Measuring Dynamical Interdependence in Small-Group Collaborations


  • Peter Halpin University of North Carolina



collaboration, interdependence, process data, temporal analytics, psychometrics


This paper addresses dynamical interdependence among the actions of group members. I assume that the actions of each member can be represented as nodes of a dynamical network and then collect the nodes into disjoint subsets (components) representing the individual group members. Interdependence among group members’ actions can then be defined with reference to a K-partite network, in which the partitions correspond to the group member components. Independence among group members’ actions can be defined with reference to a network in which the group member components are disconnected from one another. The degree to which the interactions of actual groups correspond to either of these theoretical network structures can be characterized using modified versions of existing network statistics. Taking this approach, I propose a number of network-based measures of dynamical interdependence, discuss the interpretation of the proposed measures, and consider how to assess their reliability and validity. These ideas are illustrated using an example in which dyads collaborated via online chat to complete a grade 12 level mathematics assessment.


Adams, R., Vista, A., Scoular, C., Awwal, N., Griffin, P., & Care, E. (2015). Automatic coding procedures for collaborative problem solving. In P. Griffin & E. Care (Eds.),Assessment and Teaching of 21st Century Skills(pp. 115–132). Dordrecht: Springer Netherlands.

Andrews-Todd, J., & Forsyth, C. M. (2020). Exploring social and cognitive dimensions of collaborative problem solving in anopen online simulation-based task. Computers in Human Behavior,104, 105759.

Attali, Y., & Burstein, J. (2014). Automated essay scoring with e-rater®V.2.The Journal of Technology, Learning andAssessment,4(2), i–21.

Barrat, A., Barthelemy, M., & Vespignani, A. (2011). Dynamical Processes on Complex Networks. Cambridge, UK: Cambridge University Press.

Butts, C. T. (2008).A relational event framework for social action. Sociological Methodology,38(1), 155–200.

Chen, B., Knight, S., & Wise, A. F. (2018). Critical issues in designing and implementing temporal analytics. Journal of Learning Analytics,5(1), 1–9.

Chen, S., Lawrence, J. F., Zhou, J., Min, L., & Snow, C. E. (2018). The efficacy of a school-based book-reading intervention on vocabulary development of young Uyghur children: A randomized controlled trial. Early Childhood Research Quarterly,44, 206–219.

Chi, M. T. H., & Wylie, R. (2014). The ICAP framework: Linking cognitive engagement to active learning outcomes. Educational Psychologist,49(4), 219–243.

Cohen, E. G. (1994). Restructuring the classroom: Conditions for productive small groups. Review of Educational Research,64(1), 1–35.

Daley, D. J., & Vere-Jones, D. (2003). An Introduction to the Theory of Point Processes(2nd ed.). New York: Springer.

Davis, J. H. (1992). Some compelling intuitions about group consensus decisions, theoretical and empirical research, and interpersonal aggregation phenomena: Selected examples, 1950–1990.Organizational Behavior and Human DecisionProcesses,52(1), 3–38.

Dowell, N. M. M., Nixon, T. M., & Graesser, A. C. (2019). Group communication analysis: A computational linguistics approach for detecting sociocognitive roles in multiparty interactions. Behavior Research Methods,51(3), 1007–1041.

Durbin, J., & Koopman, S. J. (2012).Time Series Analysis by State Space Methods. Oxford, UK: Oxford University Press.

Griffin, P., & Care, E. (2015). Assessment and Teaching of 21st Century Skills: Methods and Approach. New York: Springer.

Halpin, P. F., & Bergner, Y. (2018). Psychometric models of small group collaborations. Psychometrika, 83, 941–962.

Halpin, P. F., von Davier, A. A., Hao, J., & Liu, L. (2017). Measuring student engagement during collaboration. Journal of Educational Measurement,54(1), 70–84.

Hanneman, R. A., & Riddle, M. (2014). Concepts and measures for basic network analysis. In The Sage Handbook of Social Network Analysis (pp. 340–369). London, UK: SAGE Publications Ltd.

Hao, J., Chen, L., Flor, M., Liu, L., & von Davier, A. A. (2017). CPS-rater: Automated sequential annotation for conversations in collaborative problem-solving activities.ETS Research Report Series,2017(1), 1–9.

Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning(2nd ed.). New York: Springer.

Johnson, D. W., & Johnson, R. T. (2009). An educational psychology success story: Social interdependence theory and cooperative learning. Educational Researcher,38(5), 365–379.

Joint Committee for Educational and Psychological Testing. (2014). Standards for Educational and Psychological Testing. Washington, DC: AERA APA, & NCME. Jost, J. (2007). Dynamical networks. In J. Feng, J. Jost, & M. Qian (Eds.), Networks: From Biology to Theory (pp. 35–62).London, UK: Springer.

