Random Formula
A one-sided formula specifying the random effects and the grouping variables. Its form is
~ x1 + + xN | group1/ group2/ /groupM
with x1+...+xN specifying the model for the random effects and group1/.../groupM the grouping structure (M may be equal to 1, in which case no / is required). The random effects formula will be repeated for all levels of grouping, in the case of multiple levels of grouping. The expression "1" can be used for the primary covariate when there is no other suitable candidate.