Trivariate Regression a c X 1 X 2 Y Predictors Independent of Each Other b error Redundancy sr 1 2 b sr 2 2 d RedundancyExample For each X sr i and i will be smaller than ID: 416720
Download Presentation The PPT/PDF document "Redundancy and Suppression" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Redundancy and Suppression
Trivariate
RegressionSlide2
a
c
X
1
X
2
Y
Predictors Independent of Each Other
b = errorSlide3
Redundancy
For each X,
sr
i
and i will be smaller than r
yi, and the sum of the squared semipartial r’s (a + c) will be less than the multiple
R2. (a + b + c)Slide4
Formulas Used HereSlide5
Classical Suppression
r
y1
= .38, ry2 = 0,
r12 = .45.
the sign of and sr
for the classical suppressor variable may 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.
Y
X
1
X2Slide6
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 X
1 that is irrelevant to Y (area d)Slide7
Classical Suppression Math
r
2
y(1.2), the squared semipartial for predicting Y from X
1 (sr12
), is the r2 between Y and the residual (X1 – X
1.2). It is increased (relative to r2y1) by removing from X
1 the irrelevant variance due to X2 what variance is left in
partialed X1 is better correlated with Y than is unpartialed
X1.Slide8
Classical Suppression Math
is less than
Y
X
1
X
2Slide9
Net Suppression
Y
X
1
X
2
r
y1
= .65, ry2 = .25, and
r12 = .70.
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 r
yi, which is always true with any sort of suppression.Slide10
Net Suppression
If
X
1 and X2 were independent, Slide11
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.Slide12
Cooperative Suppression
T
wo
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 Yboth predictor’s
, pr, and sr increase in absolute magnitude (and retain the same sign as ryi).
Slide13
Cooperative Suppression Y = how
much the students in an introductory psychology class will
learn
Subjects are graduate teaching assistantsX1 is a measure of the graduate student’s level of mastery of general psychology.X
2 is an SOIS rating of how well the teacher presents simple easy to understand explanations.Slide14
Cooperative Suppressionr
y1
= .30,
ry2 = .25, and r12 = 0.35.
If X
1
and X
2
were independent, Slide15
Summary
When
i falls outside the range of 0 ryi, suppression is taking
placeIf 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 may be opposite the sign of
ryi.Slide16
Summary
When neither X has
r
yi 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 cooperative suppression is taking place.Slide17
Psychologist Investigating Suppressor Effects in a Five Predictor Model