# Cross-nested random intercepts in mixed model?

First, forgive my uncertain terminology. I think I have a cross-nested effect. I want to model mortgage origination in multiple MSAs (metropolitan statistical areas) vs. race, income, type of loan, etc.

My basic geographic unit (random grouping) is the census tract. Each census tract exists within an MSA and within a state. MSAs can cross state lines. Individual states have different mortgage regulations and laws, but MSAs also exert their own economic and cultural influences.

So, does this mean that I would have cross-nested random intercepts, where tract is nested within state and within MSA? Would the syntax for this be something like

Origination ~ Race + Income + ... + (1 | State/tract) + (1 | MSA/tract)?


Origination ~ Race + Income + ... + (1 | State) + (1 | MSA) + (1 | tract)

The nesting gets handled automatically. The explicit nesting syntax (1|State/tract) is most useful when tracts are not labeled uniquely. (All this syntax does is to expand internally to (1|State) + (1|State:tract), where the second term represents the combination of State and tract (AL_101, AL_102, ... AK_101, AK_102, ... AR_101, AR_102, ...)