Comments on FiveThirtyEight: Politics Done Right: We know more than we think (Big Change #2)

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2009-02-11T22:46:00.000-05:00

http://election.princeton.edu/What lessons can we ...

2008-06-21T09:16:00.000-04:00

http://election.princeton.edu/

What lessons can we learn?

I have a funnel. I drop marbles thru it onto targ...

2008-06-21T09:12:00.000-04:00

I have a funnel. I drop marbles thru it onto target. I decide to adjust the aim of the target: if the last drop was a a little south of the target, I move the funnel a little north. If it was a west of the target, I move it east.

Results: worse accuracy.

@Anon 9:37I just can't support a statistical analy...

2008-06-16T03:46:00.000-04:00

@Anon 9:37

I just can't support a statistical analysis which makes an assumption that a bounce in one state will be reflected in any other state (even a bordering state) with any degree of certainty. That just isn't plausible and certainly not supported by any statistics I know of.

Okay, let me see if I can explain this: He's trying to account for the "dogs that aren't barking", filling in the gaps for states that haven't been polled based on the data he does have, national and neighboring state polls.

Let's take an example: Connecticut. Some places are rating it as a "tossup" state because the most recent public poll gave Obama only a 3-point edge there. That makes no sense, not only is the poll extremely out of band with the earlier (but much older) polls for that state, and Connecticut is normally a very "blue" state, but since that poll was taken he's been improving everywhere that has been polled, as well as nationally. That data can't have a direct correspondence with what we don't have, a recent poll for CT, but it has to have some relationship to it.

Another way to look at it is that he's now making a projection of what a good poll for a given state would look like right *now*, and using that for his model. And every time a new poll comes out, he's got a chance to check the projection, as just happened in NV and AR, where he was very close, well within margin of error.

Benjamin Schak:Thanks very much for your thorough ...

2008-06-16T03:40:00.000-04:00

Benjamin Schak:

Thanks very much for your thorough explanation of the mathematics. I have never had the opportunity to take a class on that material so it explains a lot. I think I appreciate what you are getting at now even though I'm not fully convinced that leaving the means static is the best that we can do. My issue with the test analogy wasn't that different people would be taking the tests when matching it up to states in the elctoral map. My issue was that the mean you would be regressing toward when you predict the person's score on the second test would be predicted by the average scores of a huge population taking the second test, which hypothetically doesn't change rapidly. But, what if we had nation-wide studies showing that the average change in the mean scores for the two tests went up 3% this week. Would you still use the mean from last week for predicting what the person's score on the test would be this week? I'm unintentionally still mixing up the analogy here because I want to focus on projecting the changes in the means between tests or states and not necessarily changes over time, but I'm having trouble explaining it exactly and I hope this is clearer.

Also, thanks for the link to your blog. I think it is worthwhile to have multiple models being run by different people so I'll probably be checking it from time to time.

lilnev: Thanks for the warning about over-fitting. I always forget to avoid that in modelling, but in my line of work I rarely have to take statistics into account so it often works out anyway. I guess if we had the amount of polling data that would justify 10 parameters then we wouldn't have any states that needed projecting anyway.

Hi Poblano, I think it's a mistake to assume that ...

2008-06-16T01:27:00.000-04:00

Hi Poblano,

I think it's a mistake to assume that all states or all demographic groups will evolve with time uniformly. It's not difficult to image cases in which demographic groups may diverge and only track national opinion in the average. Assuming this may well lead to inaccurate predictions in states with "atypical" demographics.

What you're doing is certainly an improvement, but it's 0th order when what you should be shooting for is 1st order.

Dan

I understand numbers, and statistics to a point, t...

2008-06-15T22:37:00.000-04:00

I understand numbers, and statistics to a point, that is what made me intrigued by this site. But to be fair I am a political animal, not a statistician.

I said earlier and I have to reiterate, you numbers are only as good as your understanding of the events that create them. It was Tip O'Neill, a likely Obama supporter were he still alive, who said "all politics are local." I just can't support a statistical analysis which makes an assumption that a bounce in one state will be reflected in any other state (even a bordering state) with any degree of certainty. That just isn't plausible and certainly not supported by any statistics I know of.

