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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.
#This script (by Rob K.) demonstrates the use of the GREML feature in a simple but realistic example;
#the syntax is further simplified by using the default gradient-descent optimizer instead of Newton-Raphson.
#It first simulates a genomic-relatedness matrix (GRM), a phenotype, and a null covariate. Then, it
#fits a simple GREML model to estimate additive-genetic variance, residual variance, and heritability.
require(OpenMx)
options(mxCondenseMatrixSlots=TRUE) #<--Saves memory
require(mvtnorm)
#Generate data:
set.seed(476)
A <- matrix(0,1000,1000) #<--Empty GRM
A[lower.tri(A)] <- runif(499500, -0.025, 0.025)
A <- A + t(A)
diag(A) <- runif(1000,0.95,1.05) #<--GRM now complete
y <- t(rmvnorm(1,sigma=A*0.5)) #<--Phenotype 'y' has a "population" variance of 1 and h2 of 0.5
y <- y + rnorm(1000,sd=sqrt(0.5))
x <- rnorm(1000) #<--Covariate 'x' is actually independent of the phenotype.
#Merge variables into data matrix:
dat <- cbind(y,x)
colnames(dat) <- c("y","x") #<--Column names
#The GREML expectation tells OpenMx that the model-expected covariance matrix is named 'V', that the one
#phenotype is has column label 'y' in the dataset, that the one covariate has column label 'x' in the dataset,
#and that a lead column of ones needs to be appended to the 'X' matrix (for the intercept):
ge <- mxExpectationGREML(V="V",yvars="y", Xvars="x", addOnes=T)
#The GREML fitfunction object:
gff <- mxFitFunctionGREML()
#The MxData object. N.B. use of 'sort=FALSE' is CRITICALLY IMPORTANT, because the rows and columns of dataset
#'dat' and the rows and columns of GRM 'A' are already properly ordered:
mxdat <- mxData(observed = dat, type="raw", sort=FALSE)
#We will create some of the necessary objects inside the mxModel() statement. We mainly want to avoid creating
#more copies of the GRM than we need to:
testmod <- mxModel(
"GREML_1GRM_1trait", #<--Model name
#1x1 matrix containing residual variance component:
mxMatrix(type = "Full", nrow = 1, ncol=1, free=T, values = var(y)/2, labels = "ve", lbound = 0.0001,
name = "Ve"),
#1x1 matrix containing additive-genetic variance component:
mxMatrix(type = "Full", nrow = 1, ncol=1, free=T, values = var(y)/2, labels = "va", name = "Va"),
#1000x1000 identity matrix--the "relatedness matrix" for the residuals:
mxMatrix("Iden",nrow=1000,name="I"),
#The GRM:
mxMatrix("Symm",nrow=1000,free=F,values=A,name="A"),
#The model-expected covariance matrix:
mxAlgebra((A%x%Va) + (I%x%Ve), name="V"),
#An MxAlgebra for the heritability:
mxAlgebra(Va/(Va+Ve), name="h2"),
mxCI("h2"), #<--Request confidence interval for heritability
mxdat, #<--MxData object
ge, #<--GREML expectation
gff #<--GREML fitfunction
)
testrun <- mxRun(testmod,intervals = T) #<--Run model
summary(testrun) #<--Model summary
#Obtain SE of h2 from delta-method approximation (e.g., Lynch & Walsh, 1998, Appendix 1):
scm <- chol2inv(chol(testrun$output$hessian/2)) #<--Sampling covariance matrix for ve and va
pointest <- testrun$output$estimate #<--Point estimates of ve and va
h2se <- sqrt(
(pointest[2]/(pointest[1]+pointest[2]))^2 * (
(scm[2,2]/pointest[2]^2) - (2*scm[1,2]/pointest[1]/(pointest[1]+pointest[2])) +
(sum(scm)*(pointest[1]+pointest[2])^-2)
))
#Compare:
mxEval(h2,testrun,T)[1,1] + 2*c(-h2se,h2se)
testrun$output$confidenceIntervals
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