LECTURE 7: CONTINUOUS INTERACTIONS IN REGRESSION

Interactions in Regression Main Effects Models: Each source adds a Direct Effect, Unanalyzed effect: X1 X2 Y Y = b 1 X1 + b 2 X2 + b 0 b1b1 b2b2  12 Effects of X 1 on Y: Direct: b 1 Unanalyzed:  12 * b2

Interactions in Regression Interaction Effects Models: Main effects plus correlated interaction effect X1X1 X2X2 Y Y = b 1 X1 + b 2 X2 + b 3 X1X2 + b 0 b1b1 b2b2  12 Effects of X 1 on Y: Direct: b 1 Unanalyzed:  12 * b2 +(  13 * b3 x1x2  13  23 b3b3

SPSS Regression Depression predicted from Anxiety, Self Esteem, and ANX-SE interaction: First: Uncentered –Correlations –b and beta weights –Multicollinearity Second: Centered, same output

Centering Subtract mean from each predictor Construct interaction term by multiplying two centered predictors together Meaning for interaction: how much change occurs due to interaction as we move away from the means of the two predictors (eg. Beta tells us change per unit change in the product of the centered predictors) –If one centered predictor is at the mean, there is no interaction change since (x1-meanx1)(x2-meanx2)=0

SPSS Regression-Uncentered

Over 30 means multicollinearity Over 10 means multicollinearity Over 1.0 means statistical problem such as negative error variance

Covariance of Uncentered Regression weight estimates Note- extremely high correlations among b- weights

SPSS Regression-Centered

None over 30 means no multicollinearity Over 10 means multicollinearity, none hereBeta weights OK

Covariance of Centered Regression weight estimates Note- much reduced correlations among b-weights

Standard errors around regression slopes DepressiopnDepressiopn Self-Esteem Mean Low anxiety Mod anxiety High anxiety Each slope will have a different Confidence Interval around it CI around High Anx slope

Standard errors around regression slopes DepressiopnDepressiopn Self-Esteem Mean High anxiety = +1SD CI around High Anx slope at the mean- simple slope CI

Polynomial terms and Interactions Curvilinear effects (most likely quadratic) are formed by –centering all predictors –squaring a hypothesized quadratic centered predictor, –Constructing any interactions of linear or quadratic-linear or quadratic-quadratic possible centered predictors

Anxiety centered squared SelfEsteem centered squared AnxcenSq x SelfEsteemcen

AnxcenSq x SEcen (not significant)