I'd join those who are asking you to prove that theory using past polling, or drop this methodology change.

And, for the record, my dislike of the new methodology has nothing to do with whom I support.

(oh, and i do think you need to include third party candidates. While they will have no impact nationally they most certainly may have an impact on one or two states..enough to possibly make a difference.)

Re: Predicting now vs. predicting November. Consi...

2008-06-15T22:18:00.000-04:00

Re: Predicting now vs. predicting November. Consider AK. It's currently McCain +4.1. Presumably that's our best guess of what a poll taken today would show. It's also our best guess for the November outcome. Obama's win chance there is listed as 33.5%. I'm not sure what this number is supposed to mean. Is it the chance that Obama would win an election today (based on sample sizes and PIEs), or the chance that he will win in Nov (based on sqrt of # of days)?

At Anonymous 4:00 AM -- fitting a 10-dimensional hyperplane in demographic space requires adding 10 parameters. I'm afraid of overfitting.

At Modeller -- It sounds like you want to use the time series of regression coefficients as they were determined by the old method on previous dates, yes? But the coefficients determined on, say, Apr 30 would be only partly based on April's data, and partly on March and Feb (though discounted). One of those coefficients would be the "constant" term, reflecting the national margin (more technically, the margin at the demographic mean of the polls included -- the nation hasn't been uniformly sampled). Hmm, not sure where this is going; needs more thought.

Actually, it would be nice just to see what the history of the regression coefficients is, to get a sense for how stable the regression model is from week to week. Are some variables jumping in and out of the model, or are weights swinging wildly? In general, regressions onto many variables can be tricky, especially when some of them are strongly correlated. Very different looking models can sometimes produce nearly equally good fits. I wouldn't be surprised if the first few factors (the ones that capture the most variance) are stable but the last few jump around quite a bit.

'Nuff for now. G'night y'all.

Also, I know nothing about the math of your LOESS ...

2008-06-15T22:12:00.000-04:00

Also, I know nothing about the math of your LOESS regression, but looking at the graph it certainly appears to lose about half of its smoothing power for the points at the edge, which have half the neighbors. This is particularly worrisome for your use of the methodology, because the current week (recent edge of history) is used in every single correction factor. Perhaps you could just add one "next week" point, using this week, before you did your regression, in order to be a bit more conservative. Or even more conservative - you could move "next week" one this-week-standard-error (for total this week effective sample size - should be around 1%) in the direction of last week, ie, always assume that this week is an outlier until you get evidence to the contrary.

But these suggestions are just tinkering really. The suggestion in my last post is much more important, serious, and, in my opinion, mathematically justified.

This is a great methodology, and I endorse the cha...

2008-06-15T21:59:00.000-04:00

This is a great methodology, and I endorse the change - with one, significant reservation. As Benjamin Shak says (and as I thought BEFORE I skimmed this comment thread) you cannot possibly assume that your average state is correlated to the national movement with a regression coefficient of 1. The easiest way to fix this would be to just multiply your national movement by a single, global regression coefficient taken for the average state. I am sure you could figure out some way to measure this correlation; in fact, your model already implicitly has such a correlation, it is the ratio between the national error standard deviation and the state-by-state error standard deviation when you do your simulation runs.

(Most of the suggestions in this thread of how to use demographics would also need to be scaled back by such a correlation factor, although correcting for demographics is a way to get a higher correlation it is still not 1.)

Please - you already had by far the best methodology, and, with this fix, your time-based correction would be making it even better. Do not let this one mistake ruin your numbers. Even if you do not believe me that the math requires you to fix this, just apply your corrections at 50% strength. Besides being mathematically more correct, it is the conservative and sensible thing to do from a non-mathematical standpoint.

Arghh! I should have read your original response m...

