Multiple membership model

I am studying employee wages, with industries and occupations as cross-classified level-2 predictors. Someone advises me to consider time trend too.

Your advice on how to consider the structure of data will be highly appreciate! I am wondering industry, occupation, and year are not measuring the similar dimensions, so it might not make sense to put all of them on level 2 as below:
Level-2: industry, occupation, time
Level-1: individuals

What might be other options? Can I do the following?
level-3: time
level-2: industry, occupation
level-1: individual


If you’re thinking of the levels as cross-classified (which seems to make sense), then it’s not clear how you’re thinking of putting industry and occupation on the “same” level (the data don’t seem to be hierarchical).

Also, it’s not clear where the multiple membership structure comes into play. Is this because individual employees switch between industries and occupations?

Hi Jeremy,

Thanks for your reply!

Just because industry and occupation are not hierarchical, I put them as cross-classified.

Individuals do not switch. Each individual belongs to one industry and one occupation. Industry and occupation compose sparse matrix as below.

My question is, if I want to add time trend, is that possible? Seems not, right?

occ 1	occ 2	occ 3	occ 4

ind1 5 20 7 0

ind2 0 5 4 100

ind3 500 10 0 48


Hi Tracy,

I’m not entirely clear on the data structure. Are there repeated observations of employees at different time points, or does the time element simply refer to the fact that data come from multiple years?

In the former case, the repeated observations of individuals would probably merit a random effect (varying intercept) to account for the non-independence.

In general, for both scenarios, it seems straightforward to model time. If you data span, for example, 2000 to 2010, then after centering your variable, you could estimate an effect of time on wages. We did something similar to test the possibility that hunting returns decline over time (perhaps due to hunting in depleted environments):