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你看这个可以帮到你吗？
An example of this case, M is race, X is a personnel test, and Y is some job performance score. Generally, it is assumed that the effect of X on Y is linear. It is also assumed (but it can be tested, see below) that the moderation is linear. That is, as M varies, the linear effect of X on Y might vary. Thus, the linear relationship increases or decreases as M increases.
这里说道：
当M也就是调节变量增加时， X对Y的影响增加或减少
也就是说
当成绩增加时，认可对惩罚的影响增加或减少 （我从逻辑上没明白认可和惩罚有什么关系，是特指自我惩罚吗？）
It is almost always preferable to measure the linear effect by using a regression coefficient and not a correlation coefficient.
More Complex Specification
Nonlinear moderation refers to effect of X changing as function of M, but that change is nonlinear. The typical way to estimate nonlinear moderation would be to estimate the following equation:
Y = d + a1X + b1M + b2M2 + c1XM + c2XM2 + E (2)
也许你可以对照这个公式？下面有各种情况的解释：
Nonlinear moderation can be tested by determining if c2 is different from zero. (Note that M2 effects can only be estimated if M takes on at least 3 values.) The effect of X in Equation 2 is a1 + (c1 + c2M)M which would be interpreted as follows:
If c1 were positive and c2 positive, then the effect of X on Y would be increasing as M increases, and this increase is increasing as M increases, accelerating.
If c1 were positive and c2 negative, then the effect of X on Y would be increasing as M increases, but this increase is declining as M increases, de-accelerating.
If c1 were negative and c2 positive, then the effect of X on Y would be decreasing as M increases, but this decrease is declining as M increases, de-accelerating.
If c1 were negative and c2 negative, then the effect of X on Y would be decreasing as M increases, but this decrease is increasing as M increases, accelerating.
http://davidakenny.net/cm/moderation.htm
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