Path Analysis

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

2. Mediation

3. 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.

4. 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)

5. 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.

6. MODERATON

7. 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

8. 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.

9. 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

11. MODERATON GRAPH

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

13. 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

14. Example of Moderation • Binladen -> Stereotype moderated by age.

15. MODELING TECHNIQUES • Also see SEM for mediation;

16. 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.

17. 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

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