Transcript mariolecture

Predicting Elections
with Regressions
Mario Guerrero
Political Science 104
Thursday, November 13, 2008
Learning Regression
•What is a Regression?
•Effect-Descriptive or Causal Inference Coefficient
•Approval Rating versus Vote Share Example
•Interpreting a Scatterplot
•How a Regression works on SPSS and Interpretation
•Prediction Models
•How to use regression to predict dependent variable
•Predicting Vote Share
•The 2008 Presidential Election
•Did we predict Obama’s victory in June 2008?
•Research: Money and Politics
•Asking a new question based on money in elections
•Classic Case of Operationalizing
•Reworking the variables from concepts
•My Final Findings
•Was I able to predict money in elections?
What is a regression?
Think back to last week’s lectures:
We learned about two different types of coefficients:
•Those which are “correlation” that tell you how well your
relationship is being measured. (PRE, Q, Gamma)
•Those which are “effect-descriptive” that tell you how
much you independent variable affects your dependent
variable.
Regression yields an effect-descriptive coefficient.
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
How does a regression work?
In regression, we are estimating the relationship between two
interval level variables.
For example, we might be interested in seeing the relationship between
approval ratings and vote share.
So far, we’ve learned a couple of ways to estimate the relationship
between two variables:
Crosstabs, Gamma, t-tests, Scatterplots, Boxplots
Only scatterplots can really tell us how two interval level variables interact
with each other.
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
First Step – Some Data
Election Year (President)
Approval Rating
Election Year (President)
Vote Share
1972 (Nixon v. McGovern)
57%
1972 (Nixon v. McGovern)
60%
1976 (Carter v. Ford)
45%
1976 (Carter v. Ford)
48%
1980 (Reagan v. Carter)
32%
1980 (Reagan v. Carter)
41%
1984 (Reagan v. Mondale)
55%
1984 (Reagan v. Mondale)
59%
1988 (Bush v. Dukakis)
51%
1988 (Bush v. Dukakis)
53%
1992 (Clinton v. Bush)
37%
1992 (Clinton v. Bush)
37%
1996 (Clinton v. Dole)
58%
1996 (Clinton v. Dole)
49%
2000 (Bush v. Gore)
55%
2000 (Bush v. Gore)
48%
2004 (Bush v. Kerry)
49%
2004 (Bush v. Kerry)
50%
2008 (Obama v. McCain)
30%
2008 (Obama v. McCain)
46%
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
Second Step – Graphing the Data
•Scatterplots plots the interval variables so
we can visually interpret how low/high
values on one variable affects values on
another variable.
•Regressions simply estimate the
relationship between these two variables by
drawing a line through the data and
estimating its slope and intercept.
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
Third Step – Fitting a Line
•SPSS is able to plot a line through the data
in the scatterplot that best represents the
relationship between approval ratings and
vote share.
•This is regression. However, the regression
output simply represents this by using
numbers instead of a graphical
representation.
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
Doing a Scatterplot in SPSS
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
Interpreting the Output in SPSS
Dependent
Variable
(Vote Share)
y = mx + b
Independent
Variable
(Approval Ratings)
y = .500x + 25.667
Don’t forget
significance!
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
Interpretation of a Regression
y = .500x + 25.667
How is this interpreted?
•Vote Share (Dependent Variable) is represented by Y. Approval
ratings (Independent Variable) is represented by X.
•If our independent variable, approval ratings, is zero, then the value of
Y, vote share, is 25.667. Incumbent candidates begin with a 26-point
vote share, regardless of approval rating.
•On average, for every unit increase in approval ratings, we see a .500
increase in vote share. (.500 is our effect-descriptive
coefficient!!)
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
Controlling with Regression
While we can’t add additional variables to a scatterplot, the regression is able to handle more than just two
variables. Adding variables allows us to account for several different explanations for changes in our
dependent variable. This is how you run a regression, with or without additional control variables:
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
Research: Prediction Models
Research in Political Science has utilized the regression model to its advantage.
While regression yields an effect-descriptive coefficient, Political Scientists
have used it in attempt to predict who will take the White House in each
presidential election.
How does this work?
Each regression yields coefficients for each variable you’re working with. Those
coefficients give you the equation of a predicted line based on the data. For
example, we were left with the equation in the previous example:
y = .500x + 25.667
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
Research: Prediction Models
y = .500x + 25.667
In this limited example, we could have potentially predicted the outcome of the
2008 Presidential Election by using this equation.
2008 Presidential Election: (Obama vs. McCain)
Incumbent’s (Bush) Approval Rating in June 2008: 30%
Incumbent Party’s Predicted Vote Share Total: y = .500(30)+25.667 = 40.667
Incumbent Party’s Actual Vote Share Total: 46.1
The model underpredicted McCain’s performance by around 6%
2004 Presidential Election (Bush vs. Kerry)
Incumbent’s (Bush) Approval Rating in June 2004: 49%
Incumbent Party’s Predicted Vote Share Total: y = .500(49)+25.667 = 50.167
Incumbent Party’s Actual Vote Share Total: 50.0
The model almost perfectly predicted Bush’s performance.
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
Research: Prediction Models
In 1992, Lewis-Beck and Rice come up with a model that predicted the Electoral
Vote Share by taking into account four different variables.
From 1948-1988, Lewis-Beck and Rice were
pretty adept at predicting vote share.
