Ken Lee writes:

I have reviewing approaches to applying MLM to longitudinal data. It appears straightforward in the examples (and papers) I have reviewed that the time-based data is used at the lowest level. Many examples then use individuals as the second level; and second-level time invariant variables such as gender to represent the individual. My questions:

– do second-level variables have to be time-invariant? and, similarly, would third level variables have to be time-invariant and, say, invariant across individuals?

– if so, then if the second-level variable is geographical (county, state, country), most variables associated with the geographic level vary with time — so what kind of variables would you recommend that would be time-invariant?

– if not, as long as, say, state-level median income is used, or state-level population, or state-level voting results – even though they vary over time – is that a satisfactory choice of variables?

– is the interpretation of second-level effect affected by a non-time-invariant variable?

My reply: You can include all predictors at the data level if you’d like. If a predictor doesn’t vary over time, it can be convenient to include it at the level of persons (the second level, in your example) but it’s not strictly necessary. See chapters 11 and 12 for more discussion of this sort of issue.