Mapping Temporal Dynamics in Social Interactions With Unified Structural Equation Modeling: A Description and Demonstration Revealing Time-Dependent Sex Differences in Play Behavior

Abstract

Developmental science is rich with observations of social interactions, but few available methodological and statistical approaches take full advantage of the information provided by these data. The authors propose implementation of the unified structural equation model (uSEM), a network analysis technique, for observational data coded repeatedly across time; uSEM captures the temporal dynamics underlying changes in behavior at the individual level by revealing the ways in which a single person influences—concurrently and in the future—other people. To demonstrate the utility of uSEM, the authors applied it to ratings of positive affect and vigor of activity during children's unstructured laboratory play with unfamiliar, same-sex peers. Results revealed the time-dependent nature of sex differences in play behavior. For girls more than boys, positive affect was dependent upon peers' prior positive affect. For boys more than girls, vigor of activity was dependent upon peers' current vigor of activity.

Acknowledgments

This research was supported in part by National Institutes of Health Grant MH075750 to K. Buss. K. Buss' faculty position is, in part, supported by the Children, Youth, and Family Consortium at The Pennsylvania State University. Some of the data reported in this article were presented at the 2012 Society for Research in Child Development – Developmental Methodology Themed Meeting.

We thank the staff and students of the Emotion Development Lab in the Child Study Center who contributed to this work. We also thank the participants and their families.

Notes

¹Additional terms can be added to the VAR part of the model in order to examine lags beyond order 1. For example, a uSEM model with contemporaneous relations and lagged relations of order 3 would be defined as: η(t) = Aη(t) + Φ₁η(t − 1) + Φ₂η(t − 2) + Φ₃η(t − 3) + ζ(t).

²Although traditional SEM is not appropriate for autocorrelated data, simulation studies have shown that the approach used by uSEM to estimate contemporaneous relations yields parameter values close to those obtained with the genuine maximum likelihood method (e.g., Hamaker, Dolan, & Molenaar, 2005).

³To modify the LISREL input syntax in Appendix A for hypothesis-driven testing, remove the automatic search procedure command (am) from the output line and specify which relations among behaviors should be freed (1) in the BETA matrix.

⁴Criteria other than significant model improvement at an alpha of .05 can be used to terminate the automatic search procedure in LISREL. For example, alpha can be set to a more (e.g., .01) or less (e.g., .10) stringent level than .05. Moreover, model fit indices can be used; the model accepted as final could be the first model iteration in which two alternative fit indices indicate excellent fit (according to Brown, 2006; Hu & Bentler, 1999; Tucker & Lewis, 1973).

⁵The percent of relations possible among children's lagged positive affect, lagged vigor of activity, contemporaneous positive affect, and contemporaneous vigor of activity differed for groups of size three versus groups of size four. In each group, there were n(n–1) relations possible, where n is group size.

⁶For example, the equation explaining the time series of the positive affect of boy 1 (i.e., 1PA2) is: 1PA2 = .35*1PA1 + .23*1V2 + .31*2PA2 + .53.