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Interaction Terms and dummy variables in Regression

Interaction Terms and dummy variables in Regression. Dummy variables. Dichotomous independent variables Takes value of 0 or 1 Gender = female (yes or no); Democrat (yes or no); South (yes or no); Klingon v Earthling; etc. Interactions between variables.

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Interaction Terms and dummy variables in Regression

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  1. Interaction Terms and dummy variables in Regression

  2. Dummy variables • Dichotomous independent variables • Takes value of 0 or 1 • Gender = female (yes or no); Democrat (yes or no); South (yes or no); Klingon v Earthling; etc.

  3. Interactions between variables • Effect of one X variable may depend another X variable • Effect of X1 conditional on X2 • Effect of education on income may depend on gender (dummy variable) or age.

  4. Interactions • Tested with OLS regression • Easiest to understand when a dichotomous (dummy, categorical) variable interacted with a interval variable • Also works with continuous * continuous

  5. First, a dummy variable example • Data used is fake and includes the following variables as follows: • Race (Klingon = 0, Earthling = 1) • Education (4 <–> 16 years) • Age (25 <–> 60) • Income (100 <–> 280 dollars) • Income is Dependent variable

  6. Initial Model No interaction here: Each X variable is estimated to have its own independent association with Y (income)

  7. Initial Model Recall, how is t statistic calculated? How do we know if slope (Coef.) is significantly different than 0?

  8. Earthling 23+52.8 units Income Klingon 23 units Education -> In this case, the “slope” of X1 (Klingon =0 Earthling = 1) is an intercept difference. Slope of the effect of X (Educ) on Y (income) same for both...

  9. Earthling 23+52.8 units Income Klingon 23 units Education -> Klingon: Y = a + bX1 (12.8 * Educ) + bX2 (52.8 * 0) Earth: Y = a + bX1 (12.8 * Educ) + bX2 (52.8 * 1) Slope of the effect of X (Educ) on Y (income) same for both...

  10. Interactive Model • Does education affect income differently by race? • Find out by multiplying observations for Education by observations by race • Educationi * Earthlingi

  11. Interaction = product term

  12. Klingon Income Earthling Education -> In this case, the slope of X (Educ) on Y (income) is different for each group. It is conditional on whether one is from Earth of Klingon

  13. Specification • DO NOT omitting variables that are part of the interaction • All variables that are part of the interaction stay in the equation • e.g., don’t drop the Education and Earthling variables while leaving in Education * Earthling

  14. F-test • Omitting variables. • Not performing an F-test • Need to know if interaction contributes to model

  15. The F-test formula is where k denotes the number of variables, subscript 1 refers to original model and subscript 2 refers to the expanded model. F-Test Formula

  16. F-Test = (.74-.70)/(3-2) (1-.74)/(100-3-1) = 14.8 Critical value for F < 3.84 14.8 > 3.84 so interactive model is statistically significant

  17. Evaluating the Overall Model • Interactive terms lessen parsimony, increase difficulty of interpretation. • Don’t do unless the interactive adds explanatory power. • For OLS perform an F-test.

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