Preso on nate silver


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Preso on nate silver

  1. 1. Modeling the 2012 U.S. Presidential Election Exploring the Forecasting MethodsOf Nate Silver and the Five-Thirty-Eight Blog Prepared for the 3/1/13 RTP Analysts Luncheon Meetup By Bruce Conner Consolidated Behaviors and Attitudes 1 Consolidated Behaviors and Attitudes
  2. 2. Purposes of This Discussion• Walk through the elements of Nate Silver’s methods in predicting the 2012 Presidential election• “Kick around” some outstanding questions about those methods• Explore whether participating analysts are using similar methods in their day-to-day work – and how they are using them?• Sources listed in a “rough bibliography” at the back of this presentation 2 Consolidated Behaviors and Attitudes
  3. 3. Background: Nate Silver• Developed PECOTA, a highly-successful “sabremetric” model used for forecasting the performance and career development of Major League players• In 2008: – Correctly predicted 49 out of 50 states (missed on Indiana) – Correctly predicted all U.S. Senate elections – Made better predictions for some of the primaries than major polls, using a demographic prediction model• In 2010, less good predictions in U.S. House races• In 2012: – Correctly predicted all 50 states and the District of Columbia 3 Consolidated Behaviors and Attitudes
  4. 4. Nate’s Approach to Forecasting the Elections (1)• Forecast Each State – As we learned in 2000, the election is decided in the Electoral College: – Nate decomposes the election into the 50 states and the District of Columbia, and forecasts popular vote in each separately – National projections of popular vote are simply the aggregate of the state popular votes – This approach is a type of hierarchical modeling • Who is using hierarchical modeling techniques – and how are you using them?• Leverage Multiple Data/Predictor Sources – Polls within each state – Voter registration and demographics – Economic indicators – “Borrowed information” from other (similar) states – National polling (used only for inferring trends in the individual states) – Etc. 4 Consolidated Behaviors and Attitudes
  5. 5. Nate’s Approach to Forecasting the Elections (2)• Calibration of Each Poll (Offsetting “House Effects”) – Measure -- and offset -- systematic bias of each pollster – This is done by a regression for each pollster of all their national polls against a weighted average of the national polls, as well as a regression of their polls in the various states against a weighted average of the polls in each state. Nate also lowered weight of polls that seem to be consistent outliers 5 Consolidated Behaviors and Attitudes
  6. 6. Nate’s Approach to Forecasting the Elections (3)• An Economic Index is Used as an “Additional Poll.” It is based on: – The four factors used to date recessions • Job growth (nonfarm payrolls) • Personal income • Industrial production • Consumption – Inflation (CPI) – Change in S&P 500 Index – Consensus forecast of gross domestic product growth over the next two economic quarters, as taken from the median of The Wall Street Journal’s monthly forecasting panel• The economic index is used as a predictor of trend in future polls – as a “gravitational factor” that is likely to influence polls in the coming periods (with a lag effect). It is gradually removed (deweighted) from the model as the election approaches. 6 Consolidated Behaviors and Attitudes
  7. 7. Nate’s Approach to Forecasting the Elections (4)• Adjustment to state-level polls based on trend – National polls and state polls show trends over time – Particularly when some states do not have recent polls (or recent polls by a particular pollster), it is often reasonable to infer that if those polls would have been repeated today, they would be affected by trends – The method to determine trends is a regression with (1) dummy variables for each week and (2) dummy variables for each pollster in each state. – A LOESS regression is used to smooth the trend. – A “trend” correction is then applied to the older polls to reflect the effects of the trend since the poll was taken – An example of “Bayesian thinking” 7 Consolidated Behaviors and Attitudes
  8. 8. Nate’s Approach to Forecasting the Elections (5)• A multiple regression of demographics, registration, and similar factors is treated as an additional poll – Voter registration, race, gender, age, income, etc. as predictors of how a state will vote 8 Consolidated Behaviors and Attitudes
  9. 9. Nate’s Approach to Forecasting the Elections (6)• Weighted Averaging of Polls – The predictions from the demographic regression and from the economic index are treated as additional polls – Weight of the economic index is reduced as election approaches, until it disappears in the final forecast – Weighting of Polls Against Each Other Is Based On • Sample size • Recency (weighting is done using a “half life” formula – because polls closer to the election are more accurate) • Ratings of pollsters (see following slides) 9 Consolidated Behaviors and Attitudes
