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 about 33 years old (the multidimensional version, written by Nolan McCarty and Keith Poole is almost 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 114^{th} House. There have been 1200 total votes in the House as of the Thanksgiving recess of which 1039 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 0.99957 with a standard deviation of 0.000394 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. The respective Party leaders are near the modes of the two Parties.

The next five plots show the estimated ideal points for the 436 scalable Representatives along with their 95% Credible Intervals. On the left, Representative Grijalva (D-AZ) is located at -2.376. His 95% credible interval runs from -2.577 to -2.182. The five Republicans on the right end are Duncan (R TN-2) at 2.086 (1.84 – 2.30), Huelskamp (R KS-1) at 2.14 (2.37 – 1.93), Massie (R KY-4) at 3.78 (3.94 – 3.61), Amash (R MI-3) at 4.03 (3.89 – 4.17), and Jones (R NC-3) at 8.845 (8.39 – 9.29).

Walter Jones is also the most extreme member of the 113^{th} House. Indeed, many of the more extreme members of the Republican caucus continued into the 114^{th}. With the volatile issue of Planned Parenthood funding holding up the funding for fighting the Zika virus it may prove difficult for Congress to pass a Continuing Resolution that would fund the Government past the upcoming Presidential election.

*Click image to enlarge*

(TO BE CONTINUED!)