To recap: As we discussed in earlier posts, alpha-NOMINATE is a new form of NOMINATE that is fully Bayesian and is meant to replace W-NOMINATE which is now getting close to being 34 years old (the multidimensional version, written by Nolan McCarty and Keith Poole, is over 25 years old). NOMINATE was designed by Keith Poole and Howard Rosenthal during 1982-1983. It used a random utility model with a Gaussian deterministic utility function (see pages 14 – 15 of the linked 1983 paper) and logistic error (random draws from the log of the inverse exponential). The Gaussian deterministic utility function is able to capture non-voting due to indifference * and* alienation.

Alpha-NOMINATE is a mixture model in which legislators’ utility functions are allowed to be a mixture of the two most commonly assumed utility functions: the quadratic function and the Gaussian function assumed by NOMINATE. The “Alpha” is a parameter estimated by Alpha-NOMINATE that varies from 0 (Quadratic Utility) to 1 (Gaussian Utility). Hence, in one dimension with Alpha = 0, Alpha-NOMINATE is identical to the popular IRT model. Thus Alpha-NOMINATE can actually test whether or not legislators’ utility functions are Quadratic or Gaussian.

Below we apply Alpha-NOMINATE to the the 114^{th} House through mid-March 2016. There have been 834 total votes of which 718 are scalable (at least 2.5% in the minority; that is, votes that are 97-3 to 50-50). We used the R version of Alpha-NOMINATE to perform the analysis. We used 4000 samples from a slice sampler in one dimension with a burn-in of 1000. The first graph shows the Trace and Density plots for alpha.

The mean of alpha is 0.99986 with a standard deviation of 0.00014 strongly indicating that the Representatives’ utility functions were Gaussian.

Below is a smoothed histogram of the 3000 configurations after burn-in. The divide between Democrats and Republicans is a very deep one.

Of more interest, however, are the clear divisions in the Republican Party shown in the smoothed histogram. The gap between Speaker Ryan and the head of the Freedom Caucus Jim Jordan (R-OH) is very wide. Given the turmoil in the Republican Presidential Nominating process, it is growing harder and harder for Speaker Ryan to restore “regular order” and pass a budget. With Hillary Clinton leading both Donald Trump and Ted Cruz in the polls and the competition between Trump and Cruz to gain the 1237 delegates they need for the nomination likely to drag out until at least May and perhaps even to the convention in July, this is likely to paralyze the House Republican Party for some time. This potential paralysis has motivated one of the members of the Freedom Caucus, Paul Gosar (R-AZ), to lead an effort to stop any post-Presidential Election or “Lame Duck” session of Congress for fear that spending “deals” would be struck by the leaders of both Political Parties. Depending on the state of the Presidential race in September this issue could get entangled with Presidential campaign politics. (The House is scheduled to go into recess on September 30th.) All in all, it will not be a boring year!

The next five plots show the estimated ideal points for the 435 Members who served during the 114th through mid-March along with their 95% Credible Intervals. Furthest left is Grijalva (D-AZ) at -2.38 followed by Lee (D-CA) at -2.16. On the far right are Massie (R-KY) at 4.16, Amash (R-MI) at 4.52, and Jones (R-NC) at 5.73.

*Click image to enlarge*