Fig. 3. The longitudinal association and mediation analyses.
a The longitudinal association between the behavioral problems total score (TotProb CBCL Syndrome Scale) in the children and the family conflict score measured 1 year later using structural equation modeling. Higher behavioral total scores were associated with higher family conflict scores 1 year later (p < 1.0 × 10−4, n = 8836), and higher family conflict scores were associated with higher behavioral problems total scores 1 year later (p = 0.001, n = 8836), but less significantly. b The longitudinal association between the behavioral problems total score in the children and the parental monitoring score using structural equation modeling. Higher behavioral problems total scores were associated with lower parental monitoring scores 1 year later (p < 1.0 × 10−4, n = 8836) (solid diagonal line), and higher parental monitoring scores were associated with lower behavioral problems total scores 1 year later (p = 0.013, n = 8836), but less significantly. c Mediation analysis: the indirect path (A, AB, and B) shows that the behavioral problems total score in the children significantly mediates the association between the cortical area in the children and the family conflict scores (β = −0.01, p = 5.6 × 10−11, n = 8756, 14.7% variance explained). Path A: Association between the independent variable (the cortical area) and the mediator (the behavioral problems total score). Path B: association between the mediator (the behavioral problems total score) and the outcome (the family conflict score). Path C’ shows a significant reduction in the regression coefficient between the cortical area and the family conflict score when the mediator (the behavioral problems total score) is taken into account, with the association without this mediation shown in path C. Path AB indicates the extent to which taking the behavioral problems total score into account can explain 14.7% of the total variances between the cortical area in the children and the family conflict score, which is significant as noted above at p = 5.6 × 10 −11. (The variance explained is obtained by dividing β in path AB by β in path C.) d A corresponding mediation analysis showed that the behavioral problems total score in the children significantly mediates the association between the cortical area in the children and the parental monitoring score (β = 0.008, p = 2.4 × 10−9, n = 8756, 12.1% variance explained). All statistical tests here are two-sided, and pass Bonferroni correction (p < 0.05).