# A Dyadic IRT Model

## TL;DR

This paper introduces a dyadic Item Response Theory model that captures interactions between pairs of individuals, extending traditional IRT and social relations models, with applications demonstrated on speed-dating data.

## Contribution

It develops a novel dyadic IRT model incorporating pair-specific latent variables, generalizes to larger groups, and provides a flexible estimation framework using Stan.

## Key findings

- Effective estimation demonstrated via simulation
- Revealed pairwise interactions in speed-dating data
- Identified mutual attraction beyond individual traits

## Abstract

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.