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Posts tagged statistical model

With A Week To Go, October Reelection Slide Reverses

Oct29
2012
3 Comments J. Brian Adams Written by J. Brian Adams

There have been volumes written on how the presidential debates might impact the election. With their conclusion last week the polls have shown a significant impact.

Our simulation model which uses the latest state wide polls has been run each week since the beginning of summer. Its estimate of the probability of the President winning reelection peaked at 99.9% on September 28 when the electoral college math showed there was no likely way that Governor Romney could garner the necessary 270 electoral votes.

But the campaigns continued, the Benghazi attack was still making headlines, the stock market dropped, and the debates began.

With the first debate came performance critiques of the two candidates and new state polls. By the end of that week the race had tightened. Our model predicted that Governor Romney had gained in several key states primarily Florida, Virginia, and North Carolina. With this surge his probability of winning also rose – moving from 0% the week before to 11% on October 5.

The following week provided an opportunity for the Vice Presidential candidates to debate. As the debate was late in the week they could not have had significant impact on that week’s polls. Instead the new polls were more likely a continuation of the results of the first debate. On Octaber 12 our model showed a continued decline for the President with his probability of reelection dropping to 82%. At the same time Governor Romney’s probability of winning rose to 16% and for the first time in several months the probability of an electoral college tie reached significance at 2%.

The effects of the Vice Presidential debate and the third Presidential debate could be seen in the following week’s polls. As of October 19, Governor Romney’s chances continued to rise reaching a probabilty of 25%. Similarly President Obama’s probability of winning continued its slide dropping to 73%. The probability of a tie held at just under 2%.

Now the debates have been concluded and the candidates are back to the criss-crossing the country giving stump speeches in the battleground states. But with this return to the traditional campaign has also come a return to President Obama’s reelection hopes. As of last week our model shows the chance of reelection reversing, climbing from the previous week’s low back up above 92%. Similarly Romney’s chances have declined to about 7% with the probability of tie again dropping below 1%.

Why the reversal? A noticeable change has occurred in Florida. Romney had taken significant leads in the Sunshine State over the past several weeks. While still leading Florida has again tightened. Similarly Romney’s Virgninia lead has dropped to a tie. And in Ohio, a key for a Republican victory, the polls show that while Obama had been able to retain a slight lead throughout most of October, his lead has increased over the last week.

While the model does not indicate that reelection is a certainty, it does indicate good news for the President. Our model currently predicts an electoral college vote of 301 for President Obama and 237 for Governor Romney – a buffer of only 31 votes – a slim margin in electoral college math. But with only a week to go, and early voting and absentee voting already in progress, our model indcates the GOP may have a significant challenge to get those 31.

Posted in Polling - Tagged campaigns, electoral college, opinion polls

President’s Reelection Chances Rebound with a Rise to Above 96%

Jul19
2012
1 Comment J. Brian Adams Written by J. Brian Adams

With last week’s release of eight new statewide polls the probability of President Obama being reelected has rebounded eight points to a new high of over 96%. Governor Romney’s probability of winning has similarly dropped eight points to 3%. These percentages represent the probability of each candidate receiving at least 270 electoral votes. The probability of a tie remains at less than 1%

These results are based upon a statistical model that uses currently available opinion polls for each of the fifty states and the District of Columbia. It analyzes these polls determining each possible outcome with its likelihood of occurring.

Of the eight states involved in the new polls, five – New Mexico, Virginia, Maine, North Carolina, Pennsylvania, and Wisconsin – have increased their support for the President. Two states – Florida and North Dakota – show increases for Governor Romney. Polls from Virginia and North Carolina indicate strong increases for Obama with both states moving from leaning Romney to now leaning Obama.

Florida which had been showing a fractional advantage towards Obama remains close but the slight advantage has now moved to Romney.

There are still three states, Iowa, New Hampshire, and Tennessee that are in the tossup category. Tossup states are the states in which there is not a statistically clear winner.

States that are leaning Obama are currently CO, MI, NV, NC, OH, and PA.
The states that are leaning Romney are FL, IN, KS, KY, SC, and SD.

The states that are likely wins for the President are ME, NM, OR, VA, and WI.
MO, and MT are likely wins for Governor Romney.

The final category are those states that would be considered statistically certain outcomes.

For President Obama these are CA, CT, DE, DC, HI, IL, MD, MA, MN, NJ, NY, RI, VT, and WA.
For Governor Romney the certain win states are AL, AK, AZ, AR, GA, ID, LA, MS, NE, ND, OK, TX, UT, WV, and WY.

The box plots show the distribution of predicted electoral votes for each candidate over the past seven weeks. The center rectangle includes the middle 50% of the outcomes while the whiskers cover the most likely 99.5% of outcomes. The green line marks the 270 electoral vote cutoff needed to win the election.

The time series plot tracks the trend in the probability of winning since the middle of May.

Box Whisker Plots for Possible Electoral Votes

Comparison of Predicted Electoral Vote Outcomes for President Obama and Governor Romney

Trend of Probabilities of Receiving 270 or More Electoral Votes

Posted in Polling - Tagged election, electoral college, polling

Latest Polls Indicate Probability of Reelection Down But Still Strong

Jul09
2012
Leave a Comment J. Brian Adams Written by J. Brian Adams

With the release of the latest statewide polls President Obama has an 88% chance of winning reelection as compared to Gov. Romney’s 11% with a 1% chance of a tie.

These results are based upon an analysis of the combinations of possible results using Monte Carlo techniques. This simulation model combines the estimated percentage of votes that each candidate is expected to receive while further taking into account the percentage of the electorate that may still be undecided.

With each run a number of electoral votes is predicted for each of the fifty states and the District of Columbia. A simulated winner of the election is thus determined. By running the model millions of times, the technique estimates the percentage of the simulated elections that each candidate wins and thus the probability of winning the election.

The input data for the simulation model is collected from the most current public opinion polls that are available for each state. Since new polls are conducted almost daily, the probabilities frequently change.

Of course the polls only reflect the electoral vote outcome for a single state so while the results do vary, the magnitude a particular change is dependent upon the size of the state. For example, a change in the public polls for Florida with its twenty-nine electoral votes has a far larger impact on the outcome of the national election than does a change in Delaware with its three electoral votes.

The model has been run weekly since the middle of May. With the latest set of polls President Obama’s probability of winning has dropped slightly from 93% in the previous week to 88% this week. With this drop for the President, Governor Romney’s probability of winning the election has risen from 6% the previous week to just over 11%. The probability of a tie – both candidates receiving 269 electoral votes – has also risen to just under 1%.

As events unfold over the next five months the polls will reflect the opinions of the electorate to those events. With the changing polls the probability of a particular candidate winning the election can change as well. If a third party candidate enters the race and is included in the polls then that candidate’s impact can also be modeled.

While polls provide a snapshot of the opinion of the electorate, this statistical modeling technique can use these opinions to make quantitative predictions about the November outcome.

Comparison of Predicted Electoral Vote Outcomes

Trend of Probabilities for Winning the November Presidential Election

Posted in Polling - Tagged election, opinion polls

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