I flew into LAX this morning, saw the Qantas A380 off to our right being towed somewhere. Our UA pilot pointed it out to us, which resulted in oohs and ahhs.. Kind of cool.
For real. At $9.99 its an expensive app, so I’m looking for reviews.
They are counting again up there. Stevens trails in the ongoing vote count, at least in this screen shot (3 votes!):
On the Political Methodology List, Carla Osorio asked:
Hello,I would like to know what is the best way to calculate and report bivariate correlations when multiple imputation (Amelia) is employed.Is it OK if I calculate the correlations between the variables of interest in each of the imputed datasets and just average them?Also, I have read that it is fine to average coeffients over the imputated datasets, but I do not know if standard errors can also be treated in that way. thanks.
The question here is really about the right way to compute the variance of an estimand that has been multiply imputed, for which see Rubin et al various publications.
I post on this only to point out that this problem corresponds to a lovely example I trot out when teaching, using a data set that has been floating around since DLR first published on the EM algorithm in JRSS-B, due to Gordon Murray. See here. With a vague prior over the correlation, and an assumption of bivariate normality, you get a bimodal posterior density for the correlation. How pretty! See the JPG, below.
This is a story that got some exposure on HuffPost, and (independently?) was brought to my attention by my colleague Josh Cohen who in turn forwarded it from Steve Ansolabahere.
The current vote tally in Alaska seems to be indicating that substantially fewer people voted up there than in 2004. It seems hard to believe. This is worth a closer look. Does the vote just take a long time to come in up there, or was turnout way low there for some reason we just don’t know about (despite Palin on the ticket?!?) or do we have widespread voter fraud….?
The Associated Press currently has the vote count in Alaska at 221,678, a number that hasn’t changed all day. The State of Alaska Division of Elections has the count at 223,258, but that is in a report on their web site that is time-stamped 16:39 11/05/08. Bear in mind that in 2004 312,598 people are reported to have voted in AK in the presidential election (David Leip’s site).
By way of comparison, and as of about 1200 PST today, here is how the vote counts are going in a handful of states:
AK: 221,678 votes counted. 2004: 312,598. 70.9% of 2004.
CA: 10,438,754. 2004: 12,419,857. 84% of 2004.
OR (all vote by mail): 1,714,386. 2004: 1,836,782. 93.3% of 2004.
OH: 5,296,157. 2004: 5,627,908. 94% of 2004.
Alaska is a laggard in that small set of comparisons there.
Which makes me wonder, where are we ahead on 2004 in the vote count???
VA: 3,640,777. 2004: 3,198,367. 113.8% of 2004.
Incidentally, I’m increasingly skeptical we’re going to come out at anything like the 10-15 million boost in turnout over 2004 that some were initially forecasting. As of 10.30 PST tonight, the AP is saying 124.2 million votes have been counted, up from the 122.3 million that voted in 2004, but not by much.
Mo Fiorina forwarded me a report by Curtis Gans at American University:
According to a report and turnout projection released today by American University’s Center for the Study of the American Electorate (CSAE) and based, in part, on nearly final but unofficial vote tabulations as compiled by the Associated Press as of 7 p.m. Wednesday, November 5, the percentage of Americans who cast ballots for president in this year’s presidential election will reach between 126.5 million and 128.5 million when all votes have been counted by early next month.
Lower than usual Republican turnout is the leading explanation at this point. No surprise. But that doesn’t explain Alaska…
Charles Franklin has some graphs like this over at pollster.com, but I couldn’t help myself… The Master-Scraper Jeff Lewis gave me code for reading updated/quasi-real-time vote tallies from the web, so the 2008 counts reported here are hot off the press.
First up, poll margins versus actual margins, using the final state-level numbers on pollster. The 45 degree is where the data should be if the polls were perfect. The polls haven’t done too badly, particularly in the battlegrounds (the cluster of state close to the origin), where (duh) there was a lot of polling. If we could put error bands around the poll averages I think you’d find many of them overlapping the 45 degree line. This graph drops DC.
The regression has an r-squared of .96 (again dropping DC), an intercept that is zero, and a slope > 1 (1.15, with a standard error of .035). The data and the regression analysis shows that the poll averages miss the extremes, tending to underestimate Obama support where it is high, and overestimate Obama support it where it low, which is the way a shrinkage estimator would perform, which is curious. Of course, this regression analysis ignores the obvious heteroskedastic/errors-in-variables problem here: i.e., the poll averages are estimates, and some are more noisy than others, particularly the extreme states where we have relatively few polls. Omitting DC and HI, the median absolute error is 2.2 percentage points, the RMSE is 4.1. Among 11 battleground states (VA, PA, OH, NC, MO, IA, CO, FL, IN, NV, NM), the median absolute error is 0.8 percentage points and the RMSE is 2.2. Still, these measures of fit are large relative to the margins by which these states were decided.
If we just look at the “calls” per se, the performance is pretty good. That is, in each state, did the poll average have Obama ahead or behind McCain, and how does that correspond with the (provisional) outcome?
