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

[Steven J. Pierce]

Jeremy,

You might want to look into social network analysis methods, specifically
for influence models. They allow you to represent how the behavior of other
people in one's network (called "alters") affect the focal person's (called
the "ego") own behavior. You can of course also have predictors in these
models for the ego's own characteristics as well. 

Steven J. Pierce, Ph.D. 
Associate Director 
Center for Statistical Training & Consulting (CSTAT) 
Michigan State University 
178 Giltner Hall 
East Lansing, MI 48824 
E-mail: pierces1 at msu.edu 
Web: http://www.cstat.msu.edu 

-----Original Message-----
From: Jeremy Koster [mailto:helixed2 at yahoo.com] 
Sent: Thursday, September 15, 2011 12:16 PM
To: r-sig-mixed-models at r-project.org
Subject: [R-sig-ME] Within-group correlation structures

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?