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#
# Copyright 2007-2019 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.
# -----------------------------------------------------------------------------
# Program: UnivariateSaturated.R
# Author: Hermine Maes
# Date: 2009.08.01
#
# ModelType: Saturated
# DataType: Simulated
# Field: None
#
# Purpose:
# Univariate Saturated model to estimate means and variances
# Two matrix styles - Two data styles
#
# RevisionHistory:
# Hermine Maes -- 2009.10.08 updated & reformatted
# Ross Gore -- 2011.06.06 added Model, Data & Field metadata
# -----------------------------------------------------------------------------
require(OpenMx)
# Load Library
# -----------------------------------------------------------------------------
set.seed(100)
x <- rnorm (1000, 0, 1)
testData <- as.matrix(x)
selVars <- c("X")
dimnames(testData) <- list(NULL, selVars)
summary(testData)
colMeans(testData)
var(testData)
# Simulate Data
# -----------------------------------------------------------------------------
univSatModel1 <- mxModel("univSat1",
manifestVars=selVars,
mxPath(
from=c("X"),
arrows=2,
free = TRUE,
values=1,
lbound=.01,
labels="vX"
),
mxData(
observed=var(testData),
type="cov",
numObs=1000
),
type="RAM"
)
univSatFit1 <- mxRun(univSatModel1)
EC1 <- mxEval(S, univSatFit1)
LL1 <- mxEval(objective, univSatFit1)
SL1 <- univSatFit1$output$SaturatedLikelihood
Chi1 <- LL1-SL1
# example 1: Saturated Model with Cov Matrices and Path-Style Input
# -----------------------------------------------------------------------------
univSatModel1m <- mxModel("univSat1m",
manifestVars=selVars,
mxPath(
from=c("X"),
arrows=2,
free = TRUE,
values=1,
lbound=.01,
labels="vX"
),
mxPath(
from="one",
to="X",
arrows=1,
free = TRUE,
values=0,
labels="mX"
),
mxData(
observed=var(testData),
type="cov",
numObs=1000,
means=colMeans(testData)
),
type="RAM"
)
univSatFit1m <- mxRun(univSatModel1m)
EM1m <- mxEval(M, univSatFit1m)
EC1m <- mxEval(S, univSatFit1m)
LL1m <- mxEval(objective,univSatFit1m);
SL1m <- univSatFit1m$output$SaturatedLikelihood
Chi1m <- LL1m-SL1m
# example 1m: Saturated Model with Cov Matrices & Means and Path-Style Input
# -----------------------------------------------------------------------------
univSatModel2 <- mxModel("univSat2",
manifestVars= selVars,
mxPath(
from=c("X"),
arrows=2,
free = TRUE,
values=1,
lbound=.01,
labels="vX"
),
mxPath(
from="one",
to="X",
arrows=1,
free = TRUE,
values=0,
labels="mX"
),
mxData(
observed=testData,
type="raw",
),
type="RAM"
)
univSatFit2 <- mxRun(univSatModel2)
EM2 <- mxEval(M, univSatFit2)
EC2 <- mxEval(S, univSatFit2)
LL2 <- mxEval(objective,univSatFit2);
# example 2: Saturated Model with Raw Data and Path input
# -----------------------------------------------------------------------------
univSatModel2s <- mxModel(univSatModel1,
mxData(
observed=testData,
type="raw"
),
mxPath(
from="one",
to="X",
arrows=1,
free = TRUE,
values=0,
labels="mX"
),
name="univSat2s",
type="RAM"
)
univSatFit2s <- mxRun(univSatModel2s)
EM2s <- mxEval(M, univSatFit2s)
EC2s <- mxEval(S, univSatFit2s)
LL2s <- mxEval(objective,univSatFit2s);
# example 2s: Saturated Model with Raw Data and Path input built upon
# Cov/Means version
# -----------------------------------------------------------------------------
univSatModel3 <- mxModel("univSat3",
mxMatrix(
type="Symm",
nrow=1,
ncol=1,
free = TRUE,
values=1,
name="expCov"
),
mxData(
observed=var(testData),
type="cov",
numObs=1000
),
mxFitFunctionML(),mxExpectationNormal(
covariance="expCov",
dimnames=selVars
)
)
univSatFit3 <- mxRun(univSatModel3)
EC3 <- mxEval(expCov, univSatFit3)
LL3 <- mxEval(objective, univSatFit3)
SL3 <- univSatFit3$output$SaturatedLikelihood
Chi3 <- LL3-SL3
