Moderation: Interpretation David A. Kenny. The Moderated Regression Equation Y = aX + bM + cXM + E a...
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Transcript of Moderation: Interpretation David A. Kenny. The Moderated Regression Equation Y = aX + bM + cXM + E a...
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Moderation: Interpretation
David A. Kenny
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The Moderated Regression Equation
• Y = aX + bM + cXM + Ea = “main effect” of Xb = “main effect” of Mc = interaction between X and
M • Important to include both X and M
in the model.
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Interpretation of the Two Main Effects
a: “main effect” of XThe effect of X when M is zero.
b: “main effect” of MThe effect of M when X is zero.
For these effects to be meaningful, zero must be a meaningful value.
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Centering
• Make sure zero in interpretable for X and M.
• If not then center: Compute the grand mean of X and M and subtract it (or something close).
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Interpretation of the Interaction Effect (Moderation)
c = the effect of XM
For every one unit change of M, the effect of X (i.e., increases (or decreases) by c units.
Path c represents then how much a changes.
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The Moderated Effect of X on Y
• Y = aX + bM + cXM + E• Y = (a + cM)X + bM + E• The effect of X on Y is equal to a +
cM.• If we set a + cM to zero, then X has
no effect on Y when M = -a/c.
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Brief Examplestress level or Shappiness or Hsocio-economic status (C)
H = -2S + 1C + 0.1SC + E
For every one unit change of socioeconomic status, the effect of Stress levels on Happiness weakens by 0.1 units. Note that for C = 20, the effect of stress on happiness is zero.
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Other Strategies for Interpretation
•Computing simple effects•Graphing the moderation
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Simple Effects
• The effect that X has on Y at different levels of M.
• Sometimes called “pick a point.”• Two ways to compute:• Plug into a + cM the value for M
and solve.• Complicated to obtain a standard
error for this value.
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Re-centering
• Mʹ is desired value of M for which a simple effect is desired.
• Re-estimate the moderated regression equation using M - Mʹ for M.
• The new value of a will be the simple effect of X when M = Mʹ.
• Note this gives a p value and a confidence interval.
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What To Do If M Is Continuous?
• Pick two values• Typically one standard deviation
above and below the mean of M.• Make sure the values are possible
values.
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GraphingBetter than simple effects because it displays all of the effects.How?
Compute the least-squares means for each of the four combinations of
two values of Xtwo values of M
Place in the graph.Connect the sets of two points with
a common value of M.
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Graphing Programs
Paul Jose’s ModGraph http://www.victoria.ac.nz/psyc/paul-jose-files/modgraph/
Andrew Hayes’s ModProbehttp://www.afhayes.com/spss-sas-and-mplus-macros-and-code.html#modprobe
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Regions of Significance
• Johnson-Neyman• Potthoff extension
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Regions of Significance
• Useful if M is measured at the interval level of measurement.
• Tells you at what intervals of M is the X Y effect significant.
• It might tell you the when M is at least 5, the effect is positive and significant, but when M is less than 3, the effect is negative and significant.
• Can flip X and M.
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Additional Webinars
• Assumptions• Effect Size and Power• ModText