introduction to statistics: political science (class 4) revisiting the idea of confounds why mv...
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Introduction to Statistics: Political Science (Class 4)
Revisiting the Idea of ConfoundsWhy 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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Bush FT
Obam
a F
TDemocrats Republicans
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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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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%
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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
Economic Assessments (1=much better; 5=much worse)
0.750 0.081 9.32 0.000
Constant -0.749 0.365 -2.05 0.041
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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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?
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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
• 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. 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?
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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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1
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veryconservative
conservative middle-of-the-road
liberal very liberal
Ob
am
a F
av
ora
bili
tyMales Females
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. 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
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. t P
Gender (1=female) 0.163 0.094 1.740 0.082
Ideology (-2=very cons, 2=v. liberal) 0.716 0.041 17.260 0.000
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
Ideology (-2=very cons, 2=v. liberal) 0.732 0.039 18.960 0.000
Constant 2.702 0.068 39.870 0.000
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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$0
$50,000
$100,000
$150,000
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# of Firemen
Am
ou
nt
of
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e D
am
ag
e
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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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$0
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$100,000
$150,000
$200,000
$250,000
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# of Firemen
Am
ou
nt
of
Fir
e D
am
ag
eSmall Fires Big Fires
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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