Introduction to Statistics: Political Science (Class 4)

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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 whos 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 wont
  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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Bush Feeling Thermometer
Obama Feeling Thermometer
Party Affiliation
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Negative assessments of the economy ? like Obama?

• 2008 survey
• Outcome Evaluation of Obama (1very unfavorable
  4very favorable)
• IVs
• Evaluation of performance of economy over past 12
  months (1much better 5much worse)
• Party affiliation (-3strong Rep 3strong Dem)

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Assessment of Economy
Obama Favorability
Party Affiliation
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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DV Obama favorability (1-4)
Coef. Std. Err. t p
Economic Assessments (1much better 5much worse) 0.750 0.081 9.32 0.000
Constant -0.749 0.365 -2.05 0.041
Coef. Std. Err. t p
Economic Assessments (1much better 5much 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
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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 havent accounted for
alternative explanation PID
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DV Obama favorability (1-4)
Coef. Std. Err. t p
Economic Assessments (1much better 5much 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?

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Dichotomous and Nominal
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DV Obama favorability (1-4)
Coef. Std. Err. t p
Gender (1female) 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 (1female) 0.297 0.120 2.490 0.013
Constant 2.456 0.087 28.320 0.000
Coef. Std. Err. t p
Gender (1female) 0.141 0.093 1.520 0.129
Ideology (-2very cons, 2v. 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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Note given our model specification, the effect
of gender doesnt depend on the value of ideology
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DV Obama favorability (1-4)
Coef. Std. Err. t p
Gender (1female) 0.141 0.093 1.520 0.129
Ideology (-2very cons, 2v. 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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DV Obama favorability (1-4)
Coef. Std. Err. t p
Gender (1female) 0.141 0.093 1.520 0.129
Ideology (-2very cons, 2v. liberal) 0.732 0.039 18.960 0.000
Constant 2.702 0.068 39.870 0.000
Religion?
Coef. Std. Err. t P
Gender (1female) 0.163 0.094 1.740 0.082
Ideology (-2very cons, 2v. 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
Excluded category agnostic/atheist
Why didnt the coefficient on gender change
substantially?
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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
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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 Obamas
  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