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Hi,

I am running a logistic multilevel model with approximately 200,000 individuals nested in 50 states. My interest is in the state level coefficients as contextual explanatory variables. A complicating factor is that 23% of the cases are individuals that are further clustered by household (usually two people per household, but occasionally 3 or 4 per household).

If I run a 3 level empty model with MQL1 (won’t converge with PQL2) the residual household variance is 0.027(0.106) state residual variance is 0.031 (0.009). If I run MCMC residual household variance is 0.0 (0.0) and the state residual variance is 0.032 (0.009).

I haven't been able to find any literature relevant to this situation. Is it reasonable to run this as a two level model with just individuals nested within states?

Many thanks in advance

Shane

HI Shane,
It looks like in MQL1 that although a household variance is picked up it has a very large standard error which might suggest uncertainty that there are really significant household effects.
I would suggest checking that your hierarchy is correct i.e. that the data is sorted correctly. I would also suggest ensuring that the MCMC algorithm has converged and that you have run for
long enough. Given the size of your data if you were worried about households affecting estimates you could always sample just 1 individual from each household or look at whether there
is any noticeable difference in estimates when you do/do not keep the level in the model.
Best wishes,
Bill.