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#
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# -----------------------------------------------------------------------------
# Program: LatentGrowthModel_PathRaw.R  
# Author: Ryne Estabrook
# Date: 2010.09.17 
#
# ModelType: Growth Mixture
# DataType: Continuous
# Field: None
#
# Purpose: 
#      Growth Mixture Model
#      Path style model input - Raw data input
#
# RevisionHistory:
#      Ross Gore -- 2011.06.16 added Model, Data & Field metadata
#      Hermine Maes -- 2014.11.02 piecewise specification
# -----------------------------------------------------------------------------

require(OpenMx)
# Load Libraries
# -----------------------------------------------------------------------------


data(myGrowthMixtureData)
# Prepare Data
# -----------------------------------------------------------------------------

# residual variances
resVars      <- mxPath( from=c("x1","x2","x3","x4","x5"), arrows=2,
                        free=TRUE, values = c(1,1,1,1,1),
                        labels=c("residual","residual","residual","residual","residual") )
# latent variances and covariance
latVars      <- mxPath( from=c("intercept","slope"), arrows=2, connect="unique.pairs",
                        free=TRUE, values=c(1,.4,1), labels=c("vari1","cov1","vars1") )
# intercept loadings
intLoads     <- mxPath( from="intercept", to=c("x1","x2","x3","x4","x5"), arrows=1,
                        free=FALSE, values=c(1,1,1,1,1) )
# slope loadings
sloLoads     <- mxPath( from="slope", to=c("x1","x2","x3","x4","x5"), arrows=1,
                        free=FALSE, values=c(0,1,2,3,4) )
# manifest means
manMeans     <- mxPath( from="one", to=c("x1","x2", "x3", "x4","x5"), arrows=1,
                        free=FALSE, values=c(0,0,0,0,0) )
# latent means
latMeans     <- mxPath( from="one", to=c("intercept","slope"), arrows=1,
                        free=TRUE,  values=c(0,-1), labels=c("meani1","means1") )
# enable the likelihood vector
funML        <- mxFitFunctionML(vector=TRUE)
class1       <- mxModel("Class1", type="RAM",
                        manifestVars=c("x1","x2","x3","x4","x5"), 
                        latentVars=c("intercept","slope"), 
                        resVars, latVars, intLoads, sloLoads, manMeans, latMeans,
                        funML)


# latent variances and covariance
latVars2     <- mxPath( from=c("intercept","slope"), arrows=2, connect="unique.pairs",
                        free=TRUE, values=c(1,.5,1), labels=c("vari2","cov2","vars2") )
# latent means
latMeans2    <- mxPath( from="one", to=c("intercept", "slope"), arrows=1,
                        free=TRUE, values=c(5,1), labels=c("meani2","means2") )
class2       <- mxModel(class1, name="Class2", latVars2, latMeans2)

# Create an MxModel object
# -----------------------------------------------------------------------------

# request that individual likelihoods are used
# required for correct parameterization of class probabilities
classP       <- mxMatrix( type="Full", nrow=2, ncol=1, 
                        free=c(TRUE, FALSE), values=1, lbound=0.001, 
                        labels = c("p1","p2"), name="Props" )
# make a matrix of class probabilities
classS       <- mxAlgebra( Props%x%(1/sum(Props)), name="classProbs" )

algFit       <- mxAlgebra( -2*sum(log(classProbs[1,1]%x%Class1.fitfunction 
                           + classProbs[2,1]%x%Class2.fitfunction)), 
                           name="mixtureObj")
fit          <- mxFitFunctionAlgebra("mixtureObj")
dataRaw      <- mxData( observed=myGrowthMixtureData, type="raw" )
      
gmm          <- mxModel("Growth Mixture Model",
                        dataRaw, class1, class2, classP, classS, algFit, fit )      

gmmFit       <- mxRun(gmm, suppressWarnings=TRUE)

summary(gmmFit)

gmmFit$classProbs


omxCheckCloseEnough(gmmFit$output$Minus2LogLikelihood, 8739.05, 0.01)
omxCheckCloseEnough(max(mxEval(classProbs, gmmFit)), 0.6009, 0.01)
omxCheckCloseEnough(min(mxEval(classProbs, gmmFit)), 0.3991, 0.01)
# Check to see if results match within the specified bounds
# -----------------------------------------------------------------------------