#BUT THE LINEAR REGRESSION MODEL HAS MANY FLAWS I WOULD HAVE TO ADJUST IT 40 TIMES WHY CANT YOU JUST TAKE MY NON PARAMETRIC CORRELATION

[tchaikovskym]

when professors don't know the difference between correlation and regression and ask for a line in my correlation plot

HI I AM IN PAIN

[theliberaltony]

via Politics – FiveThirtyEight

We know we’ve told you that early general election polls are pretty meaningless in predicting who will win the presidency at this point in the election cycle, more than a year in advance, but we were curious: Could they tell us anything about how a candidate might perform in the primary?

For better or worse, general election polls are often used as one way to think about a candidate’s electability. For example, Joe Biden, as part of his argument for why he should be the Democratic nominee, has touted his performance in polls that ask voters who they’d support in a head-to-head matchup between Biden and President Trump. But the problem is, there’s a lot we don’t know about electability, and as a result, the debate around it can be pretty ill-informed, as voters don’t necessarily think about electability in a rational way. Plus, the data we have available for analyzing whether a candidate is (or isn’t) electable is often flawed, or limited, making it hard to draw firm conclusions. So in the leadup to the 2020 election, one thing we at FiveThirtyEight are trying to do is explore what kind of data we can use to improve our understanding of electability and what that means for the current presidential race.

First up, do early head-to-head polls like the ones Biden has cited tell us anything about how well a candidate will do in the primary? To test this idea, we collected polls conducted in the last half of the calendar year before the primary (July to December) and built two models to predict how each candidate would ultimately do in the nomination contest: One model used polls of the primary race and candidates’ name recognition, and the other model used those two factors plus incorporated how well the candidates did in head-to-head polls of the general election. We then compared the two models to see if adding in the general election polls improved our modeling. So, to spoil the ending a bit, do head-to-head polls help us predict who will win the nomination when we already know where candidates stand in the primary polls? The short answer is: No, they don’t seem to help much at all.

Now, we do know there is a relationship between what share of the national primary vote total that a candidate wins and a combination of their poll average and name recognition,1 it’s just that adding in a variable for how well the candidate is doing in polls that pit them against the opposing party’s eventual nominee doesn’t actually improve our ability to predict how much of the national primary vote share a candidate will win.

To build our models, we looked at the last four presidential cycles (from 2004 to 2016). The first version of the model incorporated both a candidate’s average standing in national primary polls and their estimated level of name recognition, numbers drawn from the second half of the calendar year (July through December)2 before a competitive presidential primary.3 Then we made a second version that used all the same data, plus each candidate’s average margin (how much they led or trailed their hypothetical opponent by) in polls that tested them against the opposing party’s eventual nominee in general election polls from the same time period.4 These variables were fed into two linear regression models to see how well each model predicted the national primary vote. (You can see some of the data that was feeding our models in the table at the bottom of the page.) What we found was that adding in a candidate’s average margin in general election polls didn’t change how well the models fit the national primary vote data.5 In other words, knowing a candidate’s standing in general election polling didn’t improve how well we could predict what percentage of the national primary vote a candidate might win.

But the number of prominent candidates and the competitiveness of each primary race can differ from cycle to cycle and affect the distribution of the national primary vote — a huge field of candidates could mean that a lot of people got a decent percentage of the vote, whereas a cycle in which a single strong candidate sails to the nomination over a few weaker competitors could concentrate most of the vote into one person’s camp. So we decided to do a second check of whether general election polls made primary predictions better. This time, we looked at whether those head-to-head polls helped us to better predict a candidate’s chances of winning the nomination, rather than concentrating on their share of the primary vote. After all, no matter how a primary goes, there’s just one nominee in the end. But it turns out that a candidate’s average general election margin doesn’t tell us much about the chances that a given candidate will become their party’s presidential nominee.6 To borrow an example from a recent presidential cycle, the fact that Jeb Bush had an average deficit of 2.8 percentage points against Hillary Clinton in general election polls from the second half of 2015 probably didn’t do much to change his chances of winning the GOP nomination even though he polled better than Trump, who trailed Clinton by an average of 6.5 points during that same time period.

