#
#   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.
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# 
#        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,
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#   See the License for the specific language governing permissions and
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# -----------------------------------------------------------------------------
# Program: LatentGrowthModel_PathRaw.R  
# Author: Ryne Estabrook
# Date: 2009.08.01 
#
# ModelType: Growth Curve
# DataType: Longitudinal
# Field: None
#
# Purpose: 
#      Latent Growth model to estimate means and 
#      (co)variances of slope and intercept
#      Path style model input - Raw data input
#
# RevisionHistory:
#      Hermine Maes -- 2009.10.08 updated & reformatted
#      Ross Gore -- 2011.06.15 added Model, Data & Field
# -----------------------------------------------------------------------------

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

data(myLongitudinalData)
# Prepare Data
# -----------------------------------------------------------------------------

growthCurveModel <- mxModel("Linear Growth Curve Model Path Specification", 
    type="RAM",
    mxData(
    	observed=myLongitudinalData,
        type="raw"
    ),
    manifestVars=c("x1","x2","x3","x4","x5"),
    latentVars=c("intercept","slope"),
    # residual variances
    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
    mxPath(
    	from=c("intercept","slope"), 
        arrows=2,
		connect="unique.pairs",
        free=TRUE, 
        values=c(1, 1, 1),
        labels=c("vari", "cov", "vars")
    ),
    # intercept loadings
    mxPath(
    	from="intercept",
        to=c("x1","x2","x3","x4","x5"),
        arrows=1,
        free=FALSE,
        values=c(1, 1, 1, 1, 1)
    ),
    # slope loadings
    mxPath(
    	from="slope",
        to=c("x1","x2","x3","x4","x5"),
        arrows=1,
        free=FALSE,
        values=c(0, 1, 2, 3, 4)
    ),
    # manifest means
    mxPath(from="one",
        to=c("x1", "x2", "x3", "x4", "x5"),
        arrows=1,
        free=FALSE,
        values=c(0, 0, 0, 0, 0)
    ),
    # latent means
    mxPath(from="one",
        to=c("intercept", "slope"),
        arrows=1,
        free=TRUE,
        values=c(1, 1),
        labels=c("meani", "means")
    )
) # close model
#Create an MxModel object
# -----------------------------------------------------------------------------
      
growthCurveFit <- mxRun(growthCurveModel, suppressWarnings=TRUE)

summary(growthCurveFit)
growthCurveFit$output$estimate


omxCheckCloseEnough(growthCurveFit$output$estimate[["meani"]], 9.930, 0.01)
omxCheckCloseEnough(growthCurveFit$output$estimate[["means"]], 1.813, 0.01)
omxCheckCloseEnough(growthCurveFit$output$estimate[["vari"]], 3.886, 0.01)
omxCheckCloseEnough(growthCurveFit$output$estimate[["vars"]], 0.258, 0.01)
omxCheckCloseEnough(growthCurveFit$output$estimate[["cov"]], 0.460, 0.01)
omxCheckCloseEnough(growthCurveFit$output$estimate[["residual"]], 2.316, 0.01)
# Compare OpenMx results to Mx results 
# -----------------------------------------------------------------------------