Y = 7.76EC + 0.86PP +
0.52PS + 19.66CA +
6.83
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
2008 Elections
Y = 7.76EC + 0.86PP + 0.52PS + 19.66CA + 6.83
Economic Conditions (EC): GDP changes 1% from 2007 Q4 to 2008 Q2.
Presidential Popularity (PP): Bush’s popularity rating is at 30% in June 2008.
Party Strength (PS): The Democrats have 36 more members in Congress at the
midterm elections.
Candidate Appeal (CA): John McCain was able to win 61% of delegates in primary,
so the value becomes 1 for candidate appeal. (Arbitrary cut-off of 60%)
Y = 7.76(1) + 0.86(30) + 0.52(36) + 19.66(1) + 6.83
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
2008 Elections
Y = 7.76(1) + 0.86(30) + 0.52(36) + 19.66(1) + 6.83
Did the model correctly predict that John McCain would lose the
election and Barack Obama would win the election in June
2008?
YES!
7.76(1) + 0.86(30) + 0.52(36) + 19.66(1) + 6.83 = 41.33
In June 2008, the forecasting models predicted that John McCain would lose the
election with only 41.33% of the vote. McCain lost with 46% of the vote. It was off by
5%, but it correctly predicted that Barack Obama would win the election.
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
My Research: Money in Politics
Research Question: Money is connected to elections in some way that researchers
have not yet been able to quantify. Are money and elections connected? If we can
predict election vote share totals, can we predict how much money campaigns
fundraise?
Hypothesis: The same variables that affect vote share affect how much money the
incumbent party will fundraise. Economic considerations, presidential popularity,
party strength, and candidate appeal cause people to donate more money to their
political parties.
Concepts: economic considerations, presidential popularity, party strength,
candidate appeal, political contributions
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
A Few Considerations…
•My research ended up being much more influenced by congressional politics than
presidential politics. While I had learned about forecasting models for predicting
presidential elections, I was much more interested in congressional elections. Thus, I
immediately had to change my focus.
•While I gathered my inspiration from Lewis-Beck and Rice’s research, I had
essentially anticipated changing each variable in the equation in order to get the best
prediction model. This is a form of operationalization.
•My dependent variable would undoubtedly change from electoral vote share to
percentage of the incumbent party’s fundraising total.
•Most of the independent variables were subject to scrutiny and criticism for their
inclusion in the model.
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
Operationalizing Variables
Independent Concepts:
economic considerations
presidential popularity
party strength
candidate appeal
Dependent Concept:
political contributions
Independent Variables:
Real GDP per capita
Real disposable income
Gallup’s popularity rating in June
How many seats the incumbent party
has against the non-incumbent party
in Congress
If the candidate won 60% of the vote
in the primary.
Dependent Concept:
Percentage incumbent has fundraised
against non-incumbent
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
Operationalizing Variables
However, Lewis-Beck and Rice claim to have adopted a model to predict House seat
change, which would be much more appropriate for our model’s purposes:
Independent Concepts:
economic considerations
presidential popularity
party strength
party appeal (not candidate)
Dependent Concept:
political contributions
Independent Variables:
Real GDP per capita
Real disposable income
Gallup’s popularity rating in June
Seat exposure calculation
Time the incumbent party has
held in the White House
Dependent Concept:
Percentage incumbent has fundraised
against non-incumbent
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
The Independent Variables
economic considerations
•Real GDP per capita
•Real disposable income
•Considerations of GDP
in both a midterm and
presidential year
•Considerations of
income in both a
midterm and presidential
year
presidential popularity
•Gallup’s
presidential
popularity rating
in June
•Gallup’s
congressional
popularity rating
in June
party strength
party appeal
•Seat exposure
•Time the
calculation
incumbent
•Difference in party has held
seats between
in the White
parties
House
•Number of
•Duration of
incumbents
majority party’s
hold in
Congress
I also attempted to add two control variables: interest groups effects and media effects.
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
Final Results -- Equation
In the beginning, I began with:
But through operationalizing, I ended up with:
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
Final Results -- Regression
These circled numbers are my coefficients
for each of the variables.
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
Final Results -- Regression
This is the intercept for my regression where
all my independent variables will equal zero.
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
Final Results -- Regression
The stars next to each of the coefficients and
intercept indicate that each one of my
coefficients turned out to be significant.
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
Final Results -- Regression
The final prediction equation that we come up
with is:
Y = -.0600(EC1) +
.0817(EC2) +
.0227(CP) +
-.0072(NI) +
-.1707(DM) + 3.089
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
Final
Results
-Predictions
Y = -.0600(EC1) + .0817(EC2) + .0227(CP) + -.0072(NI) + -.1707(DM) + 3.089
Actual Probability: The actual
percentage that the incumbent party
fundraised.
Predicted Probability: The predicted
percentage that my model predicted.
Error: The difference between the two.
For 2008, the model predicts that
Democrats would fundraise three times
as much as the Republicans (~25%).
What is a
2008
Mission:
regression?
Elections
Operationalize
Prediction
My
Final
Models
Research
Results
Learning Regression
•It all began with a regression.
•I built on previous research out there
(consistency).
•My research started with a question and a
hypothesis.
•To answer my question, prediction and
verification were absolutely necessary. My
research is a great example of
operationalizing.
•The analysis and application of my findings
is relevant to current questions about
politics.
•The topic was intrinsically interesting and
most of all, it ended up being fun.