#
#   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.

require(OpenMx)

# -----------------------------------------------------------------------------
# Program: MultipleRegression_PathRaw.R  
# Author: Ryne Estabrook
# Date: 2009.08.01 
#
# ModelType: Regression
# DataType: Continuous
# Field: None
#
# Purpose:
#      Multiple Regression model to estimate effect of independent on dependent variables
#      Path style model input - Raw data input
#
# RevisionHistory:
#      Hermine Maes -- 2009.10.08 updated & reformatted
#      Ross Gore -- 2011.06.15 added Model, Data & Field metadata
# -----------------------------------------------------------------------------

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

data(myRegDataRaw)

myRegDataRaw<-myRegDataRaw[,c("x","y","z")]
# Prepare Data
# -----------------------------------------------------------------------------

multiRegModel <- mxModel("Multiple Regression Path Specification", 
      type="RAM",
      mxData(
          observed=myRegDataRaw, 
          type="raw"
      ),
      manifestVars=c("x", "y", "z"),
      mxPath(
          from=c("x", "y", "z"), 
          arrows=2,
          free=TRUE, 
          values = c(1, 1, 1),
          labels=c("varx", "residual", "varz")
      ),
      # variance paths
	  # -------------------------------------	
      mxPath(
          from="x",
          to="z",
          arrows=2,
          free=TRUE,
          values=0.5,
          labels="covxz"
      ), 
      # covariance of x and z
	  # -------------------------------------
      mxPath(
          from=c("x","z"),
          to="y",
          arrows=1,
          free=TRUE,
          values=1,
          labels=c("betax","betaz")
      ), 
      # regression weights
      # -------------------------------------
      mxPath(
          from="one",
          to=c("x", "y", "z"),
          arrows=1,
          free=TRUE,
          values=c(1, 1),
          labels=c("meanx", "beta0", "meanz")
      )
      # means and intercepts
      # -------------------------------------
  ) # close model
# Create an MxModel object
# -----------------------------------------------------------------------------
      
multiRegFit<-mxRun(multiRegModel)

summary(multiRegFit)
multiRegFit$output


omxCheckCloseEnough(multiRegFit$output$estimate[["beta0"]], 1.6332, 0.001)
omxCheckCloseEnough(multiRegFit$output$estimate[["betax"]], 0.4246, 0.001)
omxCheckCloseEnough(multiRegFit$output$estimate[["betaz"]], 0.2260, 0.001)
omxCheckCloseEnough(multiRegFit$output$estimate[["residual"]], 0.6267, 0.001)
omxCheckCloseEnough(multiRegFit$output$estimate[["varx"]], 1.1053, 0.001)
omxCheckCloseEnough(multiRegFit$output$estimate[["varz"]], 0.8275, 0.001)
omxCheckCloseEnough(multiRegFit$output$estimate[["covxz"]], 0.2862, 0.001)
omxCheckCloseEnough(multiRegFit$output$estimate[["meanx"]], 0.0542, 0.001)
omxCheckCloseEnough(multiRegFit$output$estimate[["meanz"]], 4.0611, 0.001)
# Compare OpenMx results to Mx results 
# -----------------------------------------------------------------------------