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Self-regulation is important for child adjustment during middle childhood (McClelland & Cameron, 2011). Family chaos is a detrimental determinant for self-regulation (Vernon-Feagans et al., 2016). However, the traditional static approach rarely captures how chaos and self-regulation intertwine and evolve. Chaos and self-regulation can be seen as a two-variable dynamic system that fluctuates around an equilibrium state (Smith & Thelen, 2003). Moreover, there may be mutual influences between chaos and self-regulation because children are active agents that can shape their environment (Lerner, 2018).
Cross-lagged panel models have been widely used to examine bidirectional relations (Hamaker et al., 2015). Most of the studies focus on a generalized finding, but heterogeneity may exist. Moreover, isolated coefficients are like gears of a machine; the movements of isolated gears do not capture how the whole machine functions (Granic et al., 2003). In fact, isolated cross-lagged coefficients may not translate into holistic coupling (Butner et al., 2017). This study aims to use a dynamic system approach to examine the holistic family-specific dynamic patterns between family chaos and self-regulation by considering all coefficients simultaneously.
A total of 399 families (42% Black, 46% Latinx) were measured four times, starting when the children were 10.3 years old on average and proceeding annually until children were 13. Self-regulation was measured via the Dimensional Change Card Sort task (Gershon et al., 2013) at the first three waves. Family chaos was measured via parent-report using the Confusion, Hubbub, and Order Scale (Matheny et al., 1995). Multiple imputation was conducted to generate a comparable factor score for self-regulation for each wave and dealt with missingness in chaos. A dynamic structural equation model (DSEM) was first applied to generate family-specific autoregressive and cross-lagged coefficients, with the assumption that the autoregressive and cross-lagged remained consistent across time but varied across individuals (Hamaker et al., 2018). Vector plots were then used to visualize the holistic dynamic pattern for each family using family-specific coefficients generated by Mplus (Butner et al., 2017; Muthén & Muthén, 1998–2017).
Only the autoregression of chaos was significant, but there were significant variances in all four coefficients (Table 1). Arrows in vector plots tell where (i.e., the direction of arrow) and how fast (i.e., length of the arrow) the individual will go next given a hypothetical starting point (i.e., the end of the arrow). Arrows are short around the equilibrium state, implying little change. If there is a swirl (i.e., angular arrows), there is a holistic coupling between self-regulation and chaos (Figure 1a). If the arrows are straight, there is no holistic coupling (Figure 1b). Eigenvalues of the two autoregressive and two cross-lagged coefficients can be computed to echo the plots. If the eigenvalues included imaginary numbers, there is holistic coupling (Abraham & Shaw, 2005). Among the 399 families, 111 families showed a holistic coupling. In conclusion, local cross-lagged effects may not capture the holistic dynamic pattern, and it is important to understand the transactional relation holistically. Additional analyses will examine family and child characteristics as predictors of the holistic dynamic patterns.