2008-06-15T21:09:00.000-04:00

Arghh! I should have read your original response more thoroughly, so feel no need to answer my last attempt at a posting. You already did. Sorry about that.

Let me try that again, 'cause the first paragraph ...

2008-06-15T21:07:00.000-04:00

Let me try that again, 'cause the first paragraph got garble. It seems like the old methodology was closely correlated with current polling data. It seems as if the new methodology incorporates more of a future forecast, and that in doing so, it relies on data not from the state in question but on national numbers and (?) states thought to be paired or otherwise linked to each other.

In doing so, it's as if you've combined some coupons into a later payoff, i.e., in figurative terms you've lengthened the duration, which will increase volatility.

I know it's a really imperfect analogy, so let me go a different way at it: Will this method introduce more volatility in response to results that do not conform to an existing projection?

Take NV as an example. If the next result (or average of them) either in NV or a combo of NV and the exogenous variables not previously included in the algorithm, is meaningfully different from what the new algorithm expected when it produced that optimistic reading ON NV even though the polls show Obama 2 points behind, will there be a bigger swing in the NV results than there would have been under the old formula?

In the last couple days, we've seen Obama's post-Hillary Concession bounce starting to wear off. Am I more likely than before to be waking up to a really gloomy-looking picture in, say, a week?

Benjamin, the point is that the new methodology ap...

2008-06-15T20:59:00.000-04:00

Benjamin, the point is that the new methodology appears have a 1:1 correlation with current data as before, but rather now takes a combination of current and past data and extrapolates a future result, as in showing Obama ahead in NV when the polls show him behind.

In doing so, it's as if you've combined some coupons into a later payoff, i.e., in figurative terms you've lengthened the duration, which will increase volatility.

I know it's a really imperfect analogy, so let me go straight at it: Will this method introduce more volatility in response to results that do not conform to a projection? Take NV as an example. If the next result (or average of them) is meaningfully different from what the new algorithm expects, will there be a bigger swing in the NV results than under the old formula, and if so, why?

charles pluckhahn:I agree that the new changes wil...

2008-06-15T20:47:00.001-04:00

charles pluckhahn:

I agree that the new changes will lead to more volatility. Under the old regime, big movements in the underlying popular opinion got factored into the 538 prediction rather randomly, as new polls appeared for each state. Under the new regime, movements in underlying popular opinion should appear in all states' estimates as soon as a decent handful of polls appear in any states.

I don't see how the new method extrapolated out in time; it seems to extrapolate out in space -- the results of one state applied to another state.

(BTW, I do know all about bond coupons and duration, but didn't quite follow the analogy between them and polls.)

AnonymousYes, I do assume that the expected value ...

2008-06-15T20:47:00.000-04:00

Anonymous

Yes, I do assume that the expected value of the signed change of a state's distribution, given no other information, is 0, or "unchanged." I think this is a reasonable assumption -- after all, with no other information, why would one expect a state to move towards or away from Obama.

And yes, by "regressing to the mean," I do mean "regressing to not changing," in that, when one state turns out to be more pro-Obama than previously expected, one's expectation about other state's becomes commensurately more pro-Obama, but not by as much as the state that we know moved.

Let me try to unpack your hypothetical, since it's a compelling question.

Your hypothetical was: Suppose three states (A and B) each increased by 1sd, and another state (X) with 50% correlation to the others wasn't polled. (I increased your 5% to 50% since I believe that correlations between states are rather high, and I changed five states to three for simplicity.) The right thing to do in this case depends on the correlation between A and B. For example, if they are 100% correlated to each other, then the right thing to do is clearly to increase the estimate of X by just 0.50sd, since the extra knowledge about B provides no useful information.

Suppose, though, that A and B have correlation r with each other. Let me introduce some notation. m_A, m_B, m_X, s_A, s_B, s_X are the means and s.d.'s of the three states before taking any new information into account. m' and s' are the means and s.d.'s after taking new knowledge about A into account. m'' and s'' are the means and s.d.'s after taking new knowledge about A and B into account.

