Table 1.
Descriptive statistics for child-grade observation data, for mixed-effects modeling.
Fig 1.
Example of an indirect effect pathway.
The number at the end of the variable name refers to grade 2, 3, or 4. Black directional lines indicate significant relationships (p < .05), while gray lines indicate non-significant relationships. In this example, while declarative memory in grade 2 does not directly relate to math ability in grade 4 (i.e., the c’2 path), it can be shown to indirectly relate to grade 4 math ability through its direct relationship with math ability in grade 2 (path a), math ability in grade 2 relating to math ability in grade 3 (path b1), and math ability in grade 3 influencing math ability in grade 4 (path b2). Statistically, this indirect effect would be supported if the product of coefficients a, b1, and b2 was significantly different from zero. Also, note that the a and b paths cannot be estimated without also including the c’ paths, which are the residual direct effects of a predictor on the outcomes.
Table 2.
Descriptive statistics for child-level longitudinal data, for structural equation modeling.
Table 3.
Pairwise correlations of transformed variables, within and across grades.
Fig 2.
Final SEM model, following bootstrapping.
CFI = .97, RMSEA = .03, AIC = -1009.12, n-adjusted BIC = -1035.82, N = 109. The number at the end of each variable name refers to grade 2, 3, or 4. Lines with single arrows represent regressions, while lines with double-arrows (between declarative memory and procedural memory) show covariances. Significant paths are shown in black, while non-significant ones are gray. Unstandardized coefficients (b) are presented adjacent to the path lines. Data for the memory and math ability variables were transformed using Proportion of Maximum Scaling, and were person-centered for each grade; see Methods. The regressions for math scores included sex as well as age for that grade as covariates; these coefficients are presented below the figure. + p < .10, * p < .05, ** p < .01, *** p < .001.
Table 4.
Indirect effects of sex & age covariate model.