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A Dyadic IRT Model

Author

Listed:
  • Brian Gin

    (University of California, San Francisco)

  • Nicholas Sim

    (University of California, Berkeley)

  • Anders Skrondal

    (Norwegian Institute of Public Health
    University of Oslo
    University of California, Berkeley)

  • Sophia Rabe-Hesketh

    (University of California, Berkeley)

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.

Suggested Citation

  • Brian Gin & Nicholas Sim & Anders Skrondal & Sophia Rabe-Hesketh, 2020. "A Dyadic IRT Model," Psychometrika, Springer;The Psychometric Society, vol. 85(3), pages 815-836, September.
    • Handle: RePEc:spr:psycho:v:85:y:2020:i:3:d:10.1007_s11336-020-09718-1
    DOI: 10.1007/s11336-020-09718-1
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    References listed on IDEAS

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    1. Bakk, Zsuzsa & Kuha, Jouni, 2018. "Two-step estimation of models between latent classes and external variables," LSE Research Online Documents on Economics 85161, London School of Economics and Political Science, LSE Library.
    2. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
    3. Skrondal, Anders & Kuha, Jouni, 2012. "Improved regression calibration," LSE Research Online Documents on Economics 44135, London School of Economics and Political Science, LSE Library.
    4. Anders Skrondal & Jouni Kuha, 2012. "Improved Regression Calibration," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 649-669, October.
    5. Raymond Fisman & Sheena S. Iyengar & Emir Kamenica & Itamar Simonson, 2006. "Gender Differences in Mate Selection: Evidence From a Speed Dating Experiment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(2), pages 673-697.
    6. Steffen Nestler & Katharina Geukes & Roos Hutteman & Mitja D. Back, 2017. "Tackling Longitudinal Round-Robin Data: A Social Relations Growth Model," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1162-1181, December.
    7. Zsuzsa Bakk & Jouni Kuha, 2018. "Two-Step Estimation of Models Between Latent Classes and External Variables," Psychometrika, Springer;The Psychometric Society, vol. 83(4), pages 871-892, December.
    8. Ian R. White, 2010. "simsum: Analyses of simulation studies including Monte Carlo error," Stata Journal, StataCorp LP, vol. 10(3), pages 369-385, September.
    9. Minjeong Jeon & Frank Rijmen & Sophia Rabe-Hesketh, 2017. "A Variational Maximization–Maximization Algorithm for Generalized Linear Mixed Models with Crossed Random Effects," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 693-716, September.
    10. Harry Gollob, 1968. "A statistical model which combines features of factor analytic and analysis of variance techniques," Psychometrika, Springer;The Psychometric Society, vol. 33(1), pages 73-115, March.
    11. Dorff, Cassy & Ward, Michael D., 2013. "Networks, Dyads, and the Social Relations Model," Political Science Research and Methods, Cambridge University Press, vol. 1(2), pages 159-178, December.
    12. Jeremy Koster & Brandy Aven, 2018. "The effects of individual status and group performance on network ties among teammates in the National Basketball Association," PLOS ONE, Public Library of Science, vol. 13(4), pages 1-18, April.
    13. Anders Skrondal & Petter Laake, 2001. "Regression among factor scores," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 563-575, December.
    14. Peter D. Hoff, 2005. "Bilinear Mixed-Effects Models for Dyadic Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 286-295, March.
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