# example 3: Saturated Model with Cov Matrices and Matrix-Style Input
# -----------------------------------------------------------------------------
univSatModel3m <- mxModel("univSat3m",
mxMatrix(
type="Symm",
nrow=1,
ncol=1,
free = TRUE,
values=1,
name="expCov"
),
mxMatrix(
type="Full",
nrow=1,
ncol=1,
free = TRUE,
values=0,
name="expMean"
),
mxData(
observed=var(testData),
type="cov",
numObs=1000,
means=colMeans(testData)
),
mxFitFunctionML(),mxExpectationNormal(
covariance="expCov",
means="expMean",
dimnames=selVars
)
)
univSatFit3m <- mxRun(univSatModel3m)
EM3m <- mxEval(expMean, univSatFit3m)
EC3m <- mxEval(expCov, univSatFit3m)
LL3m <- mxEval(objective, univSatFit3m);
SL3m <- univSatFit3m$output$SaturatedLikelihood
Chi3m <- LL3m-SL3m
# example 3m: Saturated Model with Cov Matrices & Means and Matrix-Style Input
# -----------------------------------------------------------------------------
univSatModel4 <- mxModel("univSat4",
mxMatrix(
type="Symm",
nrow=1,
ncol=1,
free = TRUE,
values=1,
name="expCov"
),
mxMatrix(
type="Full",
nrow=1,
ncol=1,
free = TRUE,
values=0,
name="expMean"
),
mxData(
observed=testData,
type="raw",
),
mxFitFunctionML(),mxExpectationNormal(
covariance="expCov",
means="expMean",
dimnames=selVars
)
)
univSatFit4 <- mxRun(univSatModel4)
EM4 <- mxEval(expMean, univSatFit4)
EC4 <- mxEval(expCov, univSatFit4)
LL4 <- mxEval(objective, univSatFit4);
# examples 4: Saturated Model with Raw Data and Matrix-Style Input
# -----------------------------------------------------------------------------
# example Mx..1: Saturated Model with Cov Matrices
# -------------------------------------
Mx.EC1 <- 1.06104
Mx.LL1 <- -1.474434e-17
# example Mx..1m: Saturated Model with Cov Matrices & Means
# -------------------------------------
Mx.EM1m <- 0.01680509
Mx.EC1m <- 1.06104
Mx.LL1m <- -1.108815e-13
Mx.EM2 <- 0.01680516
Mx.EC2 <- 1.061050
Mx.LL2 <- 2897.135
# Mx answers hard-coded
# -----------------------------------------------------------------------------
cov <- rbind(cbind(EC1,EC1m,EC2),cbind(EC3,EC3m,EC4))
mean <- rbind(cbind(EM1m, EM2),cbind(EM3m,EM4))
like <- rbind(cbind(LL1,LL1m,LL2),cbind(LL3,LL3m,LL4))
cov; mean; like
# OpenMx summary
# -----------------------------------------------------------------------------
Mx.cov <- cbind(Mx.EC1,Mx.EC1m,Mx.EC2)
Mx.mean <- cbind(Mx.EM1m,Mx.EM2)
Mx.like <- cbind(Mx.LL1,Mx.LL1m,Mx.LL2)
Mx.cov; Mx.mean; Mx.like
# old Mx summary
# -----------------------------------------------------------------------------
omxCheckCloseEnough(Chi1,Mx.LL1,.001)
omxCheckCloseEnough(EC1,Mx.EC1,.001)
# 1:CovPat
# -------------------------------------
omxCheckCloseEnough(Chi1m,Mx.LL1m,.001)
omxCheckCloseEnough(EC1m,Mx.EC1m,.001)
omxCheckCloseEnough(EM1m,Mx.EM1m,.001)
# 1m:CovMPat
# -------------------------------------
omxCheckCloseEnough(LL2,Mx.LL2,.001)
omxCheckCloseEnough(EC2,Mx.EC2,.001)
omxCheckCloseEnough(EM2,Mx.EM2,.001)
# 2:RawPat
# -------------------------------------
omxCheckCloseEnough(LL2s,Mx.LL2,.001)
omxCheckCloseEnough(EC2s,Mx.EC2,.001)
omxCheckCloseEnough(EM2s,Mx.EM2,.001)
# 2:RawSPat
# -------------------------------------
omxCheckCloseEnough(Chi3,Mx.LL1,.001)
omxCheckCloseEnough(EC3,Mx.EC1,.001)
# 3:CovMat
# -------------------------------------
omxCheckCloseEnough(Chi3m,Mx.LL1m,.001)
omxCheckCloseEnough(EC3m,Mx.EC1m,.001)
omxCheckCloseEnough(EM3m,Mx.EM1m,.001)
# 3m:CovMPat
# -------------------------------------
omxCheckCloseEnough(LL4,Mx.LL2,.001)
omxCheckCloseEnough(EC4,Mx.EC2,.001)
omxCheckCloseEnough(EM4,Mx.EM2,.001)
# 4:RawMat
# -------------------------------------
# Compare OpenMx results to Mx results
# (LL: likelihood; EC: expected covariance, EM: expected means)
# -----------------------------------------------------------------------------
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