#
#   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: MultipleRegression_MatrixRaw.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
#      Matrix 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)

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


multiRegModel <- mxModel("Multiple Regression Matrix Specification", 
    mxData(
    	observed=MultipleDataRaw,
    	type="raw"
   	),
    mxMatrix(
    	type="Full", 
    	nrow=3, 
    	ncol=3,
        values=c(0,0,0,
                 1,0,1,
                 0,0,0),
        free=c(F, F, F,
               T, F, T,
               F, F, F),
        labels=c(NA,     NA, NA,
                "betax", NA,"betaz",
                 NA,     NA, NA),
        byrow=TRUE,
        name = "A"
    ),
    mxMatrix(
    	type="Symm", 
    	nrow=3, 
    	ncol=3, 
        values=c(1, 0, .5,
                 0, 1, 0,
                .5, 0, 1),
        free=c(T, F, T,
               F, T, F,
               T, F, T),
        labels=c("varx",  NA,         "covxz",
                  NA,    "residual",   NA,
                 "covxz", NA,         "varz"),
        byrow=TRUE,
        name="S"
    ),
    mxMatrix(
    	type="Iden",
    	nrow=3, 
    	ncol=3,
        name="F"
    ),
    mxMatrix(
    	type="Full", 
    	nrow=1, 
    	ncol=3,
        values=c(0,0,0),
        free=c(T,T,T),
        labels=c("meanx","beta0","meanz"),
        name="M"
    ),
    mxFitFunctionML(),mxExpectationRAM("A","S","F","M",
       dimnames=c("x","y","z"))
)
# 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 
# -----------------------------------------------------------------------------