Sticking with the script

I noted in the competitiveness piece that both Republican candidates only lead in the polls on an eighth of the last 120 days of the campaign.  So one might think that measuring “competitiveness” was the same as measuring support for President Obama. Well, it turns out there is a lot of useful information in that Republican 12% of the days.

First, here is the regression for the absolute margin between the candidates. It generates the graph shown in the earlier piece.  The value of the constant, which in this model is the 2008 predicted margin of victory on Election Day, is seven percent.  Likely voter polls may present a slightly more competitive race, but the effect is small and does not reach conventional significance levels.

Dependent variable: abslead

               coefficient   std. error   t-ratio   p-value 
  const         7.08681      0.673568     10.52     4.51e-19 ***
  LV           −0.569429     0.460187     −1.237    0.2182  
  Daysbefore   −0.0382867    0.00864958   −4.426    2.02e-05 ***
  e2012        −2.92970      1.19827      −2.445    0.0158   **
  db2012        0.0321738    0.0158566     2.029    0.0445   **

Mean dependent var   4.156866   S.D. dependent var   2.638088
Sum squared resid    762.5030   S.E. of regression   2.431229
R-squared            0.176219   Adjusted R-squared   0.150676

The two coefficients for the 2012 election are both highly significant and predict an essentially flat campaign.  The coefficent of the slope interaction term, db2012 (0.03217)  is nearly identical to the global slope for Daysbefore.  Since there are only two elections in this analysis, the global slope is identical to the slope for 2008.  So in that year we predict a less competitive race as Election Day approaches.  The 2012 election is predicted to be a flat three points more competitive (-2.93)  than 2008 but show no tendency to become either more or less competitive as the election draws nigh.

However we get very different results if we look at the trends in the President’s margin over his two opponents.  Then it turns out the campaign has so far followed the same path in 2012 as it did in 2008!

Dependent variable: DLead

               coefficient   std. error   t-ratio   p-value
  const         7.60564      0.880873      8.634    1.92e-14 ***
  LV           −1.47520      0.601820     −2.451    0.0156   **
  Daysbefore   −0.0514938    0.0113117    −4.552    1.21e-05 ***
  e2012        −2.15015      1.56706      −1.372    0.1724
  db2012        0.0299972    0.0207368     1.447    0.1504

Mean dependent var   3.549701   S.D. dependent var   3.416355
Sum squared resid    1304.084   S.E. of regression   3.179494
R-squared            0.159906   Adjusted R-squared   0.133856

The two terms for the 2012 election are only marginally significant and of opposite signs, a sure tipoff that “multicollinearity” prevails.  I tested for any 2012 effect by removing both the 2012 terms from the model  and performing the usual F-test on the sums of squared residuals.  The probability of rejecting the null hypothesis reached only the p<0.35 level of significance.

So I removed both the 2012 variables leaving us with this result:

Dependent variable: DLead

               coefficient   std. error   t-ratio   p-value 
  const         7.20290      0.835764      8.618    1.91e-14 ***
  LV           −1.54004      0.596957     −2.580    0.0110   **
  Daysbefore   −0.0439874    0.00948000   −4.640    8.34e-06 ***

Mean dependent var   3.549701   S.D. dependent var   3.416355
Sum squared resid    1325.324   S.E. of regression   3.180720
R-squared            0.146223   Adjusted R-squared   0.133188

Rather remarkably given our perceptions of the 2008 and 2012 campaigns as being very different from the each other, in terms of the President’s standing in the polls he is at the same place today as he was in 2008.

We do see a likely voter result here as expected, since LV polls have a slightly higher proportion of Republicans.  This 1.5% Republican boost is identical to what Nate Silver found using a different method.  If we assume the actual electorate will be closer in attitudes to the likely voter samples, we get a predicted Obama advantage of 5.7% (=7.2 + (-1.5)) on Election Day.