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Introduction to Statistics: Political Science (Class 4)

Explore the intricacies of multivariate regression analysis in political science, focusing on confounds and the effects of additional variables on model interpretation. Delve into examples and discussions to grasp nuances in statistical approaches.

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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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