Analysis and forecast of approval rating data
Richard Harang says:
As discussed my previous post on the topic, we are attempting to analyze both President Obama's approval ratings and the biases of various pollsters, and forecast them over the next three to twelve weeks.
We modeled both Obama's approval rating and the biases of the pollsters through a series of independent random walks with unknown variance, and considered the observable output of each poll to be the sum of two unknown processes evolving in time – Obama's "true" approval rating and the pollster's bias at the time the survey concluded – and an error term with unknown variance and unknown covariance between the pollsters.
Our original goal was to obtain forecasts for 3 and 12 weeks of approval rating data. This was accomplished, however the combined variances of the approval rating and the pollsters are so large that the corresponding prediction intervals are relatively uninformative.
The table below shows our predictions for observations from each pollster after 3 and 12 weeks, as well as the estimate for the true approval rating.
|3 Week||12 Week|
|Gallup||51.6 (33.8, 69.5)||51.5 (31.4, 72.1)|
|Rasmussen||47.2 (30.3, 64.2)||47.3 (27.7, 66.8)|
|CNN||50.3 (31.8, 69.1)||50.5 (29.6, 71.7)|
|CBS||46.6 (29.4, 63.6)||46.6 (27.0, 66.1)|
|FOX news||49.1 (28.1, 70.2)||48.9 (23.3, 75.0)|
|True approval rating||49.0 (41.7, 56.1)||49.0 (39.2, 58.9)|
The two plots below present the 95% prediction intervals for Rasmussen and CBS, the two polls identified as the most often biased, for three and twelve weeks into the future. The estimated "true" approval rating over the past 59 weeks with 95% credible sets is plotted on both figures for reference.
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