(Joint House and Senate Scaling)

Updated 2 September 2015

This is the fifth release of

These new scores for the 1

"Measuring Bias and Uncertainty in Ideal Point Estimates via the Parametric Bootstrap."
*Political Analysis*, 12:105-127, 2004, Jeffrey B. Lewis and Keith T. Poole.

"Measuring Bias and Uncertainty in DW-NOMINATE Ideal Point Estimates via the Parametric Bootstrap."Â*Political Analysis*Â 17:261-27, 2009, Royce Carroll, Jeffrey B. Lewis, James Lo, Keith T. Poole, and
Howard Rosenthal.

This research was made possible by NSF Grant 0611880 to Jeffrey B. Lewis"Measuring Bias and Uncertainty in DW-NOMINATE Ideal Point Estimates via the Parametric Bootstrap."Â

Keith T. Poole, and Howard Rosenthal. This work was also supported in part by the Rice Terascale Cluster funded by NSF under Grant EIA-0216467, and a partnership between Rice University, Intel, and HP. We thank the National Science Foundation and the San Diego Supercomputer Center for their support.

There were a total of 102,806 roll calls of which 92,182 were scalable. The number of unique legislators was 11,976 producing a total of 16,980,265 choices. In the scaling, the second dimension weight is 0.4113 and the Beta parameter (proportional to 1/s where s is the standard deviation of the error) is 7.8334. The correct classification is 87.21 percent with an APRE of 0.6215 and a geometric mean probability of 0.7533.

In order to calculate distances from these Common Space DW-NOMINATE scores you must multiply the second dimension by the weight parameter. To calculate the choice probabilities you must apply both the second dimension weight and the Beta parameter.

Please note that these files contain scores for most Presidents. For Presidents prior to Eisenhower these are based on roll calls corresponding to Presidential requests. These roll calls were compiled by an NSF project headed by Elaine Swift (Study No. 3371, Database of Congressional Historical Statistics, 1789-1989). Many of these scores are based upon a small number of roll calls

The format of the legislator files is:

1. Congress Number 2. ICPSR ID Number: 5 digit code assigned by the ICPSR as corrected by Howard Rosenthal and myself. 3. State Code: 2 digit ICPSR State Code. 4. Congressional District Number (0 if Senate or President) 5. State Name 6. Party Code: 100 = Dem., 200 = Repub. (See PARTY3.DAT) 7. Name 8. 1st Dimension Coordinate 9. 2nd Dimension Coordinate 10. 1st Dimension Bootstrapped Standard Error 11. 2nd Dimension Bootstrapped Standard Error 12. Correlation Between 1st and 2nd Dimension Bootstrapped Estimates 13. Log-Likelihood 14. Number of Votes 15. Number of Classification Errors 16. Geometric Mean Probability The format of the roll call files is: 1. Congress Number 2. Roll Call Number 3. "H" if House, "S" if Senate 4. Number of Yeas 5. Number of Nays 6. Month of Roll Call 7. Day of Roll Call 8. Year of Roll Call 9. Number Correctly Classified 10. Predicted Yea/Actual Yea 11. Predicted Yea/Actual Nay 12. Predicted Nay/Actual Yea 13. Predicted Nay/Actual Nay 14. Proportion Correctly Classified (#9 divided by #4 + #5) 15. Proportional Reduction in Error (PRE) -- (Min. on RC - Error)/Min. on RC 16. Geometric Mean Probability 17. Spread on 1st Dimension -- if the roll call was not scaled, there 18. Midpoint on 1st Dimension -- are 0.000's in all four fields 19. Spread on 2nd Dimension -- 20. Midpoint on 2nd Dimension --

Legislator Estimates 1

Legislator Estimates 1

Legislator Estimates 1

Legislator Estimates 1

Legislator Estimates 1

Roll Call Estimates 1

Roll Call Estimates 1

Roll Call Estimates 1

Roll Call Estimates 1

Roll Call Estimates 1

**A Comparison of the "Common Space" DW-NOMINATE Scores With the Separate House and
Senate 2-Dimensional Linear DW-NOMINATE Scores**

- Keith T. Poole and Howard Rosenthal. 1997.
. New York: Oxford University Press.*Congress: A Political-Economic History of Roll Call Voting* - Keith T. Poole and Howard Rosenthal. 2007.
. Piscataway, N.J.: Transaction Press.*Ideology and Congress* - Keith T. Poole. 2005. Spatial Models of Parliamentary Voting. New York: Cambridge
University Press.

The fit of the Joint Scaling is a half percentage point below the House fit but better than the Senate fit. This reflects the fact that the House fit is better than the Senate fit and the number of unique members in the House is more than five times the number of unique members of the Senate. Consequently, when the chambers are combined it is not surprising that the larger number of House members -- even with the constraint of the constant model -- will drive the fit.Joint Scaling House Only Senate Only (2-D Const.) (2-D Lin.) (2-D Lin.) .................................................................... Correct Classification 87.2100 87.7670 86.1230 APRE 0.6215 0.6377 0.5906 GMP 0.7533 0.7608 0.7440 Beta 7.8334 7.8332 10.1105 Weight-2nd 0.4113 0.3988 0.5638 .......................................... Unique Legisislators 11,976 10,731 1,895 Total Roll Calls 102,806 53,530 49,276 Scalable Roll Calls 92,182 46,865 45,317 Total Choices 16,980,265 13,879,366 3,100,516

Below is a graph of the correct classifications for these three scalings. The pattern of the classifications is essentially the same as that shown in Figure 3.1 of

The graph below shows the Aggregate Proportional Reduction in Error (APRE). The APRE controls for the margins of the roll calls and is defined as (TOTAL MINORITY VOTES - CLASSIFICATION ERROR)/TOTAL MINORITY VOTES. Hence, if the spatial model simply predicts the majority number on each roll call the classification error will equal the total of the minority votes and APRE will be zero. This controls for the fact that if you have a large number of lopsided roll calls you can have a high rate of classification. The APRE statistic accounts for this by making the benchmark correctly classifying the minority votes (so to speak).

Note that since the 1970s APRE has climbed rapidly and is about 0.85 while the average majority margin on the roll calls in the two chambers has been between 70% to 65%. Most roll call votes in the current unidimensional era are all of one party plus the closest wing of the opposite party versus the remainder of the opposite party. This is why the APRE and the Correct Classification have risen so sharply.

Below is a graph of the polarization of the House and Senate since the end of Reconstruction (1879-2014) using the joint space coordinates. Polarization is measured as the distance between the two major parties on the first, liberal-conservative dimension (see graph below). The pattern of polarization within the two chambers is almost the same with the 113

The three figures below show the Party Means for the current Post-Reconstruction Democrat-Republican two-party system. The figures pretty much speak for themselves. We have color coded the party lines and report correlations between the Party Means from the joint scaling versus the separate scalings. Note that for the graphs of the second dimension Party Means we separate out the Northern and Southern Democrats. The basic message of these graphs is that the Joint scaling is reproducing the Party trend lines during the whole Post-Reconstruction period.

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