Interactions, Dummies, and Outliers

Transcription

1 Interactions, Dummies, and Outliers

2 Modeling Interactive Relationships in Regression Income=b 1 (sex)+b 2 (education)+c Income=b 1 (sex)+b 2 (education)+b 3 (sex x education)+c In both cases, b 1 gives us the difference for being a man or woman, b 2 gives the impact of education. What does b 3 tell us? b 3 is the interaction, tells us if there is a differential impact of education among the genders For sex, let 0=m, 1=f, education in years, income in dollars

3 i n c o m e Education

4 i n c o m e Men Women Education

5 i n c o m e Men Women Education

6 i n c o m e Men Women Education

7 Using Interaction Terms Easiest when one is a dummy variable (0-1) other is either continuous or a dummy Multiply the two together Include all lesser terms (that is, in a two way, have x 1,x 2, and x 1 *x 2. In a three way, include x 1,x 2,x 3, x 1 *x 2, x 1,x 3, x 2,x 3, and x 1 *x 2 *x 3 For interpretation, you can add the slope of the interaction term to the slope of the appropriate variable, use to create two sets of predicted values

8 An Example- Internet and Personality Research question- does internet have differential impact on political knowledge for people depending on their motivation to seek information. Look at Need for Cognition and Need to Evaluate Set up regression with political knowledge as DV. NE, NC, media use, and interactions as IVs

9 Looking at Results Model 2- No interactions, but includes important traits including media use. Model 3- includes interactions between NC and all media types. NC is significant and positive. Negative interaction with cable. Model 4- interactions with NE. NE is significant and positive, Negative interaction with cable and internet

10 K n o w l e d g e No internet internet NE

11 Challenges to Interaction Terms Interpretation Dummy*continuous is tricky Continuous*continuous is trickier Three ways are especially challenging Example- Miller and Krosnick 2000 Trust*knowledge*condition Results- all three required for effect

12 Challenges to Interactions Multicolinearity Interaction terms are typically highly correlated with other terms Inflates errors of parameter estimates Makes potentially significant relationships appear non-significant

13 Outliers Growth= change in GDP X 1 = left political strength X 2 = union organizational strength Interaction is combined union organizational and political strength Numbers in parentheses are T values, political strength is significant at.10, Union strength, interaction significant at.05 level

14 Outliers

15 Outliers

16 Predicting Party ID Model 1 (Constant) age in years 1=f,0=m EDUCATIO household income RACE IDEO CHURCHAT BORNAGN UNION a. Dependent Variable: PID Coefficients a Unstandardized Coefficients Standardized Coefficients B Std. Error Beta t Sig E E E E Model 1 Model Summary Adjusted Std. Error of R R Square R Square the Estimate.560 a a. Predictors: (Constant), UNION, CHURCHAT, RACE, 1=f,0=m, BORNAGN, EDUCATIO, IDEO, age in years, household income

17 Using Dummy Variables Model 1 (Constant) age in years 1=f,0=m EDUCATIO household income RACE IDEO CHURCHAT BORNAGN UNION SOUTH NORTHEAS WEST a. Dependent Variable: PID Coefficients a Unstandardized Coefficients Standardized Coefficients B Std. Error Beta t Sig E E E E Model 1 Model Summary Adjusted Std. Error of R R Square R Square the Estimate.561 a a. Predictors: (Constant), WEST, EDUCATIO, IDEO, CHURCHAT, UNION, 1=f,0=m, RACE, BORNAGN, age in years, NORTHEAS, household income, SOUTH

18 Model 1 (Constant) age in years 1=f,0=m EDUCATIO household income RACE ENVIRON IDEO CHURCHAT BORNAGN UNION SOUTH NORTHEAS WEST RACESOUT a. Dependent Variable: PID Coefficients a Unstandardized Coefficients Standardized Coefficients B Std. Error Beta t Sig E E E E Model 1 Model Summary Adjusted Std. Error of R R Square R Square the Estimate.576 a a. Predictors: (Constant), RACESOUT, CHURCHAT, UNION, 1=f,0=m, EDUCATIO, IDEO, NORTHEAS, age in years, ENVIRON, BORNAGN, WEST, household income, SOUTH, RACE

19 Model 1 (Constant) age in years 1=f,0=m EDUCATIO household income RACE IDEO CHURCHAT BORNAGN UNION SOUTH NORTHEAS WEST RACESOUT SERVSPEN DEFSPEND WELFARE HIGHWAY FORAID STAMPS AIDPOOR ENVIRON SS PUBSC CRIME AIDS CHILDCAR TAXCUT a. Dependent Variable: PID Coefficients a Unstandardized Coefficients Standardized Coefficients B Std. Error Beta t Sig E E E E E E E E E Model 1 Model Summary Adjusted Std. Error of R R Square R Square the Estimate.648 a a. Predictors: (Constant), TAXCUT, UNION, AIDPOOR, CHURCHAT, HIGHWAY, NORTHEAS, DEFSPEND, FORAID, household income, CRIME, RACE, 1=f,0=m, BORNAGN, age in years, WEST, ENVIRON, PUBSC, STAMPS, SS, EDUCATIO, AIDS, IDEO, CHILDCAR, SERVSPEN, WELFARE, SOUTH, RACESOUT