If I write down the model `Reaction ~ Days + (Days | Subject)` :

\(\text{Reaction}_{ij}=\beta_{0j}+\beta_{1j}\text{Days}_{ij}+e_{ij}\)

\(\beta_{0j}=\gamma_{00}+u_{0j}\)

\(\beta_{1j}=\gamma_{10}+u_{1j}\)

Combining the last two equations into first one , that is , by substituting the level-2 equation to level-1 equation, we have ;

\(\text{Reaction}_{ij}=\gamma_{00}+\gamma_{10}\text{Days}_{ij}+u_{0j}+u_{1j}\text{Days}_{ij}+e_{ij}\)

Does

The second model does not--it forces the covariance to be zero.

mean for the second model \(cov(u_{0j},u_{1j})=0\) ?

Many thanks! Regards .