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I am trying to fit multilevel logistic regression of binge drinking (vs non-binge drinking) using cross-sectional data and complete cases analysis, which has a four-level hierarchical structure (pupils / classes / schools / municipalities). After fitting an empty model using second order penalised quasi-likelihood, between-municipalities variance parameters are equal to 0. However, after adding to the model child’s age, the variance estimate is different to 0, even though not significant. The levels were added to the empty model sequentially starting by classes, then schools and then municipalities. The same estimates were shown after fitting an empty model stratified by gender. In this case when the random effect parameters at municipality level are equal to 0, does it mean that the variance at municipality level is negligible in the empty model? Or have I made something wrong or missed something? Attached is a document with outputs.
With many thanks,
Francisca

Dear Francisca,

An estimate of zero for the level-4 variance looks a bit strange. You don't appear to have done anything obviously wrong in terms of your runmlwin syntax so the answer probably lies with your data. It would be worth trying to fit the model by MQL1, MQL2, PQL1 and especially MCMC to compare your results. More generally it would be worth simply calculating and plotting the observed proportion of binge drinkers in each municipality to see what the observed variation looks like.

Best wishes

George