Supplementary Information 5: Conditional Process Analysis
Supplementary Methods and Materials
Conditional Process Analysis (CPA) was conducted with the primary aim of establishing whether the utility of blood oxygenation-level dependent (BOLD) activation as an intermediary in the relationship between COMT genotype and inhibitory performance differed between boys and girls.
The CPA framework is highly adaptable permitting investigation of many specific models of mediation, moderation and their conjunction. We selected a model in which sex effects were modelled on the paths from:(i) genotype to activation;(ii) activation to performance; and (iii) genotype to performance. This thus represents the model in which sex effectson all potential paths are modelled; and was chosen above alternative models in which modelled sex effects were constrained to fewer paths, since robust specific effects in this context represent those having maximally accounted for sex effects in other parts of the model. In other words, significant sex differences in this context cannot be attributable to a failure to account for sex in another part of the model.
Statistical basis of conditional process analysis
CPA brings together multiple ordinary-least squares regression models. The paths contributing to the statistical model underlying the moderated-mediation analysis are presented in Figure S4, which also denotes their coding.
Figure S4. The statistical model implemented in the conditional process analysis, displaying the notation utilised in calculation of direct and indirect predictive effects.
Using this approach, the direct pathways between our three variables are modelled. Most importantly to the current work, however, is the evaluation of the conditional indirect effect (CIE) of X on Y through Mj, which is calculated thus:
CIE= (a1j+ a4jW) (b1j+ b9jW)
In the current investigation, this yields sex-specific measurements of the indirect pathway from COMT-genotype via BOLD activation through to inhibitory performance.
Supplementary Results
The central findings of the CPA, that is the conditional indirect effects, are presented in Table 2. To provide more information on their calculation, and path-specific coefficients in these models, Figures S5 and S6 are presented below.
Figure S5. Path coefficients associated with successful inhibition from conditional process analysis, for (A) pre-supplementary motor area, and (B) inferior frontal cortex. Bootstrapped mean coefficients and their heteroscedasticity-consistent standard errors are reported.
Figure S6. Path coefficients associated with failed inhibition from conditional process analysis, for (A) pre-supplementary motor area, and (B) inferior frontal cortex. Bootstrapped mean coefficients and their heteroscedasticity-consistent standard errors are reported.