如何从lme4获取随机效应（BLUP /条件模式）的协方差矩阵

Question

So, I've fitted a linear mixed model with two random intercepts in R:

Y = X beta  + Z b + e_i, 

where b ~ MVN (0, Sigma) ; X and Z are the fixed- and random-effects model matrices respectively, and beta and b are the fixed-effect parameters and random-effects BLUPs/conditional modes.

I would like to get my hands on the underlying covariance matrix of b , which doesn't seem to be a trivial thing in lme4 package. You can get only the variances by VarCorr , not the actual correlation matrix.

According to one of the package vignettes (page 2), you can calculate the covariance of beta: e_i * lambda * t(lambda) . And all those components you can extract from the output of lme4 .

I was wondering if this is the way to go? Or do you have any other suggestions?

Answer 1

From ?ranef :

If 'condVar' is 'TRUE' each of the data frames has an attribute called '"postVar"' which is a three-dimensional array with symmetric faces; each face contains the variance-covariance matrix for a particular level of the grouping factor. (The name of this attribute is a historical artifact, and may be changed to 'condVar' at some point in the future.)

Set up an example:

library(lme4)
fm1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
rr <- ranef(fm1,condVar=TRUE)

Get the variance-covariance matrix among the b values for the intercept

pv <- attr(rr[[1]],"postVar")
str(pv)
##num [1:2, 1:2, 1:18] 145.71 -21.44 -21.44 5.31 145.71 ...

So this is a 2x2x18 array; each slice is the variance-covariance matrix among the conditional intercept and slope for a particular subject (by definition, the intercepts and slopes for each subject are independent of the intercepts and slopes for all other subjects).

To convert this to a variance-covariance matrix (see getMethod("image",sig="dgTMatrix") ...)

library(Matrix)
vc <- bdiag(  ## make a block-diagonal matrix
            lapply(
                ## split 3d array into a list of sub-matrices
                split(pv,slice.index(pv,3)),
                   ## ... put them back into 2x2 matrices
                      matrix,2)) 
image(vc,sub="",xlab="",ylab="",useRaster=TRUE)