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. 2013 Jul 1;17(3):152-168.
doi: 10.1080/10888691.2013.805953.

Mapping temporal dynamics in social interactions with unified structural equation modeling: A description and demonstration revealing time-dependent sex differences in play behavior

Adriene M Beltz  1 , Charles Beekman, Peter C M Molenaar, Kristin A Buss
Affiliations

Mapping temporal dynamics in social interactions with unified structural equation modeling: A description and demonstration revealing time-dependent sex differences in play behavior

Adriene M Beltz et al. Appl Dev Sci. .

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.

Keywords: gender differences; interpersonal interaction; networks; observational methodology; play; socio-temporal dynamics.

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Figures

Figure 1
Figure 1
Final uSEM models for selected groups of boys (in black) and girls (in gray). Rectangles represent the time series of a behavior (positive affect or vigor of activity) for a single child, dashed arrows represent lagged relations, and solid arrows represent contemporaneous relations. The time series for each behavior of each child (coded in 10-second intervals) is explained by the time series of other modeled behaviors. For example, the positive affect of boy 1 is explained by the lagged positive affect of boy 1 (his own positive affect from 10 seconds prior), the contemporaneous vigor of activity of boy 1 (his own vigor of activity at the same time point), and the contemporaneous positive affect of boy 2 (the positive affect of boy 2 at the same time point). The presented models had excellent fit to the data:

  1. χ2(36, N=98) = 26.87, p = .860, CFI=1.00, TLI=1.00, SRMR=.048, RMSEA=.000;

  2. χ2(37, N=86) = 29.00, p = .820, CFI=1.00, TLI=1.00, SRMR=.055, RMSEA=.000;

  3. χ2(40, N=91) = 37.10, p = .600, CFI=1.00, TLI=1.00, SRMR=.076, RMSEA=.000;

  4. χ2(77, N=92) = 64.22, p = .820, CFI=1.00, TLI=1.00, SRMR=.061, RMSEA=.000;

  5. χ2(73, N=74) = 55.70, p = .930, CFI=1.00, TLI=1.00, SRMR=.061, RMSEA=.000;

  6. χ2(60, N=87) = 82.22, p = .0300, CFI=.98, TLI=.97, SRMR=.039, RMSEA=.066.

Figure 1
Figure 1
Final uSEM models for selected groups of boys (in black) and girls (in gray). Rectangles represent the time series of a behavior (positive affect or vigor of activity) for a single child, dashed arrows represent lagged relations, and solid arrows represent contemporaneous relations. The time series for each behavior of each child (coded in 10-second intervals) is explained by the time series of other modeled behaviors. For example, the positive affect of boy 1 is explained by the lagged positive affect of boy 1 (his own positive affect from 10 seconds prior), the contemporaneous vigor of activity of boy 1 (his own vigor of activity at the same time point), and the contemporaneous positive affect of boy 2 (the positive affect of boy 2 at the same time point). The presented models had excellent fit to the data:

  1. χ2(36, N=98) = 26.87, p = .860, CFI=1.00, TLI=1.00, SRMR=.048, RMSEA=.000;

  2. χ2(37, N=86) = 29.00, p = .820, CFI=1.00, TLI=1.00, SRMR=.055, RMSEA=.000;

  3. χ2(40, N=91) = 37.10, p = .600, CFI=1.00, TLI=1.00, SRMR=.076, RMSEA=.000;

  4. χ2(77, N=92) = 64.22, p = .820, CFI=1.00, TLI=1.00, SRMR=.061, RMSEA=.000;

  5. χ2(73, N=74) = 55.70, p = .930, CFI=1.00, TLI=1.00, SRMR=.061, RMSEA=.000;

  6. χ2(60, N=87) = 82.22, p = .0300, CFI=.98, TLI=.97, SRMR=.039, RMSEA=.066.

Figure 1
Figure 1
Final uSEM models for selected groups of boys (in black) and girls (in gray). Rectangles represent the time series of a behavior (positive affect or vigor of activity) for a single child, dashed arrows represent lagged relations, and solid arrows represent contemporaneous relations. The time series for each behavior of each child (coded in 10-second intervals) is explained by the time series of other modeled behaviors. For example, the positive affect of boy 1 is explained by the lagged positive affect of boy 1 (his own positive affect from 10 seconds prior), the contemporaneous vigor of activity of boy 1 (his own vigor of activity at the same time point), and the contemporaneous positive affect of boy 2 (the positive affect of boy 2 at the same time point). The presented models had excellent fit to the data:

  1. χ2(36, N=98) = 26.87, p = .860, CFI=1.00, TLI=1.00, SRMR=.048, RMSEA=.000;

  2. χ2(37, N=86) = 29.00, p = .820, CFI=1.00, TLI=1.00, SRMR=.055, RMSEA=.000;

  3. χ2(40, N=91) = 37.10, p = .600, CFI=1.00, TLI=1.00, SRMR=.076, RMSEA=.000;

  4. χ2(77, N=92) = 64.22, p = .820, CFI=1.00, TLI=1.00, SRMR=.061, RMSEA=.000;

  5. χ2(73, N=74) = 55.70, p = .930, CFI=1.00, TLI=1.00, SRMR=.061, RMSEA=.000;

  6. χ2(60, N=87) = 82.22, p = .0300, CFI=.98, TLI=.97, SRMR=.039, RMSEA=.066.

Figure 2
Figure 2
Sex differences in percent of lagged positive affect, lagged vigor of activity, contemporaneous positive affect, and contemporaneous vigor of activity relations among children in a play group in final uSEM models (N = 19). Error bars depict standard deviations; d’s indicate the effect sizes of the sex differences (Cohen, 1988). *p < .05, one-tailed.
Figure 3
Figure 3
Sex differences in percent of lagged relations between positive affect and vigor of activity of a single child, and in percent of contemporaneous relations between positive affect and vigor of activity of a single child in final uSEM models (N = 65). Error bars depict standard deviations; d’s indicate the effect sizes of the sex differences (Cohen, 1988).
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