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

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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

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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?

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

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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

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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?

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Party Affiliation Bush Feeling Thermometer Obama Feeling Thermometer

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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)

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

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DemocratsRepublicans gotten much better0.4%0.5% gotten better0.9% stayed about the same0.9%11.3% gotten worse21.9%50.0% gotten much worse75.9%37.4%

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Coef.Std. Err.tp Economic Assessments (1=much better; 5=much worse) 0.3320.0684.90.000 Party Identification0.3500.02017.50.000 Constant1.0970.3063.60.000 Coef.Std. Err.tp Economic Assessments (1=much better; 5=much worse) 0.7500.0819.320.000 Constant-0.7490.365-2.050.041 DV: Obama favorability (1-4)

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Assessment of Economy Party Affiliation Obama Favorability 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

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What’s going on here?

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Coef.Std. Err.tp Economic Assessments (1=much better; 5=much worse) 0.3320.0684.90.000 Party Identification0.3500.02017.50.000 Constant1.0970.3063.60.000 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? DV: Obama favorability (1-4)

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Dichotomous and Nominal

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DV: Obama favorability (1-4) Coef.Std. Err.tp Gender (1=female)0.2970.1202.4900.013 Constant2.4560.08728.3200.000 Why did women like Obama more?

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DV: Obama favorability (1-4) Coef.Std. Err.tp Gender (1=female)0.2970.1202.4900.013 Constant2.4560.08728.3200.000 Coef.Std. Err.tp Gender (1=female)0.1410.0931.5200.129 Ideology (-2=very cons, 2=v. liberal)0.7320.03918.9600.000 Constant2.7020.06839.8700.000 “Controlling for the effects of ideology, gender is…” Expected value: very conservative male? Middle-of the-road male? Very liberal male? Females?

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

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DV: Obama favorability (1-4) Coef.Std. Err.tp Gender (1=female)0.1410.0931.5200.129 Ideology (-2=very cons, 2=v. liberal)0.7320.03918.9600.000 Constant2.7020.06839.8700.000 What else might predict Obama favorability? Consequences of not including those measures for our estimate of The effects of gender? The effects of ideology?

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Coef.Std. Err.tP Gender (1=female)0.1630.0941.7400.082 Ideology (-2=very cons, 2=v. liberal)0.7160.04117.2600.000 Protestant-0.2000.139-1.4400.151 Roman Catholic-0.1450.1460.320 Other Religion-0.3640.144-2.5300.012 Constant2.8710.11125.8100.000 Coef.Std. Err.tp Gender (1=female)0.1410.0931.5200.129 Ideology (-2=very cons, 2=v. liberal)0.7320.03918.9600.000 Constant2.7020.06839.8700.000 DV: Obama favorability (1-4) Why didn’t the coefficient on gender change substantially? Religion? Excluded category: agnostic/atheist

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“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

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

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

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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?

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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

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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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