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Compound Symmetry Covariance structure

Ben Bolker 
A quick example of the induced covariance structure.

  Suppose you set up the simplest possible (linear) mixed model, which
has an overall intercept B; a group-level random effect on the intercept
e1_i with variance v1; and a residual error e0_ij with variance v0. The
value of x_{ij} = B + e1_i + e0_ij.  The variance of any observation
(E[(x_{ij}-B)^2]) is v0+v1.  The covariance of observations in the same
group is E[(x_{ij}-B)(x_{kj}-B)] = v1. The covariance of observations in
*different* groups is 0.  If we write out the correlation matrix for the
whole data set (assuming the observations are written out with samples
from the same group occurring contiguously), it will consist of a
block-diagonal matrix with correlation v1/(v0+v1) within each block; the
rest of the matrix will be zero.  This is a form of induced
compound-symmetric covariance structure.

  Presumably others can give good references to where this is explained
clearly in the literature (maybe even in Pinheiro and Bates, I don't
have access to my copy right now)
On 2018-12-07 1:53 p.m., Poe, John wrote:

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Yashree Mehta Compound Symmetry Covariance structure Dec 7 Poe, John Compound Symmetry Covariance structure Dec 7 Joaquín Aldabe Compound Symmetry Covariance structure Dec 8 Ben Bolker Compound Symmetry Covariance structure Dec 9 Yashree Mehta Compound Symmetry Covariance structure Dec 9 Ben Bolker Compound Symmetry Covariance structure Dec 9