[R-sig-ME] Within-group correlation structures

[Jeremy Koster]

Imagine that you are studying 100 people, divided into 25 groups of 4 people each.  You observe each of these groups at 50 randomly-selected times over the course of the year, and during each observation you note which individuals are doing a particular activity, such as smoking.

You thus have a dataset with 5,000 person-level observations.  The dataset has a header row that includes variables for:

Date/time of observation
Group name
Individual name
Smoking or not (binary)

You prepare to set up a logistic regression model.  Individuals vary in their propensities for smoking, so you specify a random effect for the individual people.  The groups might also vary in their overall propensity for smoking, so you nest the individual-level random effect within a group-level random effect.

Okay, how would you examine the within-group correlation of smoking during the same observation?  That is, imagine that these tend to be social smokers, so if one person is smoking during the observation, there's a good chance that others in the group will also be smoking?

Could one specify "Date/time of observation" as a random effect since only one group was observed at a time and therefore each date/time combo will be unique to the members of that group?  Could that factor then be included as a random effect in a cross-classified model (while preserving the nested "individual within group" random effect)?

Are there alternatives?