Mediation MODERATION THREE WAYS OF DOING ANALYSIS Kun Path Analysis Mediation MODERATION THREE WAYS OF DOING ANALYSIS Kun

Mediation C apostrophy

Baron & Kenny (1986) X1 -> X2 -> Y Three steps to test mediation: Y on X1; X2 on X1 Y on X1 and X2 If c (total effect) is significantly different from 0 and c’ (indirect effect) is not significantly different from 0, then full mediation is indicated. If c’ is only reduced in size, but still significantly different from 0, partial mediation is indicated.

Controversies Doesn’t actually test the significance of the indirect effect; (e.g., if a and b are both significant, then ab must be significant) Can have partial mediation, but a non-significant indirect effect; Can have significant indirect effect, but not meet Baron & Kenny criteria, (even if total effect is not significant, it is still possible to have indirect effect). (e.g., opposite directions for indirect and direct effects) think about if direct effect is positive, indirect effect is negative, then its possible to be zero. that does not mean no effect.

Testing indirect effects using Sobel Test Calculate ration of indirect effect parameter and its associated standard error, Sab PROCESS: Bootstrapping procedure (Preacher & Hayes, 2004) Calculate ab using large number of samples (with replacement) of size n from the data (e.g., 1000 samples) Sab is the standard deviation of ab in the 1000 samples Assumes normality of sampling distribution – otherwise, lower statistical power.

MODERATON

MODERATION -Create an interaction term as a predictor of Y; Test significance of coefficient, b3 - Model 1: y = b0 + b1 (X1) + b2 (X2) Model 2: y = b0 + b1 (X1) + b2 (X2) + b3 (X1X2) Testing for significant of change in R2

Model 1: y = b0 + b1 (X1) + b2 (X2) Regression coefficients estimate the effect of each independent variable on the dependent variable, across the levels of the other independent variables: b1 reflects the amount of change in Y with a unit change in X1 at each level of X2  general relationships Model 2: y = b0 + b1 (X1) + b2 (X2) + b3 (X1X2) Regression coefficients estimate “conditional” relationships: b1 reflects the change in Y with a unit change in X1, when X2 equals zero. The nature of the interaction effect can be seen in b3, which indicates the number of units that the slope of Y on X1 changes, given a one-unit change in X2. It is a good idea to draw the interaction on a graph.

Graph Picking high and low values for X1 and X2 (e.g., 1 SD from mean) Use final regression equation to calculate Y Plot two straight lines on graph of X1 vs. Y - one line for high value of X2 - one line for low value of X2

MODERATON GRAPH

PROCESS DV must be dichotomous or continuous; IV can be dichotomous or continuous; Mediators must be continuous; Uses listwise deletion

Example of Mediation Examining perceptions of Muslims in the U.S. when Obama announces the death of Osama bin Laden. Binladen (0, 1): before, after; Stereotype Realistic threat Restriction of Muslim civil liberties Control: age, gender, etc… Binladen -> endorsement of stereotype -> Restriction of Muslim civil liberties

Example of Moderation Binladen -> Stereotype moderated by age.

MODELING TECHNIQUES Also see SEM for mediation;

Recommendation Hayes, A. F. (2013). Introduction to mediation, moderation, and conditional process analysis: A regression-based approach. Guilford Press. Kline, R. B. (2011). Principles and practice of structural equation modeling (3rd Ed). New York: Guilford Press.

Plus, multilevel modeling technique: Clusters of individuals, e.g., children within classrooms within schools; Repeated measures of individuals Regression: y = a + b*x + e. But intercept and slope may vary across groups

Equations HLM (IBM) SPSS (generalized linear model) Mplus