So why might general election polls not tell us more about a candidate’s performance in the primary? Well, it could be that voters are factoring in a candidate’s perceived electability when they decide who to support, which means that their assessment of who can win the general election is reflected in candidates’ polling average in the primary polls. Voters may not always have complete information about the general election — one limitation of this study is that, in cycles where neither party had an incumbent running for reelection, primary voters didn’t necessarily know who their party’s eventual nominee might end up running against — but we actually have one statistical point in favor of the idea that they are factoring electability into their votes: There was a relatively strong correlation between a candidate’s primary poll average and their average general election margin in our data set.7 That is, the better a candidate performed in the primary polls, the better that candidate tended to poll in general election trial heats against the other party’s eventual nominee.

All of this doesn’t mean that general election polls don’t matter at all — 2020 Democratic voters are probably considering them when thinking about how well a candidate might perform against Trump. But they’re not very useful for anticipating who will be the Democratic nominee next year when we already have the primary polls to look at.

Many nominees did well in primary and general election polls

How candidates fared in general and primary election polls conducted in the second half of the calendar year before a competitive primary vs. their eventual national primary vote share, 2004-2016

Averages before primary Primary result Cycle Party Candidate General election margin Overall Primary Percentage National primary vote share Nominee 2004 D John Kerry -9.3% 9.3% 61.0% ✓ 2016 D Hillary Clinton +6.5 60.7 55.6 ✓ 2012 R Mitt Romney -2.3 22.2 52.4 ✓ 2008 D Hillary Clinton +2.6 42.6 48.1 2008 D Barack Obama +3.0 23.2 47.3 ✓ 2008 R John McCain -3.0 15.5 47.2 ✓ 2016 R Donald Trump -6.5 28.7 45.5 ✓ 2016 D Bernie Sanders +4.9 26.3 42.9 2016 R Ted Cruz -4.3 9.3 24.7 2008 R Mitt Romney -14.3 11.3 21.7 2012 R Rick Santorum -12.8 2.7 20.3 2008 R Mike Huckabee -10.4 7.3 20.1 2012 R Newt Gingrich -8.2 19.1 14.3 2016 R Marco Rubio -2.9 8.8 11.0 2012 R Ron Paul -6.7 9.0 10.7 2004 D Howard Dean -13.2 15.5 5.5 2004 D Wesley Clark -9.0 9.2 3.3 2008 R Rudy Giuliani -3.7 27.4 2.8 2016 R Ben Carson +0.4 14.5 2.8 2008 D John Edwards +2.4 12.3 2.7 2004 D Joe Lieberman -10.6 11.6 1.7 2008 R Fred Thompson -12.4 16.5 1.3 2016 R Jeb Bush -2.8 9.2 0.9 2004 D Dick Gephardt -11.2 9.8 0.4 2012 R Jon Huntsman -9.8 1.8 0.4 2012 R Rick Perry -8.3 12.1 0.2 2012 R Michele Bachmann -11.9 6.4 0.2 2016 R Chris Christie -3.3 3.3 0.2 2016 R Rand Paul -6.3 3.3 0.2 2016 R Mike Huckabee -7.0 4.1 0.2 2012 R Herman Cain -8.7 7.5 0.1 2016 R Carly Fiorina -5.2 4.5 0.1 2016 R Scott Walker -7.3 4.0 0.0

General election margin is average margin in percentage points of polls measuring a candidate against the other party’s eventual presidential nominee. Primary percentage is an average of national primary polls for each candidate. The national primary vote is each candidate’s vote share in all primaries for that election cycle. The second half of the year before a primary is July through December. Competitive primaries are those in which no incumbent is running for that party.

Source: Congressional Quarterly, Dave Leip’s Atlas of U.S. Presidential Elections, Polls