1. Ch 12 Prediction/Regression Part 3: Nov 30, 2006

2. Extensions of multiple regression Some hypotheses may involve model testing –We’re interested in comparing multiple models with multiple predictors Can examine different combinations of predictors Which model has the largest R 2 ? If I add one more predictor, does it improve R 2 significantly over the previous model?

3. (cont.) More specifically, you may be interested in testing mediated and/or moderated regression models –Mediated models involve testing for mediator effects Does variable x have a direct effect on variable y (model 1) or does its effect on y ‘go through’ variable z (model 2)? Model 1:x  y Model 2: x  z  y If model 2 fits the data the best, then z is a mediator of the x-y relationship

4. Testing mediator models Baron & Kenney (1986) – famous article specifying the steps involved in this: –Step 1: use a regression model with x as the IV and z as the DV (is there any relation between x  z?) –Step 2: use a regression model with x as the IV and y as the DV (this tests model 1 on previous page) –Step 3: use a regression model with x and z as IVs and y as DV If the beta for x in this model is now non-significant (or zero), but the beta for z is significant, then z mediates the x-y relationship.

5. Moderator variables A moderator is a variable that changes the strength or nature of the relationship between x and y. –Example? –Usually drawn as: xy moderator

6. (cont.) Can test moderator variables using stepwise regression (a form of multiple regression): –Step 1: run a regression model with x as IV and y as DV –Step 2: run a regression model with x and the moderator as IVs and y as DV Be sure to ask for change in R 2 at Step 2. Is the change in R 2 significant at Step 2? –If yes, then you have a moderator variable.

7. Issues with Moderator and Mediators Mediators: –It’s possible to have either complete or partial mediation Difference? Moderators: –Difficult to find in field research Why?