  10. 10. Nate’s Approach to Forecasting the Elections (7)• Pollster Ratings* Reflect Accuracy of Each Pollster in Predicting Actual Election Results – Raw ratings scores are done based on a multiple regression – Each data point is a published poll taken by a pollster in one of: • A presidential, gubinatorial, senatorial, congressional, or “generic house” race • A full range of elections/primaries/caucuses • Within 21 days of an election, primary, or caucus • For elections starting with the 1998 election cycle – The rating of each pollster is based on all of the polls attributed to that pollster – across the years and in the different types of elections – The dependent variable is the size of the error in predicting the gap between the top two candidates *For more detail on pollster ratings methods, see additiona l slides near end of this presentation 10 Consolidated Behaviors and Attitudes
  11. 11. Nate’s Approach to Forecasting the Elections (8)• Pollster Ratings (Continued) – Some properties of the raw rating regression: • Pollsters are “rewarded” for accurately predicting results (minimizing error) further away from the election • Pollsters are also “rewarded” for “degree of difficulty” of predictions – It’s harder to accurately predict state and local elections than national popular vote in a presidential election, and to predict primaries than “generals” – as demonstrated in the following average percent error bar chart 11 Consolidated Behaviors and Attitudes
  12. 12. Nate’s Approach to Forecasting the Elections (9)• Nearest Neighbor – Particularly useful for states that have low levels of polling • This tends to be true for states with lower population and for states “not in play” – Nate Silver is a big fan of Bayesian approaches and Bayesian thinking – could he have used such approaches, instead of Nearest Neighbor, to “borrow” information from similar states? 12 Consolidated Behaviors and Attitudes
  13. 13. Nate’s Approach to Forecasting the Elections (10)• Modeling Uncertainty: based on a number of factors, each state forecast includes both a point forecast and an “uncertainty distribution” (a normal curve????). Uncertainty is influenced by: – Number of (reliable) polls – Sample sizes – Number of undecided voters – Consistency of the polls being averaged (size of standard deviation) – Time until election • Has Nate modeled levels of uncertainty in various kinds of elections at various removes from the election? How is this analysis done? – NOTE: Nate provides both a “Now Forecast” (“If the election were held today …”) and a true forecast. These completely converge as election nears 13 Consolidated Behaviors and Attitudes
  14. 14. Nate’s Approach to Forecasting the Elections (11)• Monte Carlo Simulation: on a regular basis (eventually every night), 10,000 simulations of the election are run – Results for each state in each simulation is arrived at separately, providing both the “expected” (mean) result and the uncertainty (a normal curve???) – Some approach is used to take account that states are not independent of each other (e.g., Minnesota and Wisconsin tend to move in tandem) – nearest neighbor? Trending? – For each simulation, a winner is picked – and electoral votes assigned accordingly – For each simulation, electoral votes are totaled and a winner picked – The thousands of simulations provide a distribution of probable electoral college outcomes and a distribution of popular vote outcomes (by state and national) 14 Consolidated Behaviors and Attitudes
  15. 15. Nate’s Approach to Forecasting the Elections (12)• Major event adjustments – Based on previous elections, certain predictable events are expected to have a somewhat predictable effect over the course of the campaign cycle • In 2012, both candidates were “expected” to get a “convention bounce” of a certain magnitude • As challenger, Romney was also “expected “ to get a bounce of a certain magnitude from the 1st debate. • Bounces from previous elections tend to be “noisy” but do show average effects – The effect of the bounces s expected (predicted) to decay in predictable way – Nate Silver: • Factored in expected bounces and decays in making forecasts of final results • Recognized increased uncertainty during periods when bounces were most recent • Temporarily penalized or rewarded candidates who under- or over-performed the expected bounces 15 Consolidated Behaviors and Attitudes
  16. 16. Projected (Expected)Convention Bounces 16 Consolidated Behaviors and Attitudes
