Dear Doug
I sent my reply twice (* copied below) but I cannot see it
Can you pls check?
Thank you
Pietro
(*)
Yes, I was referring to the conditional variance-covariance structure
of the response given the random effects, which is referred to as R in
the book of West, Welch, Galecki that I found mathematically
affordable (I am studying the R language now, and trying to learn more
about correlated data for study design purposes). And yes, I meant
"non-zero", as stated in the erratum.
Looking at the output of the getVarCov() function in R, I see that
choosing "conditional" as "type" I obtain a matrix with the estimate
of the error "variance" on the diagonal (which can be heterogeneous,
i.e. vary within cluster/group by values of cluster level co-variates)
and all "zeros" off the diagonal. I thought this is what LMM do:
explaining the group heterogeneity in the data (and the resulting
correlation in the responses) through splitting the random portion of
the statistical model into two layers, the random effects and the
random errors. These random errors - conditioning on the random
effects - I thought were normally distributed with zero mean and some
variance sigma2 (on the diagonal of the R matrix) and independent
(thus with zero co-variances off the diagonal of the R matrix).
Typing "marginal" in the above cmd tells R to give me what I thought
it was the combination (marginal model implied by the LMM) of the 2
VCV matrices, D (matrix of the random effects parameters) and R
(matrix of the random error parameter). The fact that different
structures (of the R matrix?) - mentioned in the previous emails
(compound symmetry, AR 1, Toeplitz, etc) - can be specified in the
lme() function via the correlation argument confuses me, unless they
refer to the resulting marginal model matrix (not the R matrix
conditional on the random effects). I have the impression I am lost
(although I know I have much more to learn).
Directions re math friendly sources / learning tools (especially using
R) would be very appreciated of course
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