Some Models in Relational Systems
This dissertation contains two distinct parts. The first part presents a theory for the observation process in surveys of human populations. Focus resides on the effect of survey instrument structure on the observed responses. If the effect of instrument structure on a survey question can be estimate and certain exchangeability conditions hold, sampling from the set of all possible survey instrument structures provides a way to assess the observed sample. This part then introduces probability distributions that aggregate over the of possible instrument structures thereby defining a way to view data without an instrument structure. Methods to incorporate instrument structure are demonstrated in several examples including a survey of a large organization. This dataset requires new techniques to account for dependence between units in the population. The second part introduces a method to estimate latent networks of interacting nodes when a group-level response variable is available. In large populations, the number of possible ties between nodes grows large. The models named CoordiNet and TriadNet place a prior over the dyads included in the model for the group-level response. Doing so induces parsimony in the estimated social structures. This method is applied to data from professional sports.