I experimented with the model for predicting elections discussed in my last post. I couldn't exactly reproduce Norpoth's results, but the regression coefficients were about the same. Specifically, using the data from 1912 to 2012, the coefficient for the NH primary vote share was .463 for the incumbent party and -.172 for the opposition party, with standard errors of .075 and .053. The resulting predictions for the share of the two-party vote in November 2016:
Clinton vs. Trump: 39.8%
Clinton vs. Other: 45.0%
Sanders vs. Trump: 50.4%
Sanders vs Other: 55.6%
That is, Sanders is predicted to do about 10 percentage points better than Clinton, because he got about 61% of the top-two vote in New Hampshire and she got 39% (22 times .463=10.1). Sanders is predicted to win narrowly against Trump, while Clinton is predicted to lose in a McGovern/Goldwater type performance.
My basic problem with these predictions, setting aside any specific knowledge of the 2016 campaign, is that the predicted difference is implausibly large. I'd say that a reasonable value would be 2 or 3 percentage points, which would mean a coefficient between about .1 and .15. But that's just my intuition: the 99.9% confidence interval for the NH vote share of the incumbent party is (.216,.740). That is, the evidence of the data seems to be inconsistent with the parameter values that I proposed.
However, suppose we distinguish between the incumbent party with an incumbent president and the incumbent party with no incumbent. Then the parameter estimates are .350 for an incumbent party without an incumbent president and .551 for an incumbent president. .35 is still a lot bigger than what I proposed as a plausible value, but the standard error is .132. That is, the 95% confidence goes as low as 0.9, so values I find reasonable are consistent with the data.
You could start with the model of incumbent vs. opposition party and ask if the difference between incumbent party with and without incumbent president is statistically significant. No: the t-ratio for the interaction effect is only about 1.0. But you could start with a three-way division and ask if the difference between opposition party and incumbent party without an incumbent is statistically significant. No: the relevant t-ratio is about 1.5. Although the incumbent/opposition model fits better, the difference is minimal.
The reason that the confidence interval for an incumbent party without an incumbent president is wide is that it's an unusual situation--it's happened only eight times between 1912 and 2012--so the data doesn't tell us much. It seems to me that we should start by assuming that there is a difference between elections with and without an incumbent president. As an example, Jimmy Carter got 55.6 of the top-two Democratic vote in 1976. His share in 1980 was almost the same: 55.8. But the meaning was very different--in the first, it helped him to become the front-runner; in the second, it was a sign of trouble. If you're just one of a field of contenders, a win is a win; if you're the president, you should win by an overwhelming margin.
In any case, the 2016 election will tell us a lot about this issue, especially if Clinton gets the Democratic nomination.