The two-level model written above can be re-written as a single-level model by substituting equation 2 into a block form of equation 1, giving

where now all the first-level GLMs have been combined such that

The two error terms in equation 3 can simply be combined such that

where

and

It is easy to see that this *model* is equivalent to the
two-level version presented as equations 1
and 2.

Christian Beckmann 2003-07-16