Because we are interested in the quartiles of NHses, which already reduces the 200 neighbourhoods into 5 categories, I thought we'd already have the issue of small cell size covered. Is there any reason why NHses can't go in the position of habneigh2? Or does habneigh2 have to remain at the top level in the code because it's the initial sampling frame and most fine grain option available.
By the way, my earlier suggestion to split income around the median was based on computational considerations only: it would minimize the number of tiny interactions between neighborhood and income. And, again, not knowing anything about your data or your research question beyond what you disclose, I could not know that doing that would obstruct the pursuit of your specific research goals. Certainly, there is no point in getting a computationally improved model that doesn't answer the research question! Were it not for the NHses (or similar) solution to the problem of cutting things too fine, it probably would have meant that your data set is incapable of addressing your research question. But it is likely that if you replace habneigh2 by NHses and return to your original income09 classification scheme (without the non-response category) you will get a usable answer.
Added: By replacing habneigh2 with NHses you will lose the ability to estimate variation down to the fine-grained neighborhood level. But it is by now apparent that your data set is not capable of providing that level of detail in any case. I raise this point simply to emphasize that you need to evaluate all modeling options relative to the specific research questions you are trying to ask. I'm getting the impression that variation at the fine-grained neighborhood level is not actually that important to you in any case that you are mostly interested in socio-economic effects anyway.
Also added: With only 5 categories of NHses, it's not at all clear that you need a multi-level model for this. You can just leave NHses as a fixed effect here and include its interactions with income09 in the model. With just 5 categories, your variance estimates for NHses itself and the random slopes are going to be very imprecise: for those parameters it is more or less as if you were doing a study with a sample size of 5.
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