A latent space representation of overdispersed relative propensity in “How many X’s do you know?” data

We present a novel latent space representation of the relative propensity for a respondent to form ties with members of a particular social group, a quantity related to overdispersion. In many applications collecting complete network data is financially or practically infeasible. Instead, we use data where respondents are asked for the number of ties they have with members of various subpopulations or “How many X’s do you know?” data. We connect this data with recent work using models which represent dependence in a fully observed network through distance in an unobservable “social space,” known as latent space models (Hoff et al., 2002). This yields a latent space representation of overdispersion, further elucidates how these data measure social structure indirectly, and suggests a latent space model for such data.