Multilevel modeling, lots of levels

Alexis Le Nestour writes:

I am currently fitting a model explaining the probability of seeking a treatment in Senegal. I have 4513 observations at the individual level nested in 505 households. Our sampling was a two stage stratified sampling procedure. Our clusters are farming organizations picked up in function of their size, then we randomly chose 5 households per farming organization and finally we interviewed all the household members.

The log likelihood ratio test shows me that it’s worth to add a random intercept at the household level. It makes sense to me, people in the same household share some unobservable characteristics. But my issue is to add or not another level and which level.

– I can add the farming organization as a level. It is maybe the most logical in regard with my sampling procedure. But people from the same farming organization are not necessarily neighbors. It’s often the case but not always. There are 93 farming organizations.
– Since my households are nested in villages, I could use the villages as a level. It would make sense as well because there is some unobservable heterogeneity in villages and they face the same health offer. I have 39 villages.
– The last solution is to use the health facilities as a cluster. We interviewed the 16 health facilities of the area and we can cluster households by facilities. We consider that they usually go to the closest facility. But I fear that the number of clusters would be too low for a multilevel modeling.

I have some covariates at the individual level (age, gender, education), some at the household level (wealth, insurance, size), some at the village level (distance to the closest health facility) and some at the facility level (prices and quality). When I fit the model with any of the levels above, the log likelihood tests show me that it fits the data better than a 2 level model. The log likelihoods for the 3 specifications are very close and the coefficients don’t vary a lot from a specification to another.

Is there a way to know which level I should use? According to you, which one would make more sense?

My recommendation: Why not simply use all these levels? That would seem to make the most sense to me. And there’s no need for these levels to be nested.