Could you please help me out with notation in lme4?

I am trying to implement a bivariate outcome (Poisson response with offset N) over incidence of 2 diseases, dis1 and dis2, using dummy indicators, dis1 and dis2, and fixed effects duplicated into dis1*fixed_eff_i and dis2*fixed_eff_i.  My data is nested in states, counties, and diseases (possibly, also genders).  Could you please help me to check that the following notation corresponds to 3-level model?

Out  <- glmer(formula = Outcomes ~ 1 + offset(log(N)) + (0 + dis1|State) + (0 + dis2|County) + (0 + dis1|State) + (0 + dis2|County) + dis1.Gender + dis2.Gender, naGQ = 7,verbose=FALSE,family=poisson,REML=FALSE,data=data,na.action = na.exclude, maxIter=200000, maxFn=10000000)")

Would be very grateful for any clarification/correction.

Thank you!

Andy


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