Longitudinal models of skill development: conceptual and statistical considerations

Several conceptual and statistical decisions must be considered when estimating longitudinal models of skill development. Conceptual decisions refer to how skill development processes are hypothesized to influence one another over the developmental period of focus. Statistical decisions are primarily related to how to rule out confounding explanations (i.e., in efforts to provide stronger causal inference) and how to account for between- and within-person variation over time. Statistical considerations typically receive greater attention, but the current study aims to bring complementary focus to the importance of conceptual decisions, which are often insufficiently considered and should inform statistical decisions. To illustrate these considerations, we focus on the cross-domain associations between executive function (EF) and math skills. The sample (N = 684 children; 48% Female; M_age = 4.80 years, SD = 0.31; 42.07% Black/African American, 31.12% White, 13.11% Hispanic or Latinx, and 10.37% multiracial) included children from low-income households tested over four waves from the fall of preschool to the spring of kindergarten. We found that standardized estimates of EF predicting math ranged from -.24 to .48 (M = .06, SD = .08), math predicting EF ranged from -.08 to .55 (M = .13, SD = .13), and bivariate and model-imposed correlations ranged from .00 to .96 (M = .28, SD = .24). We conclude by discussing strategies to improve intentionality around testing plausible, and competing, hypothesized pathways to better inform theoretical explanations for cross-domain associations.