  17. 17. Additional Issues (Related to Polling)Not Addressed in This Presentation • Differing Sampling Approaches of Polls • Differing Likely Voter Models of Polls • Differing Survey Media of Polls – Web only? – Include cell phones in sample? • Differing Weighting Schemes of Polls – To correct for demographic bias – To offset biases of particular survey media 17 Consolidated Behaviors and Attitudes
  18. 18. How Did Nate Do? Obama Won! 18 Consolidated Behaviors and Attitudes
  19. 19. How Did Nate Do?Obama Got 332 Electoral Votes: Exactly the Mode (Most Likely Outcome) of His Distribution Projection 19 Consolidated Behaviors and Attitudes
  20. 20. How Did Nate Do? Popular Vote: An Error of 1.3%• Silver predicted a 2.5% gap – final result was a 3.8% gap 20 Consolidated Behaviors and Attitudes
  21. 21. How Did Nate Do?• He correctly called all 51 states – and called Florida as the only “tossup” – with Obama having a 50.3% chance of victory 21 Consolidated Behaviors and Attitudes
  22. 22. Forecast Errors of the States• 2 of 51 states were outside of the expected margin of error (we would have expected 1 state)• On average, Nate forecast the states 0.2% too Republican (skewed slightly Republican)• Skewness = -0.6• Kurtosis = 0.75 “Too Democratic” “Too Republican” 22 Consolidated Behaviors and Attitudes
  23. 23. Errors in Key (Swing) States and States With Largest Errors Swing States State Pct Too RepublicanColorado 2.2Florida 0.6Iowa 2.4Michigan 1.4Nevada 2.1 States With Greatest ErrorsNew Hampshire 2.2 State Pct Too RepublicanNorth Carolina (0.5) West Virginia (10.6)Ohio 1.7 Mississippi 9.1Pennsylviania (0.8) Hawaii 9.0Virginia 1.0 Alaska 7.6 Montana (5.1) North Dakota (5.1) Utah (5.1) New Jersey 5.0 Arizona (4.6) 23 Consolidated Behaviors and Attitudes
  24. 24. Nate’s Approach to Forecasting the Elections• Drilling Down Into Pollster Ratings (1) – Raw Scores Are Produced By a Multiple Regression – Variables in the regression include: • Dummy variables representing each pollster (the “B” of these dummy variables is the raw score for the pollster) • The square root of the number of days between the median polling date and the election (separate variables for primaries and general elections – because primaries are harder to predict) • Sample size (this variable is only marginally significant) • Dummy variables to represent the type of election and the cycle (e.g., a single variable represents a 2000 senatorial election) • A separate dummy variable to indicate primary vs. caucus • A set of dummy variables indicating particular races – for those races that have “robust” amounts of polling – Non-robust races lack these dummy variables, and are therefore compared against each other 24 Consolidated Behaviors and Attitudes
  25. 25. Nate’s Approach to Forecasting the Elections• Drilling Down Into Pollster Ratings (2) – Regression data points are weighted based on: • How many surveys the pollster did for each particular election • How recent the election was (e.g., in 2010, 2008 elections were weighted twice as much as 1998 elections) – Raw rating scores are “regressed against the mean” to produce a final pollster rating • For the 2012 cycle, two raw regressions were done – one for the election cycles through 2008, and another for the 2010 election cycle. • The purpose was to understand how well the earlier regression predicted the 2010 regression for each pollster – and to “discount” each rating to account for how much of the rating was the result of “signal” and how much “noise” (don’t fully understand this) • The resulting formula provided a “reversion parameter” that calculated how much the raw score should be discounted, based on the following formula: reversionparameter = 1 - (0.06 * sqrt(number of surveys)) 25 Consolidated Behaviors and Attitudes
  26. 26. Nate’s Approach to Forecasting the Elections• Drilling Down Into Pollster Rations (3): – Example of regression against the mean of raw rating scores: • A particular pollster has a raw score of -0.50 (i.e., on a weighted average, their polls produce a 0.5% reduction in error compared to the average for all pollsters) • The same pollster has 25 polls in the sample • reversionparameter = 1 - (0.06 * sqrt(number of surveys)) = 1 – (0.06 * sqrt(25)) = 0.7 • Final rating score = 0.50 * (1-0.7) = 0.15 – In the regression against the A dummy variable representing whether the pollster has made one of two commitments to methodological transparency (a predictor of accuracy) 26 Consolidated Behaviors and Attitudes
  27. 27. Principal Sources (1)• tenuous-advantage/• how-to-improve/• economy-on-elections/•• n.html• the-2012-presidential-race/•• election 27 Consolidated Behaviors and Attitudes
  28. 28. Principal Sources (2)••• firms/•• the-2012-presidential-race/#more-37396•••••• 28 Consolidated Behaviors and Attitudes