Hello,

I have a question:
In the case of multiple nested effects one can be provided with
correlations for a grouping's subgroups; how are these correlations
computed? What is the correct reference for the computational calculation
of the nested random effects and their correlation in lmer()?
I believe an LDL^t decomposition of a scaled precision matrix might be
involved but I looked in the three lme4 vignettes, Bates & DebRoy (2004) in
J. of Multivariate Analysis as well as the DebRoy & Bates' Technical Report
No. 1076 but none mentions something explicitly (eg. the Implementation.pdf
vignette specifically sets "corr = FALSE" in the case of nested factors
actually). Could someone please suggest to me references in regard with
that?
Only indirect references I could find was: 1. subsection 2.2.7 on Pinheiro
& Bates "Mixed-Effects Models in S and S-Plus" but even there nothing is
stated specifically for correlation calculations and 2. the Bell Labs
Technical Memorandum "Computational Methods for Multilevel Modelling" by
Bates & Pinheiro that mentions correlations in regard with the Nonlinear
multilevel model. Additionally both references are mostly referring on
lme().
Finally, the "lme4: Mixed-effects modeling with R" book in subsection 3.2.1
while looking at nested effect correlations it does not provide
computational aspects of it.

Thank you very much in advance.

All best,
Pantelis

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