"To mediate these effects" means to intervene or moderate the impact or consequences of something in order to alleviate or reduce them. Full definition
The results indicated that women's attachment anxiety mediated the effect of need for parenthood on the psychological well - being of themselves and their partner. (link.springer.com)
All factors either partially or fully mediated the effect of forgiveness on health; however, the strongest mediator for both state and trait forgiveness was reduction in negative affect. (link.springer.com)
It also has been hypothesized that the timing of exposure to artificial nipples is important in mediating effects on breastfeeding.2 — 4,15 Thus, according to this hypothesis, mother — infant dyads who begin pacifier use before breastfeeding is well established incur a higher risk for problems than do couplets who have successfully established breastfeeding before pacifier introduction. (pediatrics.aappublications.org)