Random-slope linear mixed model
= Random-slope linear mixed model
The Gaussian model $Y=X\beta+Zb+\varepsilon$ with $b\sim N(0,D)$ and independent $\varepsilon\sim N(0,\sigma^2I)$ has marginal law $N(X\beta,ZDZ^T+\sigma^2I)$. Its group coefficients are integrated out of the marginal <likelihood function>. The special random-slope model uses predictor values in the grouping columns of $Z$.