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A Dyadic IRT Model

Published online by Cambridge University Press:  01 January 2025

Brian Gin Open the ORCID record for Brian Gin [Opens in a new window] ,
Nicholas Sim Open the ORCID record for Nicholas Sim [Opens in a new window] ,
Anders Skrondal Open the ORCID record for Anders Skrondal [Opens in a new window]  and
Sophia Rabe-Hesketh Open the ORCID record for Sophia Rabe-Hesketh [Opens in a new window]
Brian Gin
Affiliation:
University of California, San Francisco
Nicholas Sim*
Affiliation:
University of California, Berkeley
Anders Skrondal
Affiliation:
Norwegian Institute of Public Health University of Oslo University of California, Berkeley
Sophia Rabe-Hesketh
Affiliation:
University of California, Berkeley
*
Correspondence should be made to Nicholas Sim, University of California, Berkeley, 2121 Berkeley Way, Berkeley, CA94720, USA. Email: sim_nicholas@berkeley.edu
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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 models for measurement and the Social Relations Model 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.

Keywords

item response theorysocial relations modeldyadic dataMarkov-chain Monte CarloStan

Information

Type
Application Reviews and Case Studies
Information
Psychometrika , Volume 85 , Issue 3 , September 2020 , pp. 815 - 836
Copyright
Copyright © 2020 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11336-020-09718-1) contains supplementary material, which is available to authorized users.

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