There are just 2 misses here. In Missouri, the Pollster.com final average had Obama on 48.5, McCain on 47.4; it is currently Obama 49.3 trailing McCain 49.5. In Indiana, the Pollster.com final average had Obama 46.9, McCain 48.1; it is currently Obama 49.9, McCain 49.0. Again, not bad.
Exercise for reader: how much sample do you need to reliably detect differences of 0.9 percentage points at conventional levels of statistical significance? Or 0.2 percentage points?
More below. (more…)
Here is a shot at putting the Obama win into some perspective. Let’s look at when the party of the presidency has changed from 1932 onwards. What kind of popular vote did the new, incoming president win?
1932, FDR: 57.4%
1952, Eisenhower: 55.2%
2008, Obama: 52.4% (provisional)
1980, Reagan: 50.8%
1976, Carter: 50.1%
1960, JFK: 49.7%
2000, GWB: 47.9%
1968, Nixon: 43.4%
1992, Clinton: 43.0%
Obama comes to power with the biggest popular vote of any new Democratic president since FDR.
Update (Thursday). There is (of course) another way to look at this, and that is with the 2-party vote, or even better, swing in the 2-party vote. Again, looking just at “change” elections:
1932, FDR: 17.9pp (yikes: it bears remembering that Hoover beat Smith 58.2 to 40.1 in 1928).
1976, Carter: 12.8pp
1968, Nixon: 11.7pp
1960, JFK: 7.9pp
1952, Eisenhower: 7.6pp
1992, Clinton: 7.4pp
1980, Reagan: 6.4pp
2000, GWB: 4.5pp
2008, Obama: 4.4pp (provisional)
Here is a shot at putting the Obama win into some perspective. Let’s look at when the party of the presidency has changed from 1932 onwards. What kind of popular vote did the new, incoming president win?
1932, FDR: 57.4%
1952, Eisenhower: 55.2%
2008, Obama: 52.4% (provisional)
1980, Reagan: 50.8%
1976, Carter: 50.1%
1960, JFK: 49.7%
2000, GWB: 47.9%
1968, Nixon: 43.4%
1992, Clinton: 43.0%
Obama comes to power with the biggest popular vote of any new Democratic president since FDR.
Its almost 1am here in California. CNN says Obama has 60,150,608 votes to McCain’s 53,917,080 votes. On these numbers Obama has won 52.7% of the vote at this point, and this 5.4 percentage point margin has been increasing as the count continues late into the night here.
We have about 114 million votes counted at this point. 122.3 million people voted in 2004. We think that 2008 turnout is up sharply, perhaps a lot, over 2004. If so, then there are an awful lot of votes still out there, 10 million, maybe even 20 million. The 5.4 percentage point margin Obama has could well grow as this as yet uncounted set of votes continues to be counted.
The 5.4 margin (and growing margin) that we have now compares with the 7.6 margin we had on Pollster.com and RealClear at the end of the campaign. I think we’re going to wind up at a place where the actual popular vote margin isn’t too far off the final poll average, which would seem to indicate the Bradley effect hypothesis is refuted.
The state-by-state poll versus actual comparisons will be worth a look as well.
Update (8.30am Wednesday): Obama’s margin on the two-party vote is now up to 6.0 percentage points.
Update (9.35am Thursday): 122,282,151 votes counted, according to the AP. That is close to the final 2004 number, so perhaps there are yet many more votes to be counted. Obama has 52.5% of the popular vote, a margin over McCain of 6.2 percentage points. Of the two-party vote, Obama has 53.1%.
Here’s another take on the election. Jeff Lewis dumped me the current (last?) set of state-by-state poll numbers from pollster.com. If we plot these against the Kerry vote from 2004 (as in the PDF file below; click on the thumbnail), we see the swing to Obama quite clearly (the darker line is a regression fit; the gray line is a 45 degree line, and if there was no change from the 2004 all the data points would lie on this line).
Consider VA, CO, NV, IA, and NM: all are “red” states (meaning that Bush > Kerry in 2004) but are currently showing Obama above 50% in the polls, and sit in the upper left quadrant of the graph. Add to this FL, MO, NC and OH: these went for Bush in 2004, but 50% > Obama > McCain according to pollster. There is a bigger swag of electoral votes in the 2nd set of states, but the 1st set of states that seem to be easier wins for Obama will be enough.
Note that VA is among that st set of states, and will be among the first cabs off the rank this evening. I tend to (1) if VA goes to Obama then (2) it less likely that PA goes to McCain, and we’re just about done. McCain simply has a lot more real estate at risk than Obama, and can’t afford to lose any of it, unless he’s taking back a state like PA, which I tend to think it unlikely.
The trend revealed by the regression is interesting. It sits above the 45 degree line, and at the 50-50 point is about 2.2 percentage points above 50 (i.e., on average, a state that broke 50-50 Bush-Kerry this year is showing Obama on 52.2 in the polls on Election Morning). The fit has to be considered pretty rough and ready given the fact that we’ve got poll aggregates as the dependent variable, and some of those data points in the tails are noisy (i.e., there isn’t much polling in UT, MA, etc).
By the way, a similar plot appeared over at Andrew Gelman’s red-state/blue-state blog.
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