Knight, S., Friend Wise, A., & Chen, B. (2017). Time for change: Why learning analytics needs temporal analysis. Journal of Learning Analytics,4(3), 7–17.

Kozlowski, S. W. J., & Chao, G. T. (2018). Unpacking team process dynamics and emergent phenomena: Challenges, conceptual advances, and innovative methods. American Psychologist,73(4), 576–592.

Laughlin, P. R. (2013). Group Problem Solving. Princeton, NJ, USA: Princeton University Press. Retrieved from

Leenders, R. T. A. J., Contractor, N. S., & DeChurch, L. A. (2016). Once upon a time: Understanding team processes as relational event networks. Organizational Psychology Review, 6(1), 92–115.

Liu, L., Hao, J., von Davier, A. A., Kyllonen, P., & Zapata-Rivera, D. (2015). A tough nut to crack: Measuring collaborative problem solving. In Y. Rosen, S. Ferrara, & M. Mosharraf (Eds.), Handbook of Research on Computational Tools for Real-World Skill Development (pp. 344–359). Hershey, PA, USA: IGI-Global.

Lord, F. M. (1980). Applications of Item Response Theory to Practical Testing Problems. New York: Routledge.

Lorge, I., & Solomon, H. (1955). Two models of group behavior in the solution of eureka-type problems. Psychometrika, 20(2), 139–148.

Lutkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Berlin, New York: Springer.

Madhyastha, T. M., Hamaker, E. L., & Gottman, J. M. (2011). Investigating spousal influence using moment-to-moment affect data from marital conflict. Journal of Family Psychology, 25(2), 292–300.

Mathieu, J. E., Tannenbaum, S. I., Donsbach, J. S., & Alliger, G. M. (2014). A review and integration of team composition models: Moving toward a dynamic and temporal framework. Journal of Management, 40(1), 130–160.

Mehrabi, N., Morstatter, F., Saxena, N., Lerman, K., & Galstyan, A. (2019). A survey on bias and fairness in machine learning. (arXiv:1908.09635)

Mohan, K., Bergner, Y., & Halpin, P. (2020). Predicting group performance using process data in a collaborative assessment. Technology, Knowledge and Learning, 25, 367–388.

Molenaar, P. C. M. (1985). A dynamic factor model for the analysis of multivariate time series. Psychometrika, 50(2), 181–202.

Oehlert, G. W. (1992). A note on the delta method. The American Statistician, 46(1), 27–29.

Oviatt, S., Schuller, B., Cohen, P., Sonntag, D., Potamianos, G., & Kr¨uger, A. (2018). The Handbook of Multimodal-Multisensor Interfaces: Signal Processing, Architectures, and Detection of Emotion and Cognition (Vol. 2). Morgan & Claypool.

Quera, V. (2018). Analysis of interaction sequences. In E. Brauner, M. Boos, & M. Kolbe (Eds.), The Cambridge Handbook of Group Interaction Analysis (1st ed., pp. 295–322). Cambridge University Press.

Rack, O., Zahn, C., & Mateescu, M. (2018). Coding and counting: Frequency analysis for group interaction research. In E. Brauner, M. Boos, & M. Kolbe (Eds.), The Cambridge Handbook of Group Interaction Analysis (1st ed., pp. 277–294). Cambridge University Press.

Spedicato, G. A. (2017). Discrete time Markov chains with R. The R Journal, 9(2), 84.

Suthers, D. D., Dwyer, N., Medina, R., & Vatrapu, R. (2010). A framework for conceptualizing, representing, and analyzing distributed interaction. International Journal of Computer-Supported Collaborative Learning, 5(1), 5–42.

Swiecki, Z., Ruis, A. R., Farrell, C., & Shaffer, D. W. (2019). Assessing individual contributions to collaborative problem solving: A network analysis approach. Computers in Human Behavior, 104, 105876.

Teasley, S. D. (1997). Talking about reasoning: How important is the peer in peer collaboration? In L. B. Resnick, R. Saljo, C. Pontecorvo, & B. Burge (Eds.), Discourse, Tools and Reasoning: Essays on Situated Cognition (pp. 361–384). Berlin, Heidelberg: Springer. 16

Thissen, D., & Wainer, H. (2001). Test Scoring. Mahwah, NJ, USA: Lawrence Earlbaum Associates.

Woolley, A. W., Chabris, C. F., Pentland, A., Hashmi, N., & Malone, T. W. (2010). Evidence for a collective intelligence factor in the performance of human groups. Science, 330(6004), 686–688.




How to Cite

Halpin, P. (2021). Measuring Dynamical Interdependence in Small-Group Collaborations. Journal of Learning Analytics, 8(1), 95-112.



Special Section: Collaboration Analytics