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Introduction to Statistics: Political Science (Class 4)

Introduction to Statistics: Political Science (Class 4). Revisiting the Idea of Confounds Why MV Regression? Redundancy v. Suppression. A few words about covering multivariate regression over a few weeks My hope – you will: Understand the mechanics of interpreting MV models

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Introduction to Statistics: Political Science (Class 4)

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  1. Introduction to Statistics: Political Science (Class 4) Revisiting the Idea of Confounds Why MV Regression? Redundancy v. Suppression

  2. A few words about covering multivariate regression over a few weeks • My hope – you will: • Understand the mechanics of interpreting MV models • Have a basic grasp of what MV analysis does and does not “get us” • Today we will: • Revisit the issue of what happens when we “control for a variable” and why we do it • Talk a bit more about interpretation of dichotomous and nominal IVs

  3. Why do multivariate regression? • Why did most people vote for Republicans in the midterm? • John Boehner: “The American people [were] concerned about the government takeover of healthcare.” • What else are the pundits/ officials saying? What do you think? What went into individuals’ vote choices this election? • How do we know who’s right?

  4. Why do multivariate regression? • Problem: potential explanations are often related to one another (confounded) • Identify independentrelationships between predictors and outcomes • I.e., relationships after accounting for confounds

  5. What happens when we add an IV? • It depends on: • the relationship between the new IV and the other IVs in the model • the relationship between the new IV and the outcome variable (DV) • Typically: Added variable has to be related to other IV(s) and the DV to affect coefficients on other IVs in a meaningful way • There are some (unusual) exceptions we won’t discuss • Note: adding a new variable will always change the estimates somewhat

  6. In most cases… • Adding a confounding variable – i.e., a variable associated with another IV and the DV – to a model will attenuate the coefficient on the original IV • Sometimes referred to as “redundancy” – IVs are redundant explanations for the outcome • Why does this happen?

  7. Bush Feeling Thermometer Obama Feeling Thermometer Party Affiliation

  8. Negative assessments of the economy  like Obama? • 2008 survey • Outcome: Evaluation of Obama (1=very unfavorable; 4=very favorable) • IVs: • Evaluation of performance of economy over past 12 months (1=much better; 5=much worse) • Party affiliation (-3=strong Rep; 3=strong Dem)

  9. Assessment of Economy Obama Favorability Party Affiliation One possibility? Consequences of using bivariate regression if this is the case?

  10. DV: Obama favorability (1-4)

  11. Obama Favorability Assessment of Economy Party Affiliation The regression suggests this ↑ So… relationship between economic assessments and Obama favorability appears to be biased in bivariate analysis. Why? Because we haven’t accounted for alternative explanation – PID

  12. What’s going on here?

  13. DV: Obama favorability (1-4) • Should we be confident in our estimate of the independent relationship between: • Economic Assessments and Obama favorability? • Party Identification and Favorability? • Other variables missing from this model? • Consequences?

  14. Dichotomous and Nominal

  15. DV: Obama favorability (1-4) Why did women like Obama more?

  16. DV: Obama favorability (1-4) “Controlling for the effects of ideology, gender is…” Expected value: very conservative male? Middle-of the-road male? Very liberal male? Females?

  17. Note: given our model specification, the effect of gender doesn’t depend on the value of ideology

  18. DV: Obama favorability (1-4) What else might predict Obama favorability? Consequences of not including those measures for our estimate of The effects of gender? The effects of ideology?

  19. DV: Obama favorability (1-4) Religion? Excluded category: agnostic/atheist Why didn’t the coefficient on gender change substantially?

  20. “Suppression” • Omitting a variable from the model CAN suppress the estimate of an independent relationship • I.e., adding a variable can make the coefficient on an original predictor larger or even change signs

  21. Do firemen help reduce amount of damage caused by a fire? Number of Fireman at Fire Fire Damage

  22. Severity of Fire Do firemen help reduce amount of damage caused by a fire? Number of Fireman at Fire Fire Damage

  23. Regression and Causality • Can we answer these questions? • Did feelings about Bush and Party Identification cause feelings about Obama? • Did assessments of the economy, party identification and ideology cause Obama’s favorability?

  24. Regression and Causality • Regression usually can not decisively determine causality • Potential for reverse causality • Unmeasured confounds • Instead we: • Rely on theory • Use multivariate regression to try to rule out (account for) the most compelling alternative explanations / confounds

  25. Notes and Next Time • Homework • TAs have homework 1 to return to you • Model answers are posted online • We are one class behind • Homework 2 will be handed out Thursday and due on Tuesday (it will cover dichotomous and nominal IVs and non-linear relationships) • Next time: • Functional form in multivariate regression

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