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#
# Copyright 2007-2021 by the individuals mentioned in the source code history
#
# 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.
#------------------------------------------------------------------------------
# Author: Michael D. Hunter
# Date: 2014.12.17
# Filename: ModelIdentification.R
# Purpose: Check the model identification checking function.
#------------------------------------------------------------------------------
#--------------------------------------------------------------------
# Load OpenMx
library(OpenMx)
library(testthat)
context("Model Identification")
#--------------------------------------------------------------------
# Read in and set up the data
IndManExo <- 1:8
IndManEnd <- 9:12
# The data
data(latentMultipleRegExample1)
# Rearange Columns to separate exogenous and endogenous variables
rawlisdat <- latentMultipleRegExample1[, c(IndManEnd, IndManExo)]
rawlisy <- latentMultipleRegExample1[, IndManEnd]
rawlisx <- latentMultipleRegExample1[, IndManExo]
# Take covariance and means
covlisdat <- cov(rawlisdat)
mealisdat <- colMeans(rawlisdat)
# Number of manifest and latent exogenous and endogenous variables
numLatExo <- 2
numLatEnd <- 1
numManExo <- 8
numManEnd <- 4
# Dimnames
LatExo <- paste('xi', 1:numLatExo, sep='')
LatEnd <- paste('eta', 1:numLatEnd, sep='')
ManExo <- names(rawlisdat)[(numManEnd+1):(numManEnd+numManExo)]
ManEnd <- names(rawlisdat)[1:numManEnd]
#--------------------------------------------------------------------
# Specify the 13 extended LISREL matrices
lx <- mxMatrix("Full", numManExo, numLatExo,
free=c(T,T,T,T,F,F,F,F,F,F,F,F,F,T,T,T),
values=c(1, .2, .2, .2, 0, 0, 0, 0, 0, 0, 0, 0, 1, .2, .2, .2),
labels=c( paste('l', 1, 1:4, sep=''), rep(NA, 8), paste('l', 2, 5:8, sep='')),
name='LX',
dimnames=list(ManExo, LatExo)
) #DONE
ly <- mxMatrix("Full", numManEnd, numLatEnd,
free=c(F,T,T,T),
values=c(1, .2, .2, .2),
labels= paste('l', 3, 9:12, sep=''),
name='LY',
dimnames=list(ManEnd, LatEnd)
) #DONE
be <- mxMatrix("Zero", numLatEnd, numLatEnd, name='BE', dimnames=list(LatEnd, LatEnd)) #DONE
ga <- mxMatrix("Full", numLatEnd, numLatExo,
free=T,
values=.2,
labels=c('b13', 'b23'),
name='GA',
dimnames=list(LatEnd, LatExo)
) #DONE
ph <- mxMatrix("Symm", numLatExo, numLatExo,
free=c(T,T,T),
values=c(.8, .3, .8),
labels=c('varF1', 'covF1F2', 'varF2'),
name='PH',
dimnames=list(LatExo, LatExo)
) #DONE
ps <- mxMatrix("Symm", numLatEnd, numLatEnd,
free=T,
values=.8,
labels='varF3',
name='PS',
dimnames=list(LatEnd, LatEnd)
) #DONE
td <- mxMatrix("Diag", numManExo, numManExo,
free=T,
values=.8,
labels=paste('d', 1:8, sep=''),
name='TD',
dimnames=list(ManExo, ManExo)
) #DONE
te <- mxMatrix("Diag", numManEnd, numManEnd,
free=T,
values=.8,
labels=paste('e', 9:12, sep=''),
name='TE',
dimnames=list(ManEnd, ManEnd)
) #DONE
th <- mxMatrix("Zero", numManExo, numManEnd, name='TH', dimnames=list(ManExo, ManEnd)) #DONE
tx <- mxMatrix("Full", numManExo, 1,
free=T,
values=.1,
labels=paste('m', 1:8, sep=''),
name='TX',
dimnames=list(ManExo, "TXMeans")
) #DONE
ty <- mxMatrix("Full", numManEnd, 1,
free=T,
values=.1,
labels=paste('m', 9:12, sep=''),
name='TY',
dimnames=list(ManEnd, "TYMeans")
) #DONE
ka <- mxMatrix("Zero", numLatExo, 1, name='KA', dimnames=list(LatExo, "KAMeans")) #DONE
al <- mxMatrix("Zero", numLatEnd, 1, name='AL', dimnames=list(LatEnd, "ALMeans")) #DONE
#--------------------------------------------------------------------
#--------------------------------------------------------------------
# Define the model
xmod <- mxModel(
name='LISREL Exogenous Model with Means',
mxData(observed=cbind(rawlisx, extra=NA), type='raw'),
lx, ph, td, tx, ka,
mxExpectationLISREL(
LX=lx$name,
PH=ph$name,
TD=td$name,
TX=tx$name,
KA=ka$name
),
mxFitFunctionML()
)
#--------------------------------------------------------------------
#--------------------------------------------------------------------
# Model identification
id <- mxCheckIdentification(xmod)
omxCheckEquals(id$status, FALSE)
omxCheckEquals(id$non_identified_parameters, c("l11", "l12", "l13", "l14", "varF1", "covF1F2"))
#--------------------------------------------------------------------
#--------------------------------------------------------------------
# Add constraint, now I know what to do
xmod2 <- mxModel(xmod, mxConstraint(TX[1,1] == TX[2,1], name='conman'))
id2 <- mxCheckIdentification(xmod2)
omxCheckEquals(id2$status, FALSE)
omxCheckEquals(id$non_identified_parameters, c("l11", "l12", "l13", "l14", "varF1", "covF1F2"))
xmod3 <- mxModel(xmod, mxConstraint(PH[1,1] == PH[2,2], name='convar'))
id3 <- mxCheckIdentification(xmod3)
omxCheckEquals(id3$status, TRUE)
#--------------------------------------------------------------------
# End
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