Redundancy and Suppression

1. Redundancy and Suppression Trivariate Regression

2. Predictors Independent of Each Other X1 X2 a c Y b = error

3. Redundancy • For each X, sri and i will be smaller than ryi, and the sum of the squared semipartialr’s (a + c) will be less than the multiple R2. (a + b + c)

4. Formulas Used Here

5. Classical Suppression Y • ry1 = .38, ry2 = 0,r12 = .45. • the sign of and sr for the classical suppressor variable will be opposite that of its zero-order r12. Notice also that for both predictor variables the absolute value of  exceeds that of the predictor’s r with Y. X2 X1

6. Classical Suppression WTF • adding a predictor that is uncorrelated with Y (for practical purposes, one whose r with Y is close to zero) increased our ability to predict Y? • X2 suppresses the variance in X1 that is irrelevant to Y (area d)

7. Classical Suppression Math • r2y(1.2), the squared semipartial for predicting Y from X2(sr22), is the r2 between Y and the residual (X1– X1.2). It is increased (relative to r2y1) by removing from X1 the irrelevant variance due to X2  what variance is left in partialedX1is better correlated with Y than is unpartialedX1.

8. Classical Suppression Math • is less than Y X2 X1

9. Net Suppression ry1 = .65, ry2 = .25, and r12 = .70. Y X1 X2 Note that 2 has a sign opposite that of ry2. It is always the X which has the smaller ryi which ends up with a  of opposite sign. Each  falls outside of the range 0 ryi, which is always true with any sort of suppression.

10. Reversal Paradox • Aka, Simpson’s Paradox • treating severity of fire as the covariate, when we control for severity of fire, the more fire fighters we send, the less the amount of damage suffered in the fire. • That is, for the conditional distributions (where severity of fire is held constant at some set value), sending more fire fighters reduces the amount of damage.

11. Cooperative Suppression • Two X’s correlate negatively with one another but positively with Y (or positively with one another and negatively with Y) • Each predictor suppresses variance in the other that is irrelevant to Y • both predictor’s , pr, and sr increase in absolute magnitude (and retain the same sign as ryi).

12. Cooperative Suppression • Y = how much the students in an introductory psychology class will learn • Subjects are graduate teaching assistants • X1 is a measure of the graduate student’s level of mastery of general psychology. • X2 is an SOIS rating of how well the teacher presents simple easy to understand explanations.

13. Cooperative Suppression • ry1 = .30, ry2 = .25, and r12 = 0.35.

14. Summary • When i falls outside the range of 0 ryi, suppression is taking place • If one ryi is zero or close to zero , it is classic suppression, and the sign of the  for the X with a nearly zero ryi will be opposite the sign of r12.

15. Summary • When neither X has ryi close to zero but one has a  opposite in sign from its ryi and the other a  greater in absolute magnitude but of the same sign as its ryi, net suppression is taking place. • If both X’s have absolute i > ryi, but of the same sign as ryi, then cooperativesuppression is taking place.

16. Psychologist Investigating Suppressor Effects in a Five Predictor Model