Predicting Elections with Regressions

Mario GuerreroPolitical Science 104Thursday, November 13, 2008

Learning Regression •What is a Regression?

•Prediction Models

•The 2008 Presidential Election

•Research: Money and Politics

•Classic Case of Operationalizing

•My Final Findings

•Effect-Descriptive or Causal Inference Coefficient•Approval Rating versus Vote Share Example•Interpreting a Scatterplot

•How a Regression works on SPSS and Interpretation

•How to use regression to predict dependent variable•Predicting Vote Share

•Did we predict Obama’s victory in June 2008?

•Asking a new question based on money in elections

•Reworking the variables from concepts

•Was I able to predict money in elections?

What is a regression?

What is a

regression?

Prediction

Models

2008 Election

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Mission:Operationa

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Think back to last week’s lectures:

•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.

We learned about two different types of coefficients:

How does a regression work?

What is a

regression?

Prediction

Models

2008 Election

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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.

First Step – Some DataElection Year (President) Approval Rating

1972 (Nixon v. McGovern) 57%

1976 (Carter v. Ford) 45%

1980 (Reagan v. Carter) 32%

1984 (Reagan v. Mondale) 55%

1988 (Bush v. Dukakis) 51%

1992 (Clinton v. Bush) 37%

1996 (Clinton v. Dole) 58%

2000 (Bush v. Gore) 55%

2004 (Bush v. Kerry) 49%

2008 (Obama v. McCain) 30%

What is a

regression?

Prediction

Models

2008 Election

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Election Year (President) Vote Share

1972 (Nixon v. McGovern) 60%

1976 (Carter v. Ford) 48%

1980 (Reagan v. Carter) 41%

1984 (Reagan v. Mondale) 59%

1988 (Bush v. Dukakis) 53%

1992 (Clinton v. Bush) 37%

1996 (Clinton v. Dole) 49%

2000 (Bush v. Gore) 48%

2004 (Bush v. Kerry) 50%

2008 (Obama v. McCain) 46%

Second Step – Graphing the Data

What is a

regression?

Prediction

Models

2008 Election

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•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.

Third Step – Fitting a Line

What is a

regression?

Prediction

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2008 Election

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•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.

Doing a Scatterplot in SPSS

What is a

regression?

Prediction

Models

2008 Election

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Mission:Operational

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Interpreting the Output in SPSS

What is a

regression?

Prediction

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2008 Election

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y = mx + bDependent Variable

(Vote Share)

Independent Variable

(Approval Ratings)

y = .500x + 25.667

y = mx + by = mx + by = mx + by = mx + b

Don’t forget significance!

Interpretation of a Regression

What is a

regression?

Prediction

Models

2008 Election

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y = .500x + 25.667How 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!!)

Controlling with Regression

What is a

regression?

Prediction

Models

2008 Election

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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:

Research: Prediction Models

What is a

regression?

Prediction

Models

2008 Election

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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

Research: Prediction Models

What is a

regression?

Prediction

Models

2008 Election

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Mission:Operational

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In this limited example, we could have potentially predicted the outcome of the 2008 Presidential Election by using this equation.

y = .500x + 25.667

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 = 40.667Incumbent 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 = 50.167Incumbent Party’s Actual Vote Share Total: 50.0

The model almost perfectly predicted Bush’s performance.

Research: Prediction Models

What is a

regression?

Prediction

Models

2008 Election

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Mission:Operational

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In 1992, Lewis-Beck and Rice come up with a model that predicted the ElectoralVote 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

2008 Elections

What is a

regression?

Prediction

Models

2008 Election

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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

2008 Elections

What is a

regression?

Prediction

Models

2008 Election

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Mission:Operationa

lize Final Results

Y = 7.76(1) + 0.86(30) + 0.52(36) + 19.66(1) + 6.83

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.

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

My Research: Money in Politics

What is a

regression?

Prediction

Models

2008 Election

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Mission:Operational

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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

A Few Considerations…

What is a

regression?

Prediction

Models

2008 Election

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Mission:Operational

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•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.

Operationalizing Variables

What is a

regression?

Prediction

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2008 Election

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Independent Concepts:economic considerationspresidential popularityparty strengthcandidate appeal

Dependent Concept: political contributions

Independent Variables:Real GDP per capitaReal disposable incomeGallup’s popularity rating in JuneHow many seats the incumbent party has against the non-incumbent party in CongressIf the candidate won 60% of the vote in the primary. Dependent Concept: Percentage incumbent has fundraised against non-incumbent

Operationalizing Variables

What is a

regression?

Prediction

Models

2008 Election

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Mission:Operationa

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Independent Concepts:economic considerationspresidential popularityparty strengthparty appeal (not candidate)

Dependent Concept: political contributions

Independent Variables:Real GDP per capitaReal disposable incomeGallup’s popularity rating in JuneSeat exposure calculationTime the incumbent party has held in the White HouseDependent Concept: Percentage incumbent has fundraised against non-incumbent

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:

The Independent Variables

What is a

regression?

Prediction

Models

2008 Election

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Mission:Operationa

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economic considerations presidential popularity party strength party appeal•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

•Gallup’s presidential

popularity rating in June

•Gallup’s congressional

popularity rating in June

•Seat exposure calculation

•Difference in seats between

parties•Number of incumbents

•Time the incumbent party has

held in the White House•Duration of

majority party’s hold in Congress

I also attempted to add two control variables: interest groups effects and media effects.

Final Results -- Equation

What is a

regression?

Prediction

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2008 Election

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In the beginning, I began with:

But through operationalizing, I ended up with:

Final Results -- Regression

What is a

regression?

Prediction

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These circled numbers are my coefficients for each of the variables.

Final Results -- Regression

What is a

regression?

Prediction

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2008 Election

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This is the intercept for my regression where all my independent variables will equal zero.

Final Results -- Regression

What is a

regression?

Prediction

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2008 Election

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The stars next to each of the coefficients and intercept indicate that each one of my coefficients turned out to be significant.

Final Results -- Regression

What is a

regression?

Prediction

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2008 Election

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The final prediction equation that we come up with is:

Y = -.0600(EC1) + .0817(EC2)

+ .0227(CP) + -.0072(NI) +

-.1707(DM) + 3.089

Final Results -- Predictions

What is a

regression?

Prediction

Models

2008 Election

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Mission:Operationa

lize Final Results

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%).

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.