V matrix and Z matrix in mixed model

[fatemeh]

Hello all,

I am looking for a source, an article or a book with examples that give me interpretation of V matrix and Z matrix in V=ZGZ'+R in mixed model with repeated measure, fixed and random effects. Any help will be appreciated. 

[Rick_SAS · Accepted solution]

See Chapter 1 of Littel et al, "SAS for Mixed Models" (or pretty much any other mixed model book). Also see the Appendix 1: "Linear Mixed Model Theory"

In the model
Y = X*beta + Z*u + epsilon
Z is the design matrix for the random effects. G is the covariance matrix for the random effects: u ~ MVN(0,G). R is the covariance matrix for the error distribution, which is assumed to be epsilon ~ MVN(0,R). The marginal distribution of Y is Y ~ MVN(X*beta, V), where V = Z`*G*Z + R = Var[Y].