"Common Space" DW-NOMINATE Scores With Bootstrapped Standard Errors
(Joint House and Senate Scaling)
Royce Carroll, Jeff Lewis, James Lo, Nolan McCarty, Keith Poole, and Howard Rosenthal
Updated 2 September 2015
This is the fifth release of Common Space DW-NOMINATE scores for the House and Senate. The House and Senate were scaled as
if they were one legislature using the 650 Legislators who served in both the House and Senate as "glue" (bridge observations). That is, we estimated a single ideal point for each
member of Congress based upon his/her entire record of service in Congress. In the Poole-Rosenthal framework we used the Constant model so that each unique legislator has the same ideal point throughout his or her
career. After the download links we show some comparisons of these Common Space scores
with our regular DW-NOMINATE Scores for the House and Senate.
These new scores for the 1st to the 113th Congresses (1789 - 2014) contain parametric bootstrapped standard errors. For an explanation of the basic theory of the parametric bootstrap see:
This research was made possible by NSF Grant 0611880 to Jeffrey B. Lewis
"Measuring Bias and Uncertainty in Ideal Point Estimates via the Parametric Bootstrap."
, 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
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
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. Use the Yea and Nay outcome coordinates with considerable caution because, as we explain
in Congress: A Political Economic History of Roll Call Voting, they are poorly identified. However, the cutting line is identified and can be used
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 so use them with caution!
In the files below the House Coordinates for each Congress are stacked on top of the
Senate coordinates. If you have questions or need help with these files please send us e-mail at firstname.lastname@example.org (Jeff Lewis) or email@example.com (Keith Poole).
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)
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
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 1st to 113th Houses and Senates (Text File, 46,506 lines)
Legislator Estimates 1st to 113th Houses and Senates (Stata 14 File, 46,506 lines)
Legislator Estimates 1st to 113th Houses and Senates (Stata 12 File, 46,506 lines)
Legislator Estimates 1st to 113th Houses and Senates (Eviews File, 46,506 lines)
Legislator Estimates 1st to 113th Houses and Senates (Excel File, 46,506 lines)
Roll Call Estimates 1st to 113th Houses and Senates (Text File, 102,806 lines)
Roll Call Estimates 1st to 113th Houses and Senates (Stata 13 File, 102,806 lines)
Roll Call Estimates 1st to 113th Houses and Senates (Stata 12 File, 102,806 lines)
Roll Call Estimates 1st to 113th Houses and Senates (Eviews File, 102,806 lines)
Roll Call Estimates 1st to 113th Houses and Senates (Excel File, 102,806 lines)
A Comparison of the "Common Space" DW-NOMINATE Scores With the Separate House and
Senate 2-Dimensional Linear DW-NOMINATE ScoresThe Joint Scaling of the House and Senate utilizes the 2-dimensional constant model developed by Poole and Rosenthal in which each legislator has a single ideal
point throughout his or her career. In contrast, the standard DW-NOMINATE scores use
the 2-dimensional linear model in which a legislator is allowed to move on a straight line throughout his
or her career. These models are discussed in detail in:
In the table below we show the fit statistics for the Joint Scaling and the separate
scalings for the House and Senate posted on the DW-NOMINATE Scores Page.
- Keith T. Poole and Howard Rosenthal. 1997. Congress: A Political-Economic History of Roll Call Voting. New York: Oxford University Press.
- Keith T. Poole and Howard Rosenthal. 2007. Ideology and Congress. Piscataway, N.J.: Transaction Press.
- Keith T. Poole. 2005. Spatial Models of Parliamentary Voting. New York: Cambridge
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 3,100,516The 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.
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 Ideology and Congress. The correct classification of the joint scaling closely tracks that for the separate
House DW-NOMINATE scaling. The Pearson correlation between the two is 0.988. The corresponding
correlation between the joint scaling and the separate Senate DW-NOMINATE scaling
is 0.807. However, the correlation between the correct classifications for the Senates within the joint scaling and the separate Senate DW-NOMINATE scaling is 0.986. The corresponding correlation
between the correct classifications for the Houses within the joint scaling and the separate House DW-NOMINATE scaling is 0.998. What these correlations show
is that, although constraining the members of Congress to having a single ideal point
throughout their careers, the patterns of overall chamber classifications are almost exactly reproduced even though on average
the classifications of the joint model are lower.
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 113th House being the most polarized chamber since the end of Reconstruction.
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
NOMINATE Data, Roll Call Data, and Software
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