----------------------------------------------------------------------
# (LL: likelihood; EC: expected covariance, EM: expected means)
omxCheckCloseEnough(LL_AE,Mx.LL_AE,.001)
omxCheckCloseEnough(A,Mx.A,.001)
omxCheckCloseEnough(C,Mx.C,.001)
omxCheckCloseEnough(E,Mx.E,.001)
omxCheckCloseEnough(M,Mx.M,.001)

LRT_ACE_AE <- LL_AE - LL_ACE

#Print relevant output
# -----------------------------------------------------------------------
ACEest
AEest
LRT_ACE_AE