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### Marginal correlations from lmer

The book does give the formula for the marginal covariance (matrix) of the response $Y_i$ of individual $i$ (several times, f.i. on page 201):  \Sigma_i=\mathrm{Cov}(Y_i)=Z_iG{Z}^{\top}_i+R_i\...
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Remember that $\text{Cov}(\mathbf{Y}_i)$ is a function of time, $\mathbf{t}_i$. ...
I presume that $\mu_i$ are supposed to be individual-dependent offsets and $\eta_t$ time-dependent offsets. You could run two separate regressions, but using the dummy variable (in interaction terms) ...