mxExpectationGREML: Create MxExpectationGREML Object
View source: R/MxExpectationGREML.R
| mxExpectationGREML | R Documentation |
Create MxExpectationGREML Object
Description
This function creates a new MxExpectationGREML object.
Usage
mxExpectationGREML(V, yvars=character(0), Xvars=list(), addOnes=TRUE, blockByPheno=TRUE,
staggerZeroes=TRUE, dataset.is.yX=FALSE, casesToDropFromV=integer(0),
REML=TRUE, yhat=character(0))
Arguments
V |
Character string; the name of the |
yvars, Xvars, addOnes, blockByPheno, staggerZeroes |
Passed to |
dataset.is.yX |
Logical; defaults to |
casesToDropFromV |
Integer vector. Its elements are the indices of the rows and columns of covariance matrix 'V' (and if applicable, of the rows of 'yhat') to be dropped at runtime, usually because they correspond to rows of 'y' or 'X' that contained missing observations. By default, no cases are dropped from 'V.' Ignored unless |
REML |
Logical; defaults to |
yhat |
Character string; the name of the |
Details
"GREML" stands for "genomic-relatedness-matrix restricted maximum-likelihood." In the strictest sense of the term, it refers to genetic variance-component estimation from matrices of subjects' pairwise degree of genetic relatedness, as calculated from genome-wide marker data. It is from this original motivation that some of the terminology originates, such as calling 'y' the "phenotype" vector. However, OpenMx's implementation of GREML is applicable for restricted maximum-likelihood analyses from any subject-matter domain, and in which the following assumptions are reasonable:
Conditional on 'X' (the covariates), the phenotype vector (response variable) 'y' is a single realization from a multivariate-normal distribution having (in general) a dense covariance matrix, 'V'.
The parameters of the covariance matrix, such as variance components, are of primary interest.
The random effects are normally distributed.
Weighted least-squares regression, using the inverse of 'V' as a weight matrix, is an adequate model for the phenotypic means. Note that the regression coefficients are not actually free parameters to be numerically optimized.
No variables in the model are treated both as phenotypes in 'y' and as covariates in 'X'.
Computationally, the chief distinguishing feature of an OpenMx GREML analysis is that the phenotype vector, 'y,' is a single realization of a random vector that, in general, cannot be partitioned into independent subvectors. For this reason, definition variables are not compatible (and should be unnecessary with) GREML expectation. GREML expectation can still be used if the covariance matrix is sparse, but as of this writing, OpenMx does not take advantage of the sparseness to improve performance. Partly because of the limitations of restricted maximum likelihood, GREML expectation is incompatible with ordinal variables; with GREML expectation, ordinal phenotypes must be treated as though they were continuous.
When REML is TRUE, the phenotypic means are always modeled "implicitly" via weighted least-squares regression onto the covariates in 'X', using the inverse of 'V' as the weight matrix. The phenotypic means can also be modeled "implicitly" in the same way when REML is FALSE. However, the case of REML=FALSE also allows the user to model the phenotypic means explicitly, as 'yhat', an arbitrary MxAlgebra or MxMatrix to serve as the model-expected phenotypic mean vector. So long as the appropriate care is taken, use of 'yhat' allows one to enter variables into one's model both as phenotypes in 'y' and covariates in 'X'.
When REML is FALSE and the user provides yhat, the assumptions of a GREML analysis may be stated as follows:
Phenotype vector 'y' is equal to mean vector 'yhat' plus normally distributed random effects, at least one of which is a single realization from a multivariate-normal distribution having (in general) a dense covariance matrix, 'V'.
The parameters of the covariance matrix and the mean vector are both explicit free parameters of interest.
Value
Returns a new object of class MxExpectationGREML.
References
Kirkpatrick RM, Pritikin JN, Hunter MD, & Neale MC. (2021). Combining structural-equation modeling with genomic-relatedness matrix restricted maximum likelihood in OpenMx. Behavior Genetics 51: 331-342. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s10519-020-10037-5")}
The first software implementation of "GREML":
Yang J, Lee SH, Goddard ME, Visscher PM. (2011). GCTA: a tool for genome-wide complex trait analysis. American Journal of Human Genetics 88: 76-82. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.ajhg.2010.11.011")}
One of the first uses of the acronym "GREML":
Benjamin DJ, Cesarini D, van der Loos MJHM, Dawes CT, Koellinger PD, et al. (2012). The genetic architecture of economic and political preferences. Proceedings of the National Academy of Sciences 109: 8026-8031. doi: 10.1073/pnas.1120666109
The OpenMx User's guide can be found at https://openmx.ssri.psu.edu/documentation/.
See Also
See MxExpectationGREML for the S4 class created by mxExpectationGREML(). More information about the OpenMx package may be found here.
Examples
dat <- cbind(rnorm(100),rep(1,100))
colnames(dat) <- c("y","x")
ge <- mxExpectationGREML(V="V",yvars="y",Xvars=list("X"),addOnes=FALSE)
gff <- mxFitFunctionGREML(dV=c(ve="I"))
plan <- mxComputeSequence(freeSet=c("Ve"),steps=list(
mxComputeNewtonRaphson(fitfunction="fitfunction"),
mxComputeOnce('fitfunction',
c('fit','gradient','hessian','ihessian')),
mxComputeStandardError(),
mxComputeReportDeriv(),
mxComputeReportExpectation()
))
testmod <- mxModel(
"GREMLtest",
mxData(observed = dat, type="raw"),
mxMatrix(type = "Full", nrow = 1, ncol=1, free=TRUE,
values = 1, labels = "ve", lbound = 0.0001, name = "Ve"),
mxMatrix("Iden",nrow=100,name="I",condenseSlots=TRUE),
mxAlgebra(I %x% Ve,name="V"),
ge,
gff,
plan
)
str(testmod)
