A moderator (or effect modifier) is a variable that influences the very association between the x-variable and the y-variable. Put differently, the association between x and y looks different depending on the value of z.

Some examples We want to examine the association between social support (x) and mental health (y). We think that the association may be moderated by gender (z). For example, we may expect social support to be more important for mental health among women than among men.   We are interested in the association between mother’s educational attainment (x) and babies’ birth weight (y). It is reasonable that mother’s smoking (z) affects that association: there may be an association between x and y if the mother smokes, but no association between x and y if the mother does not smoke.