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cmlN = function(y, X, latentVars=NULL){
# Complete Maximum Likelihood estimates for a p-variate Normal model.
# Arguments:
# y: data matrix
# X: a design matrix
# latentVars: an empty list
n = nrow(y)
p = ncol(y)
#
# pmat.indices.w = triangleIndices(p, side='u', dgn=T, dataframe=T)
# pmat.indices.wo = triangleIndices(p, side='u', dgn=F, dataframe=T)
# n.pmat.indices.w = p * (p+1) / 2
# n.pmat.indices.wo = p * (p-1) / 2
# Complete Maximum Likelihood estimates
if(is.null(X)){
# xi & G
xiCML = apply(y, 2, mean)
GCML = (n-1) * var(y) / n
# SigmaCML = GCML
# omegaCML = diag(sqrt(diag(SigmaCML)))
# OmegaCML = cov2cor(SigmaCML)
# rho.ijCML = OmegaCML[pmat.indices.wo]
thetaCML = list(xi=xiCML, G=GCML)
} else {
# B & G
k = ncol(X)
BCML = matrix(0, k, p)
GCML = matrix(0, p, p)
constFlag = identical(as.integer(X[,1]), as.integer(rep(1,n)))
if(constFlag){
lmFit = stats::lm(y ~ X - 1)
} else {
lmFit = stats::lm(y ~ X)
}
lmCoeff = lmFit$coefficients
if(any(is.na(lmCoeff))) stop('cmlN.R: X is misspecified.\n')
BCML = matrix(lmCoeff, k, p)
BX = lmFit$fitted.values # Conditional mean of y given X
#
e = y - BX
GCML = (n-1) * var(e) / n
thetaCML = list(B=BCML, G=GCML)
}
return(thetaCML)
}
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