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

Introduction to Statistics: Political Science (Class 4)

Revisiting the Idea of ConfoundsWhy 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– 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

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?

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

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

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?

Party Affiliation

Bush Feeling Thermometer

Obama Feeling Thermometer

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Bush FT

Obam

a F

TDemocrats Republicans

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)

Assessment of Economy

Party Affiliation

Obama Favorability

One possibility? Consequences of using bivariate regression if this is the case?

Democrats Republicans

gotten much better 0.4% 0.5%

gotten better 0.9% 0.9%

stayed about the same 0.9% 11.3%

gotten worse 21.9% 50.0%

gotten much worse 75.9% 37.4%

Coef. Std. Err. t p

Economic Assessments (1=much better; 5=much worse)

0.332 0.068 4.9 0.000

Party Identification 0.350 0.020 17.5 0.000

Constant 1.097 0.306 3.6 0.000

Coef. Std. Err. t p


0.750 0.081 9.32 0.000

Constant -0.749 0.365 -2.05 0.041

DV: Obama favorability (1-4)

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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gotten much better gotten better stayed about thesame

gotten worse gotten much worse

Obam

a Fav

ora

bili

ty (1-

4)

All Democrats Republicans

What’s going on here?

Coef. Std. Err. t p


0.332 0.068 4.9 0.000

Party Identification 0.350 0.020 17.5 0.000

Constant 1.097 0.306 3.6 0.000

• 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?


Dichotomous and Nominal

DV: Obama favorability (1-4)Coef. Std. Err. t p

Gender (1=female) 0.297 0.120 2.490 0.013

Constant 2.456 0.087 28.320 0.000

Why did women like Obama more?

DV: Obama favorability (1-4)Coef. Std. Err. t p

Gender (1=female) 0.297 0.120 2.490 0.013

Constant 2.456 0.087 28.320 0.000

Coef. Std. Err. t p

Gender (1=female) 0.141 0.093 1.520 0.129

Ideology (-2=very cons, 2=v. liberal) 0.732 0.039 18.960 0.000

Constant 2.702 0.068 39.870 0.000

“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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veryconservative

conservative middle-of-the-road

liberal very liberal

Ob

am

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av

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tyMales Females

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


Coef. Std. Err. t p

Gender (1=female) 0.141 0.093 1.520 0.129


Constant 2.702 0.068 39.870 0.000

What else might predict Obama favorability? Consequences of not including those measures for our estimate of

The effects of gender? The effects of ideology?

Coef. Std. Err. t P

Gender (1=female) 0.163 0.094 1.740 0.082


Protestant -0.200 0.139 -1.440 0.151

Roman Catholic -0.145 0.146 -1.000 0.320

Other Religion -0.364 0.144 -2.530 0.012

Constant 2.871 0.111 25.810 0.000

Coef. Std. Err. t p

Gender (1=female) 0.141 0.093 1.520 0.129


Constant 2.702 0.068 39.870 0.000


Why didn’t the coefficient on gender change substantially?

Religion?

Excluded category: agnostic/atheist

“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

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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eSmall Fires Big Fires

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?

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

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

Documents

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