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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
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.

References

Ackerman, R. A., Kashy, D. A., & Corretti, C. A. (2015). A tutorial on analyzing data from speed-dating studies with heterosexual dyads. Personal Relationships, 22 92– 110. CrossRefGoogle Scholar
Alexandrowicz, R. W., Stemmler, M., von Eye, A., & Wiedermann, W. (2015). Analyzing dyadic data with IRT models. Dependent data in social sciences research, New York: Springer. 173– 202. CrossRefGoogle Scholar
Back, M. D., & Kenny, D. A. (2010). The social relations model: How to understand dyadic processes. Social and Personality Psychology Compass, 4 855– 870. CrossRefGoogle Scholar
Bagozzi, R. P., & Ascione, F. J. (2005). Inter-role relationshis in hospital-based pharmacy and therapeutics committee decision making. Journal of Health Psychology, 10, 45– 64. CrossRefGoogle Scholar
Bakk, Z., & Kuha, J. (2018). Two-step estimation of models between latent classes and external variables. Psychometrika, 83 871– 892. CrossRefGoogle ScholarPubMed
Bonito, J. A., & Kenny, D. A. (2010). The measurement of reliability of social relations components from round-robin designs. Personal Relationships, 17, 235– 251. CrossRefGoogle Scholar
Burt, R. S. (1976). Interpretational confounding of unobserved variables in structural equation models. Sociological Methods & Research, 5, 3– 52. CrossRefGoogle Scholar
Card, N. A., Little, T. D., & Selig, J. P. Card, N. A., Little, T. D., & Selig, J. P. (2008). Using the bivariate social relations model to study dyadic relationships: Early adolescents’ perceptions of friends’ aggression and prosocial behavior. Modeling dyadic and interdependent data in the developmental and behavioral sciences, New York: Routledge. 245– 276. Google Scholar
Christensen, P. N., & Kashy, D. A. (1998). Perceptions of and by lonely people in initial social interactions. Personality and Social Psychology Bulletin, 24, 322– 329. CrossRefGoogle Scholar
Cockerham, C. C., & Weir, B. S. (1977). Quadratic analysis of reciprocal crosses. Biometrics, 33, 187– 203. CrossRefGoogle ScholarPubMed
De Boeck, P., & Wilson, M. (2004). Explanatory item response models: A generalized linear and nonlinear approach, New York: Springer. CrossRefGoogle Scholar
Dorff, C., & Ward, M. D. (2013). Networks, dyads, and the social relations model. Political Science Research and Methods, 1, 159– 178. CrossRefGoogle Scholar
Fisman, R., Iyengar, S. S., Kamenica, E., & Simonson, I. (2006). Gender differences in mate selection: Evidence from a speed dating experiment. The Quarterly Journal of Economics, 121 673– 697. CrossRefGoogle Scholar
Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models. Bayesian Analysis, 1, 515– 533. CrossRefGoogle Scholar
Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7 457– 472. CrossRefGoogle Scholar
Gill, P. S., & Swartz, T. B. (2001). Statistical analyses of round robin interaction data. Canadian Journal of Statistics, 82, 321– 331. CrossRefGoogle Scholar
Goldstein, H. (1987). Multilevel variance components models. Biometrika, 74, 430– 431. CrossRefGoogle Scholar
Gollob, H. F. (1968). A statistical model which combines features of factor analytic and analysis of variance techniques. Psychometrika, 33, 73– 115. CrossRefGoogle ScholarPubMed
Gong, G., & Samaniego, F. J. (1981). Pseudo maximum likelihood estimation: Theory and applications. The Annals of Statistics, 74, 861– 869. Google Scholar
Hoff, P. D. (2005). Bilinear mixed-effects models for dyadic data. Journal of the American Statistical Association, 100, 286– 295. CrossRefGoogle Scholar
Hoff, P. D. (2015). Dyadic data analysis with amen. arXiv:1506.08237.Google Scholar
Hoffman, M. D., & Gelman, A. (2014). The No-U-Turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research, 15, 1593– 1623. Google Scholar
Jeon, M., Rijmen, F., & Rabe-Hesketh, S. (2017). A variational maximization-maximization algorithm for generalized linear mixed models with crossed random effects. Psychometrika, 82, 693– 716. CrossRefGoogle Scholar
Kenny, D. A. (1994). Interpersonal perception: A social relations analysis, New York: Guilford. Google ScholarPubMed
Kenny, D. A. (1996). Models of nonindependence in dyadic research. Journal of Social and Personal Relationships, 13 279– 294. CrossRefGoogle Scholar
