My original forecasts for Ron Paul’s primary performances are here. Those forecasts were based simply on the Iowa result, so it was quite possible that there would substantial error, and indeed there has been. Paul significantly overperformed his forecast in New Hampshire and South Carolina, the forecast was dead on in Florida, and then Paul underperformed significantly in Nevada. In yesterday’s elections, Paul did significantly worse than expected in Colorado, slightly worse than expected in Minnesota, and slightly better than expected in Missouri. In general, he seems to be doing worse than expected since Florida.
Why is that? It could be that my forecast model was an unbiased model at the time, but that circumstances have changed unfavorably for Paul’s candidacy. Certainly, recent good economic news probably doesn’t help an antiestablishment candidate like Paul. Perhaps his poor Florida performance, although it should have been anticipated, demoralized some of his supporters. On the other hand, my forecast model could have been wrong, particularly in assuming that Paul’s vote shares would continue to feature overdispersion. It’s possible that with a broadening voter base, Paul’s caucus advantage has declined. Thus, Paul should improve on his 2008 performances everywhere, but not in a manner proportionate to his 2008 performances: there will be some apparent regression to the mean.
To see how Paul’s 2012 performances are stacking up against his 2008 performances, I ran a regression on the states with results so far. First, I regressed 2012 performance against 2008 performance linearly. Here are the results:
Call: lm(formula = vote12 ~ vote08) Residuals: Min 1Q Median 3Q Max -5.0465 -3.8563 0.8463 2.0316 6.8799 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 6.9290 3.4156 2.029 0.0888 . vote08 1.1807 0.3632 3.251 0.0175 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 4.444 on 6 degrees of freedom Multiple R-squared: 0.6378, Adjusted R-squared: 0.5775 F-statistic: 10.57 on 1 and 6 DF, p-value: 0.01745
These results suggest that for every 1% in 2008 vote share in a state, Paul is now receiving 1.2% in 2012, in addition to a base of 6.9% everywhere – so getting 5% in a 2008 primary would be associated with a forecast of about 12.9% in 2012. With these eight data points, the simple model explains 63.8% of the variance in 2012 performance.
Next, I turn to a log-linear model, which would be more appropriate if Paul’s performances continue to experience overdispersion. Here are the results:
Call: lm(formula = lnvote12 ~ lnvote08) Residuals: Min 1Q Median 3Q Max -0.36483 -0.22250 0.06901 0.15519 0.35117 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.5376 0.3628 4.238 0.00545 ** lnvote08 0.6086 0.1768 3.442 0.01377 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.2805 on 6 degrees of freedom Multiple R-squared: 0.6638, Adjusted R-squared: 0.6078 F-statistic: 11.85 on 1 and 6 DF, p-value: 0.01377
Although the coefficient estimate is not so easily interpreted, this model actually does a slightly better job than the simple linear model. (I also test various transformations of the independent variable to get at other nonlinearities, but none of those models improves significantly over this one.) So I use these estimates to get new forecasts of the remaining contests. Here they are:
|District of Columbia||3-Apr||16.6%|
In general, these new forecasts are lower for Paul in his best states and higher in his worst states. (So yes, his support is less overdispersed this time around, suggesting that his new support is less enthusiastic than his core support – not really surprising.) With the new forecasts, it’s looking unlikely that Paul will win any states outright, although Idaho, North Dakota, and Maine present possibilities.