Analyzing choice data

Mathis Schulte writes,

We have collected 3 waves of survey data from 80 teams of approximately 12 people each. Each team has a formally designated leader. At Time 3, we asked an open ended question: “If you had to choose one member from your team (not including yourself) to be your team’s new leader, who would you choose? Please write this person’s first and last name in the space below.”

We regard this as a measure of emergent leadership and want to predict the number of ‘votes’ (or nominations) a person receives from his/her team members with predictors at multiple levels (characteristics of voter, votee, and team). But clearly, there’s negative interdependence among the team members’ votes (i.e., the more votes one team member gets, the fewer votes other team members can get).

What can we do to use ‘votes’ as our DV?

That’s a good question. My first thought is that 12 is enough people in a group that you can pretty much ignore the correlation and just do the analysis. Strictly speaking, it’s an unordered multinomial outcome, and there are models for these, but maybe it’s simplest to start with something like a logistic regression predicting the probabilty that person i picks person j. If you model #votes as an outcome, I’d be sure to use an overdispersed model (rather than a straight binomial or Poisson). You also might want to use jackknife or bootstrap (on the 80 groups) to get standard errors.

The problem is so open-ended, though, that I expect there are a lot of good solutions that you’d only think of after playing with the data.