Kenny, D. A., & Kashy, D. A. (1994). Enhanced co-orientation in the perception of friends: A social relations analysis. Journal of Personality and Social Psychology, 67, 1024– 1033. CrossRefGoogle ScholarPubMed
Kenny, D. A., Kashy, D. A., & Cook, W. L. (2006). Dyadic data analysis, New York: Guilford. Google Scholar
Kenny, D. A., & La Voie, L. (1984). The social relations model. Advances in Experimental Social Psychology, 18, 141– 182. CrossRefGoogle Scholar
Koster, J. M., & Brandy, A. (2018). The effects of individual status and group performance on network ties among teammates in the National Basketball Association. PLoS ONE, 13, e0196013. CrossRefGoogle ScholarPubMed
Koster, J. M., & Leckie, G. (2014). Food sharing networks in lowland Nicaragua: An application of the social relations model to count data. Social Networks, 38, 100– 110. CrossRefGoogle Scholar
Li, H. Loken, E. (2002). A unified theory of statistical analysis and inference for variance components models for dyadic data. Statistica Sinica, 12, 519– 535. Google Scholar
Loncke, J., Eichelsheim, V. I., Branje, S. J. T., Buysse, A., Meeus, W. H. J., & Loeys, T (2018). Factor score regression with social relations model components: A case study exploring antecedents and consequences of perceived support in families. Frontiers in Psychology, 9, 1699 CrossRefGoogle ScholarPubMed
Lüdtke, O., Robitzsch, A., Kenny, D. A., & Trautwein, U. (2013). A general and flexible approach to estimating the social relations model using Bayesian methods. Psychological Methods, 18, 101– 119. CrossRefGoogle ScholarPubMed
Lüdtke, O., Robitzsch, A., & Trautwein, U. (2018). Integrating covariates into social relations models: A plausible value approach for handling measurement error in perceiver and target effects. Multivariate Behavioral Research, 53, 102– 124. CrossRefGoogle ScholarPubMed
Malloy, T. E., & Kenny, D. A. (1986). The social relations model: An integrative method for personality research. Journal of Personality, 54, 199– 225. CrossRefGoogle Scholar
Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149– 174. CrossRefGoogle Scholar
Metropolis, N., & Ulam, S. (1949). The Monte Carlo method. Journal of the American Statistical Association, 44, 335– 341. CrossRefGoogle ScholarPubMed
Nestler, S. (2018). Likelihood estimation of the multivariate social relations model. Journal of Educational and Behavioral Statistics, 43, 387– 406. CrossRefGoogle Scholar
Nestler, S., Geukes, K., Hutteman, R., & Back, M. D. (2017). Tackling longitudinal round-robin data: A social relations growth model. Psychometrika, 82, 1162– 1181. CrossRefGoogle Scholar
Rubin, D. B. (1987). Multiple imputation for nonresponse in surveys, New York: Wiley. CrossRefGoogle Scholar
Sim, N., Gin, B., Skrondal, A., & Rabe-Hesketh, S. (2019). A dyadic item response theory model: Stan case study. Stan Case Studies, 6. https://mc-stan.org/users/documentation/case-studies/dyadic_irt_model.html.Google Scholar
Skrondal, A., & Kuha, J. (2012). Improved regression calibration. Psychometrika, 77, 649– 669. CrossRefGoogle Scholar
Skrondal, A., & Laake, P. (2001). Regression among factor scores. Psychometrika, 66, 563– 575. CrossRefGoogle Scholar
Snijders, T. A. B., & Kenny, D. A. (1999). The social relations model for family data: A multilevel approach. Personal Relationships, 6, 471– 486. CrossRefGoogle Scholar
Stan Development Team. (2018a). RStan: The R interface to Stan. R package version, 2(17), 3.Google Scholar
Stan Development Team. (2018b). Stan modeling language users guide and reference manual, version 2.18.0.Google Scholar
van der Linden, W. J. (2016). Handbook of item response theory. Volume one: Models, Boca Raton: CRC Press. CrossRefGoogle Scholar
Warner, R., Kenny, D. A., & Stoto, M. (1979). A new round robin analysis of variance for social interaction data. Journal of Personality and Social Psychology, 37, 1742– 1757. CrossRefGoogle Scholar
White, I. R. (2010). simsum: Analysis of simulation studies including Monte Carlo error. The Stata Journal, 10, 369– 385. CrossRefGoogle Scholar
Wong, G. Y. Round robin analysis of variance via maximum likelihood. Journal of the American Statistical Association, (1982). 77, 714– 724. CrossRefGoogle Scholar
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