Dear group,

I would like to do a logistic regression of vaccination coverage of, for 
example, HPV. Let's assume that we have 50 states (S). 30 states have an 
urban part and a country part (urbanity variable U). The other 20 have 
only a country area. 10 of the states have population areas where 
individuals speaks only Spanish and other areas only English (L). The 
linguistic region correlates only slightly with urbanity. For example:

S: 1,.., 50; U: urban/country; L: English/Spanish.

State 1:
     S(1)-U(urban)     /    S(1)-L(english)
     S(1)-U(country)   / S(1)-L(english)
     S(1)-U(urban)      /    S(1)-L(spanish)
     S(1)-U(country)   / S(1)-L(spanish)

State 2:
     S(2)-U(urban)     /    S(2)-L(english)
     S(2)-U(urban)     /   S(2)-L(spanish)

State 3:
     S(3)-U(urban)     /     S(3)-L(english)
     S(3)-U(country)   / S(3)-L(english)

State 4:
     S(4)-U(urban)      /    S(4)-L(english)
     S(4)-U(country)   / S(4)-L(spanish)

...

where the number indicate a state.

The situation is that U is nested in S but not each S has both levels of 
U. This is also the case for the linguistic variable: L is nested in S 
but not each S has both levels of L. If U would be nested completely in 
S and L completely in S, the model would look like (in R-terminology for 
lmer):
  y ~ (1|S) +(1|S/U) + (1|S/L)
where y: 0/1 vaccinated

Is it possible to estimate odds ratio using this model even if variables 
U and L are not completely nested? Or Should be used another model, for 
example:
y ~ (1/S) + U + L
where(1|S) is random variable and U and L are fixed variables.

With fixed levels U and L the nesting character would be lost and the 
variables would be characterstics of the individuals, that is, the 
aggregation of individuals in distinct areas would not be considered.
Problem which arise using fixed variables: it would give significant 
results or narrow CI due to the high number of individuals.
Problem with random effect: with only 2 levels the sigma (L~N(0,sigmaL 
and U~N(0,sigmaU) would be a bad estimate due to only two levels. Also 
some literature suggests to use random effects if there are at least 3 
or 5 levelsbut they give no direction how to cope if there are only 2 
levels.

I would be very happy if someone could give me some hints how to cope 
with partially nested variables  and few levels.

Fabio

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