Suppressor and distort variables
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1. A suppressor variable is one that weakens the relationship between two other variables by suppressing error or noise in one of the variables. 2. For example, education level (X2) acts as a suppressor variable in the relationship between religious affiliation (X1) and suicide rates (Y) by suppressing some of the error variance in religious affiliation. 3. Suppressor and distort variables are important to consider because they can reveal a variable's true predictive power and change the direction of a relationship, emphasizing the need to include all relevant variables in models.
Suppressor and distort variables
- 1. Suppressorand distort variablesWANG ChengjunCity University of HONG KONG20110304
- 2. Suppressor and SuppressionA suppressor is one which weakens a relationship, which conceals its true strength.Context: zero order correlation.
- 3. This is the relationship between two variables, while ignoring the influence of other variablesThe general idea:there is some kind of noise (error) in X1 that is not correlated with Y, but is correlated with X2.
- 4. By including X2 we suppress this noise, and leave X1 as an improved predictor of Y.Suppressor Variable
- 5. Normal situationBecause the variables share variance and influence .each semi-partial correlation, and the corresponding beta, will be less than the simple correlation between Xi and Y. YX1
- 6. Classical suppression: rY2 = 0The presence of X2 will increase the multiple correlation, even though it is not correlated with Y. X2 suppresses some of error variance in X1.
- 7. Suicide rate and religionDurkheim argues that if we control the variable of education, the suicide rate of Jews people will be even smaller.Jews are assumed to be a more integrated group.
- 8. Distort variablesYY-Distort variable converts a positive relationship into a negative relationship.+ X2X1X1-
- 10. Distort variablesZero order correlation between marriage and suicide rates indicates that marriage make people tend to suicide.Marriage make people more integrated, so the married people should have less suicide rate.
- 11. Keep model completeFor regression: y=b1*x1+b2*x2, if |ry1|<|b1|For regression: y=b1*x1+b2*x2, if ry1*b1<0Suppressor and distort variables remind us to keep the model complete.
- 12. Appendix 1 A simulation of suppression################Jonathan'sexample############################# see http://zjz06.spaces.live.com/blog/cns!3F49BBFB6C5A1D86!341.entryy<-c(1,2,3,4,5)x1<-c(2,3,4,5,1)x2<-c(3,2,1,4,5)cor(y,x1);cor(y,x2);cor(x1,x2)################## partialcorrelations######################library(ggm) data<-cbind(y,x1,x2)# partial correlation between y and x1controlling for x2pcor(c('y','x1','x2'),var(data))pcor(c('y','x2','x1'),var(data))# regression partials the effect ofsupressionfit12<-lm(y~x1+x2)summary(fit1);summary(fit2);summary(fit12)library(QuantPsyc)lm.beta(fit12)#########visualize the data in correlationmatrices###########library(corrgram)#install.packages('corrgram')corrgram(data, order=TRUE,lower.panel=panel.shade, upper.panel=panel.pie,text.panel=panel.txt, main="Suppression in zero ordercorrelation")
- 13. Appendix 11 A simulation of distortionset.seed(20110303)y<-rnorm(10000) x2<--0.1*y+0.01*rnorm(10000)x1<-0.8*x2+0.01*rnorm(10000)cor(x1,x2);cor(x1,y);cor(x2,y);plot(data.frame(cbind(y,x1,x2)),col='3')f1<-lm(y~x1)f2<-lm(y~x2)f3<-lm(y~x1+x2)f4<-lm(x1~x2)summary(f1);summary(f2);summary(f3);summary(f4)