After taking information about A into account, the new estimate of A is 1sd above the old estimate, and the new uncertainty about A is 0. That is, m'_A = m_A + s_A, and s'_A = 0. By what I was saying before about regression to the mean, the new estimate of B is m'_B = m_B + r s_B, and the new uncertainty about B is s'_B = s_B * sqrt(1-r^2). The new estimate of X is m'_X = m_X + 0.5 s_X, and the new uncertainty about X is s'_X = s_X * sqrt(1-0.5^2).

Now let's take the information about B into account. We are given that m''_B = m_B + s_B (i.e., B had a 1sd jump in terms of the a priori distribution). Thus,
m''_B = (m'_B - r s_B) + s_B
= m'_B + (1-r) * s_B
= m'_B + (1-r) * s'_B / sqrt(1-r^2)
= m'_B + s'_B * sqrt((1-r)/(1+r)).
In other words, B turns out to be sqrt((1-r)/(1+r)) standard deviations (post-A standard deviations, that is) better than our post-A expectations. The new estimate of X is then 50% * sqrt((1-r)/(1+r)) * s'_X better than m'_X. Hence,
m''_X = m'_X + 0.5 * sqrt((1-r)/(1+r)) * s'_X
= (m_X + 0.5 s_X) + 0.5 * sqrt((1-r)/(1+r)) * s_X / sqrt(1-0.5^2)
= m_X + s_X * (1/2 + sqrt((1-r)/(3+3r))).

This result fits intuition well, and the same result would be achieved if you applied B's result and then A's. When r=1, B provides no extra information from A, so m''_X simply equals m_X + s_X * 50%, as expected. When r=0.5 (a reasonable enough number), B contributes some information but not much, so X rises 61% of a standard deviation. When r=-1, we get nonsense, which is right, since it's impossible for A and B both to rise if they're perfectly negatively correlated.

Another interesting if unrealistic boundary case is when X = A+B and s_A=s_B and r=-0.5 (the minimum possible value for r). In this case, A's and B's anticorrelated movements are expected to cancel, so that it's quite unexpected for X = A+B to rise as much as it does. And indeed, the above formula has X rising by 1.5sd, even though it would only rise by 0.5sd given information about either A or B rising.

All this is implicitly incorporated into the technique I use on my own site (I hate to shill, but here goes). I took assumed correlations from an analysis that got me a formula based on distance between states and racial composition. (I think I got the correlations in a pretty crappy way, but the main point is that I believe they're positive and fairly high, 50-100%.) For the expected values, I essentially use Bush/Kerry as a starting point (as, IIRC, Nate here does), and tweak the expected value as each new poll comes along (and there have been enough polls that the current expected values don't look much like Bush/Kerry any more).

You're right that I fundamentally assume that movements in elections follow a normal distribution, and that this is probably an incorrect assumption. After all, a major scandal might cause a 15sd event. I recognize that this is a flaw, and have been thinking about how to fix it, maybe using one of the platykurtic distributions people sometimes use for the stock market.

I don't think your comment about the test analogy makes sense. I wasn't talking about multiple people taking tests; I was talking about one person talking multiple tests. The two test results for one person are analogous to two states' movements for one election. In the one case, one test result implies something about the same person's other test result. In the other case, one state's result implies something about the other state's result.

I do agree, or at least suspect, that correlations that correlations between states are accounted for mostly by demographics in the states.

BTW, I also have little background in stats, other than some absorption here and there from being in math undergrad and grad.

lilnev,A couple of points:-- We are not trying to...

2008-06-15T20:02:00.000-04:00

lilnev,

A couple of points:

-- We are not trying to predict the results of an election held today. We're trying to predict the results of one held in November (see Big Change #1)

-- Using the demographic model to track changes over time adds no new variables to the model. The "time" component is automatically included through the weighting mechanism.

Also, could you explain how mixing state and national data has anything to do with time trends? They are separate problems, especially if you consider the nation to simply be another state (as Nate does).

