Get Residual Variance-Covariance Matrix in lme4

问题

I am fitting a linear mixed effects model using lme4:

library(lme4)
data(Orthodont)
dent <- Orthodont
d.test <- lmer(distance ~ age + (1|Subject), data=dent)

If we say generically Y = X * B + Z * d + e is the form of a linear mixed effects model, then I am trying to get Var(Y) = Z * Var(d) * Z^t + Var(e) from the results of the model.

Is the following formulation the right way to do this?

k <- table(dent$Subject)[1]
vars <- VarCorr(d.test)
v <- as.data.frame(vars)
sigma <- attr(vars, "sc")
s.tech <- diag(v$vcov[1], nrow=k)
icc <- v$vcov[1]/sum(v$vcov)
s.tech[upper.tri(s.tech)] <- icc
s.tech[lower.tri(s.tech)] <- icc
sI <- diag(sigma^2, nrow=length(dent$age))
var.b <- kronecker(diag(1, nrow=length(dent$age)/k), s.tech)
var.y <- sI + var.b

I think this is a simple question, but I can't find anywhere code for doing this, so I'm asking if I'm doing it right.

回答1:

You can do this a bit more easily if you know about getME(), which is a general purpose extract-bits-of-a-lmer-fit function. In particular, you can extract the transposed Z matrix (getME(.,"Zt")) and the transposed Lambda matrix - the Lambda matrix is the Cholesky factor of the scaled variance-covariance matrix of the conditional models (BLUPs); in your notation, Var(d) is the residual variance times the cross-product of Lambda.

The answer cited here is pretty good but the answer below is slightly more general (it should work for any lmer fit).

Fit model:

library(lme4)
data(Orthodont,package="nlme")
d.test <- lmer(distance ~ age + (1|Subject), data=Orthodont)

Extract components:

var.d <- crossprod(getME(d.test,"Lambdat"))
Zt <- getME(d.test,"Zt")
vr <- sigma(d.test)^2

Combine them:

var.b <- vr*(t(Zt) %*% var.d %*% Zt)
sI <- vr * Diagonal(nrow(Orthodont))
var.y <- var.b + sI

A picture:

image(var.y)

来源：https://stackoverflow.com/questions/45650548/get-residual-variance-covariance-matrix-in-lme4

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lme4