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LECTURE 7: CONTINUOUS INTERACTIONS IN REGRESSION

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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

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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

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

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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

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SPSS Regression-Uncentered

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

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

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SPSS Regression-Centered

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

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

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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

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

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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

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Anxiety centered squared SelfEsteem centered squared AnxcenSq x SelfEsteemcen

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AnxcenSq x SEcen (not significant)

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