I agree that the concern on this thread is a good indication of how successful Nate has been, and how much we like his work.

lilnev:I may be wrong (I haven't run any simulatio...

2008-06-15T19:59:00.000-04:00

lilnev:

I may be wrong (I haven't run any simulations and I have to run right now so I probably won't) but I think my method (proposed at June 15, 2008 4:00 AM) would keep the same overall volatility of Poblano's current method, but just assign more of that volatility to states similar to those which show the greatest changes in the polling. Benjamin Schak's proposed method (and even the one with the modified correlations and means), on the other hand, actually reduces the volatility by regressing to a mean.

As I see it now, the underlying assumptions:Suppor...

2008-06-15T19:46:00.000-04:00

As I see it now, the underlying assumptions:

Support in a state is the sum of a demographic component, a state-specific residual from the demographic component, and a time trend that is the same for all states. We're thus trying to fit a two-dimensional space -- states and times. (Previously, we collapsed across time and only tried to fit the states.)

The new approach is to remove the demographic and state-specific components in order to estimate the time trend. Hence the dummy variables to isolate the tracking polls and the pollster-state pairs. (Incidentally, is this a tacit admission that the expected value of a Ras. poll is not necessarily the same as the expected value of a SUSA poll in the same state, i.e. that pollsters may be biased?)

Then, the time trend is removed by adding the LOESS figure to each poll, and we try to estimate the regression model and state-specific components.

The concerns people have voiced seem to be twofold (well, threefold, but I don't count "Poblano is hacking the numbers because he's an Obama shill." He, and most of us, are here because we want the clearest insight we can get from the available data. If we wanted cherry-picked hackery, there are plenty of other sites available....).

First, that state data shouldn't be contaminated with national data. This is basically asking to go back to the zeroeth-order approximation, where it was assumed that there was no time trend.

Second, that the current approach isn't sophisticated enough, because it's only a first-order approximation of time trends and therefore assumes that the trend will be uniform across all states/demographics. These people are asking for a model that includes interaction terms between time and states/demographics.

I don't know. Overall I think the changes yesterday are an improvement, though we need to be clear that we're now explicitly trying to predict the results of a poll/election held today, rather than a backward-looking indicator of past support. The additional time-demographic interaction terms that some people would like are both appealing and dangerous. They would add a lot of new variables to the model, increasing the risk of overfitting and hence too much volatility to each new datapoint. I'm already concerned about the volatility added yesterday. Let's see some tests of the current models stability and predictive power before we call for even more to be added to it.

Nate: You should take the amount of concern in this thread as a compliment (excepting those of the "Nate is Obama's BFF lol" flavor). It means that you've managed to attract an intelligent and critical audience.

John H,You are right in that national polls should...

2008-06-15T19:45:00.000-04:00

John H,

You are right in that national polls should be used, and Nate is doing the right thing by treating the nation as a state.

The regression model still gives more weight to recent polling, but in my opinion it actually overweights recent polling. Instead of being based on high-weighted recent polls and low-weighted older polls, it is based on high-weighted recent polls and low-weighted older polls that have been adjusted to more closely resemble recent polls.

One of the problems is that by running a regression on polls that have been adjusted based on national trends, the regression will be trying to fit noise that has nothing to do with the underlying demographics of the states. The predictive power of the resulting regression is very likely reduced as a result.

For non-finance types, a bit of trivia. Because a ...

2008-06-15T19:16:00.000-04:00

For non-finance types, a bit of trivia. Because a 10-year bond has a duration of 7 years, and because the average household mortgage borrower moves every 7 years, the 30-year fixed rate mortgage has historically been tied to the 10-year Treasury bond.

They start with the Treasury bond because it's the so-called "risk free rate," i.e., because the government creates the currency, you'll always get paid. The difference, or "spread," between 10-year Treasury rates and mortgage rates is a function (in theory) of default rates, competitive factors, and costs such as underwriting and servicing.

The current residential mortgage crisis notwithstanding, that relationship endures. For how long is another question, of course, and beyond the scope of this exercise in Trivial Pursuit.

