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Moderation: Interpretation David A. Kenny The Moderated Regression Equation • Y = aX + bM + cXM + E a = “main effect” of X b = “main effect” of M c = interaction between X and M • Important to include both X and M in the model. Interpretation of the Two Main Effects a: “main effect” of X The effect of X when M is zero. b: “main effect” of M The effect of M when X is zero. For these effects to be meaningful, zero must be a meaningful value. 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). 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. 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. Brief Example stress level or S happiness or H socio-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. Other Strategies for Interpretation • Computing simple effects • Graphing the moderation 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. 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. 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. Graphing Better 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 X two values of M Place in the graph. Connect the sets of two points with a common value of M. Graphing Programs Paul Jose’s ModGraph http://www.victoria.ac.nz/psyc/pauljose-files/modgraph/ Andrew Hayes’s ModProbehttp://www.afhayes.com/ spss-sas-and-mplus-macros-andcode.html#modprobe Regions of Significance • Johnson-Neyman • Potthoff extension 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. Additional Webinars • Assumptions • Effect Size and Power • ModText 17