Dummies and Interactions
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1 Dummies and Interactions Prof. Jacob M. Montgomery and Dalston G. Ward Quantitative Political Methodology (L32 363) November 16, 2016 Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
2 Roadmap Last time: Multivariate Regression Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
3 Roadmap Last time: Multivariate Regression This time: Indicators for categorical variables Fixed effects Interactions In-class activity Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
4 Example: 2009 health care poll Support for Obama health care plan CNN/ORC poll, September 11 13, Strongly oppose Moderately oppose Moderately support Strongly support Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
5 Example: 2009 health care poll Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
6 Example: 2009 health care poll Strongly favor Support for Obama health care plan Moderately favor Moderately oppose Strongly oppose Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
7 Dummy variables in regression What is the association between party and support for HCR controlling for age? Party (GOP=0, Independent=1, Democrat = 2) HCR support (Strongly oppose = 1, Moderately oppose = 2, Moderately favor = 3, Strongly favor = 4) Recode age variable (18-29=1, 30-44=2, 45-64=3, 65+=4) into dummy variables Equation: HCR support = β 0 + β 1 Party + β 2 Age β 3 Age β 4 Age 65+ Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
8 Dummy variable regression results Variable Constant (0.116) Party (0.031) Age (0.13) Age (0.117) Age (0.121) N = 981 R 2 = Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
9 Dummy variable regression Strongly favor Support for Obama health care plan Moderately favor Moderately oppose Strongly oppose GOP Independent Democrat Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
10 Things to note For k levels of your categorical variable, you need to create k 1 dummy variables. The choice of baseline is arbitrary, but you need to know which is the baseline category in order to interpret the results correctly All effects are relative to the baseline category Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
11 Fixed Effects Regression When you panel data... you have observations of the same units (e.g. states) over time. you are interested in a treatment that varies over time within units. you need to account for time-invariant differences across units. We do this by including fixed effects: for the k units in our data, we include k 1 dummy variables in our regression. Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
12 Fixed Effects Example Question: Are elections fought over non-economic issues more when globalization increases? Data: Repeated observations of Canada, France, U.K., and U.S. DV: Non-economic issue emphasis in elections IV: Globalization Index We will consider two regressions: Non-economic = β 0 + β 1 Globalization Non-economic = β 0 + β 1 Globalization + β 2 Canada + β 3 U.K. + β 4 U.S. Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
13 Fixed Effects Variable No FE With FE Globalization (0.178) (0.160) Canada (3.936) U.K (3.866) U.S (3.493) Intercept (11.882) (9.945) N R Note: Standard errors in parentheses Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
14 Fixed Effects Emphasis on Non Economic Issues Normal Regression Globalization Index Score Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
15 Fixed Effects Emphasis on Non Economic Issues Canada France U.K. U.S. Fixed Effects Regression Globalization Index Score Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
16 Pause Take away points so far: Use dummy variables for nominal variables. (Interpret their effects as changes to the intercept.) Use fixed-effects regression when studying time-varying treatments (fixed effects are simply k 1 dummy variables for k units of study) Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
17 Pause Take away points so far: Use dummy variables for nominal variables. (Interpret their effects as changes to the intercept.) Use fixed-effects regression when studying time-varying treatments (fixed effects are simply k 1 dummy variables for k units of study) Now... interactions Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
18 The relationship between X 1 and Y can change for different values of X 2 Interaction Y X2 = 0 X2 = X1 E (Y ) = X 1 + 2X 2 + 1(X 1 X 2 ) Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
19 The relationship between X 1 and Y can change for different values of X 2 Interaction Y X2 = 0 X2 = X1 E (Y ) = X 1 + 2X 2 + 1(X 1 X 2 ) Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
20 The relationship between X 1 and Y can change for different values of X 2 Interaction Y X2 = 0 X2 = X1 E (Y ) = X 1 + 2X 2 + 1(X 1 X 2 ) Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
21 Back to our health care poll Support for Obama health care plan CNN/ORC poll, September 11 13, Strongly oppose Moderately oppose Moderately support Strongly support Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
22 Interaction terms As you d expect, opinions about HCR were sharply divided along party lines Strongly favor Support for Obama health care plan Moderately favor Moderately oppose Strongly oppose GOP Ind. Dem. Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
23 Interaction terms Suppose we want to know whether education strengthens the relationship between party ID and HCR opinion We can model this by including an interaction term We will use college education (0=no college degree, 1=college degree) The interaction term is simply the college variable multiplied by the party variable (0=GOP, 1=Ind., 2=Dem.) Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
24 Interaction terms The equation then becomes: HCR support = β 0 + β 1 Party + β 2 College + β 3 (Party College) In other words, When College=0, the slope is given by β 1 and the y-intercept by β 0 When College=1, the slope is given by β 1 + β 3 and the y-intercept by β 0 + β 2 We make inferences about the interaction term, β 3, like normal. Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
25 Interaction term Variable Constant (0.055) Party (0.039) College (0.085) Party College (0.061) N = 981 R 2 = Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
26 Interaction terms Support for Obama health care plan Strongly favor Moderately favor Moderately oppose Strongly oppose GOP Ind. Dem. GOP Ind. Dem. Non college College Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
27 Interaction terms Strongly favor Support for Obama health care plan Moderately favor Moderately oppose Strongly oppose GOP Independent Democrat Non college College Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
28 Equations Variable Constant (0.055) Party (0.039) College (0.085) Party College (0.061) N = 981 R 2 = All: HCR support = Party.11 College +.33 Party College Non-college: HCR = Party College: HCR = Party Lecture 21 (QPM 2016) Dummies and Interactions November 16, / 26
Class business PS is due Wed. Lecture 20 (QPM 2016) Multivariate Regression November 14, / 44
Multivariate Regression Prof. Jacob M. Montgomery Quantitative Political Methodology (L32 363) November 14, 2016 Lecture 20 (QPM 2016) Multivariate Regression November 14, 2016 1 / 44 Class business PS
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