Correction: Duration is the average maturity of bo...

2008-06-15T19:11:00.000-04:00

Correction: Duration is the average maturity of bond cash flows, i.e., including principal, not just interest payments.

benjamin, I hear you, and perhaps that will be the...

2008-06-15T19:10:00.000-04:00

benjamin, I hear you, and perhaps that will be the case. But I think one impact of the new methodology is likely to be an increase in volatility of the projections here.

Because I'm not a mathematician, I'm going to use an analogy here that might or might not work. (Please forgive me if this is basic knowledge to you.) In the bond world, there's a concept called "duration," which is the average maturity of interest payments.

Imagine a 10-year bond with a face value of $1,000, paying 5% interest. Every six months, you get a "coupon" (interest) payment of $25. At the end of 10 years, you get your principal (the $1,000) plus your final coupon payment of $25. If you throw all those payments into a spreadsheet, you'll find that, due to the time value of money, the average maturity of the "10 year" bond is actually 7 years, because a bunch of those coupons were paid early.

Now, let's imagine two of these bonds. One is the 10-year bond I've mentioned. The other is a 10-year "zero coupon" bond, which pays all of its interest, plus the principal, at the end.

If interest rates should happen to change before the maturity date, the current price of the zero-coupon bond will fluctuate a lot more than the current price of the standard bond. This is because, by putting everything at the end, changes in the time value of money are focused on one point, way in the future.

Nate's new model still allows for the equivalent of "coupons," i.e., new poll results, but it seems to me that he's using some manipulations to extrapolate change patterns farther out in time than his old model did.

So, for example in Nevada, if a new poll comes out showing Obama 6 points back, or a new national poll shows a significant slippage, you'll trigger a cascade of new trend assumptions, state by state.

Maybe I'm wrong about this, but I'm thinking the new methodology is going to be giving us all somewhat (how much, I'm not sure, because I'm rotten at geektitude) more thrills 'n chills along the way. It'll be interesting to watch.

Benjamin Schak:I realize all that you said in your...

2008-06-15T18:54:00.000-04:00

Benjamin Schak:

I realize all that you said in your last post, but what you are saying seems to be based wholly on the following assumption (correct me if I'm wrong):

The mean for a state's distribution should be at "unchanged". That is, by going r n s.d. above where you were, you are starting with the mean at wherever it was the last time a poll was done, and then increasing that number by r n s.d. So, by "regressing to the mean", you are essentially regressing to things not changing.

This assumption seems contrary to Poblano's intentions with this whole extrapolation and seems like it would always produce very conservative results. If five states each increased by one standard deviation for Obama and a state with 5% correlation with those states wasn't polled, would you assign a 5% s.d. increase there? a 25% s.d. increase? If the whole country in fact did increase a standard deviation, you would be missing most of the change in most of the states. And the problem with going with 25% there is that a state which was highly correlated with those five states, say 60% with each, would then have to increase 3 standard deviations for Obama.

I feel the test analogy is faulty because standardized tests are based around the assumption that the whole population doesn't make sudden shifts, and that for each person that scores high there is one that scores low. But elections don't fit under unchanging (or even slowly changing) bell curves. The whole population or any portion can move one way or the other suddenly meaning you can never predict where the mean is likely to be.

Now, having said all of that, I think there is a way that what you are proposing could be modified slightly to produce very accurate results, and that is if we simply had a way to determine the means separate from the correlations, and to determine the correlations separate from the means. I'm not a stats person (MS in pure math only) so I wouldn't know how, but my guess is if you subtract the country-wide average change from each state change before determining their correlations to eachother and then only use the correlations to determine changes on top of the country-wide averages, you might be able to model what you want with country-wide polling change + "unchanged" as your new expected mean.

Something like this would be good, but I'm still not sure it achieves what Poblano's intentions are (especially considering the stark contrast it holds to his current method). In the end, though, your model (with the modified mean) and mine would predict roughly the same thing if you assume that the correlations between states is accounted for mostly by demographics in the states.