  We propose a dyadic Item Response Theory (dIRT) model for measuring
interactions of pairs of individuals when the responses to items represent the
actions (or behaviors, perceptions, etc.) of each individual (actor) made
within the context of a dyad formed with another individual (partner). Examples
of its use include the assessment of collaborative problem solving, or the
evaluation of intra-team dynamics. The dIRT model generalizes both Item
Response Theory (IRT) models for measurement and the Social Relations Model
(SRM) for dyadic data. The responses of an actor when paired with a partner are
modeled as a function of not only the actor's inclination to act and the
partner's tendency to elicit that action, but also the unique relationship of
the pair, represented by two directional, possibly correlated, interaction
latent variables. Generalizations are discussed, such as accommodating triads
or larger groups. Estimation is performed using Markov-chain Monte Carlo
implemented in Stan, making it straightforward to extend the dIRT model in
various ways. Specifically, we show how the basic dIRT model can be extended to
accommodate latent regressions, multilevel settings with cluster-level random
effects, as well as joint modeling of dyadic data and a distal outcome. A
simulation study demonstrates that estimation performs well. We apply our
proposed approach to speed-dating data and find new evidence of pairwise
interactions between participants, describing a mutual attraction that is
inadequately characterized by individual properties alone.
