Experimental condition with multilevel model

Question

I am working with a survey experiment. The data is set at three levels: individual, county, and state.

The experimental condition was randomized at the individual level 1. That is, some individuals in a county received the experimental condition while others did not.

How should I set the random intercept, multilevel model? I want the model to know that the experimental condition was set at the level 1.

I am working with this baseline model:

library(lme4)

model1 <- lmer(outcome ~ 1 + experimental.condition + (1|state) + 
                         (1|state:city), REML=FALSE, data = df)

Is this correct?

Answer 1

If your "city" random effect here is supposed to be "county", then your model would be correct. Otherwise, if you were trying to fit states, counties, and cities, it would instead be this:

library(lme4)

model1 <- lmer(outcome ~ 1 + experimental.condition + 
                (1|state/county/city), REML=FALSE, data = df)

This is also assuming that the individuals didn't have their own cluster due to repeated measurements, which I'm guessing isn't the case from what you described.