"Common Space" DW-NOMINATE Scores With Bootstrapped
(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:
"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.
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." Political Analysis 17:261-27, 2009, Royce Carroll, Jeffrey B. Lewis, James Lo, Keith T. Poole, and Howard Rosenthal.
Keith T. Poole, and
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,
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. 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 safely.
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 Scores
The 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.:
- Keith T. Poole. 2005. Spatial Models of Parliamentary Voting.
New York: Cambridge University Press.
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
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.
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 Post-Reconstruction period.
NOMINATE Data, Roll Call Data, and Software
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