There are 4 kinds of NOMINATE Coordinates:

- The original D-NOMINATE Coordinates

These 2-dimensional dynamic coordinates were originally estimated on the CYBER 205 supercomputer at Purdue University during 1988-89 and they are extensively analyzed in our book, Oxford University Press, 1997). Each legislator's point is dynamic and is allowed to move as a linear function of time as measured by the Congress number (higher polynomials in time did not appreciably increase the fit). A legislator's point is constant within a Congress but "jumps" along a linear path between Congresses. A member had to serve at least 3 Congresses for the linear model to be estimated.*Congress: A Political-Economic History of Roll Call Voting*

Because of the "overlapping generations" nature of the estimation, scores in one Congress are**directly comparable**with scores in another Congress. However, as we caution in our book, cross-Congress comparisons should be conducted*only*between Congresses occurring during one of the stable 2-party periods of American History. Also, the D-NOMINATE scores*cannot be compared across chambers*.

Please see Chapters 1 -3 of our book for a description of the spatial model underlying D-NOMINATE and Appendix A of our book for the technical details and Monte-Carlo tests of the D-NOMINATE procedure. - W-NOMINATE Coordinates

W-NOMINATE is a static (i.e., meant to be applied to only one Congress) version of D-NOMINATE, with a number of improvements being designed to increase the efficiency of the algorithm so that it can be run on a desktop personal computer. To this end W-NOMINATE differs from D-NOMINATE in two ways: It uses a slightly different deterministic utility function; and, because it is a static algorithm, it constrains the legislators and roll call midpoints to lie within an s-dimensional hypersphere of radius one (in contrast to the rather flexible constraint structure necessitated by the dynamic model).

The original D-NOMINATE deterministic utility function was:**u**_{ijy}= b e^{[- (w2dijy2)/2]}

which is simply a normal distribution multiplied by a constant. Note that there is no index on**w**-- namely the weight is the same for all dimensions. Experimentally, we found that estimating both**b**and**w**was unnecesary so we set**w**= 1/8 (see Appendix A of our book for all the details).^{2}/2

The W-NOMINATE deterministic utility function is:**u**_{ijy}= b e^{[- Ã¥k=1,s (wk2dijy2)/2]}

The weight on the first dimension,**w**, is set equal to one and the other dimension weights are estimated (see Appendix A of our book for all the details)._{1}

The W-NOMINATE coordinates are highly correlated with the D-NOMINATE coordinates for most Congresses (Pearson r's typically greater than .95 for both the 1st and 2nd dimensions). However, unlike the D-NOMINATE scores, W-NOMINATE scores*are not directly comparable between Congresses*.

See Appendix A of our book for the technical details of the W-NOMINATE procedure. Jeff Lewis and I are computing Legislator Coordinate files with parametric bootstrapped standard errors for all Houses and Senates in American History. They can be found on the Parametric Bootstrap Page. For an explanation of how these are computed see:

"Measuring Bias and Uncertainty in Ideal Point Estimates via the Parametric Bootstrap" by Jeffrey B. Lewis and Keith T. Poole.

- Common Space Coordinates

The common space scores place the members of the House and Senate in the same space. This allows members to be compared across Chambers and across Congresses. The scores are derived from the W-NOMINATE scores utilizing a scaling technique explained in "Estimating a Basic Space From a Set of Issue Scales,"pp. 954-993.*American Journal of Political Science*, 42 (July 1998),

The W-NOMINATE coordinates of all members serving in both the House and Senate from 1937 - 2000 (Congresses 75 - 106) were used to estimate the common space coordinates. Each legislator is assigned a single coordinate throughout his or her career so that**members who served in both chambers will have the same coordinate in both**. The 1st dimension coordinates correlate with the corresponding DW-NOMINATE coordinates at .94 or higher for all Houses and Senates.

The Presidents from Eisenhower through Clinton were scaled using the CQ Presidential Support Roll Calls in W-NOMINATE. See "Veto Power and Legislation: An Empirical Analysis of Executive and Legislative Bargaining from 1961-1986,", 1995, 282-312 (with Nolan M. McCarty), for an analysis of these W-NOMINATE scores. A President's W-NOMINATE scores were treated like any other member of the House and Senate for the purposes of fitting them into the common space.*Journal of Law, Economics, and Organization*, 11

Note that the common space coordinates are adjusted so that the two dimensions are*equally salient and lie within a unit circle*. This assumption plus the assumption that a legislator serving in both Chambers of Congress has the same coordinate throughout his or her career means that these coordinates should be used with caution. - DW-NOMINATE Coordinates

DW-NOMINATE is a dynamic version of W-NOMINATE and is very similar to the original D-NOMINATE procedure. The only differences are that DW-NOMINATE is based on normally distributed errors rather than on logit errors and that each dimension has a distinct (salience) weight (the weight of the first dimension is always 1.0). DW-NOMINATE scores in one Congress are**directly comparable**with scores in another Congress. However, cross-Congress comparisons should be conducted*only*between Congresses occurring during one of the stable 2-party periods of American History. Also, the DW-NOMINATE scores*cannot be compared across chambers*. In addtion, because these coordinates were estimated using a weighted utility model,This was not true of the original D-NOMINATE coordinates.*if distances are computed between legislators, this weighting must be taken into account*!

When Howard Rosenthal and I began our research in 1982, computer memory and speeds were a significant problem, and we took the logit approach because it was computationally more tractable. Because computer memory and speed are now minor impediments, we developed DW-NOMINATE because the normal distribution allows us to develop much more sophisticated models of correlated error (that work is now underway).

We applied DW-NOMINATE to all roll call votes taken since the end of World War II as part of an on going study of post-War American politics. Our preliminary results are reported in(joint with Nolan McCarty, 1997, AEI Press).*Income Redistribution and the Realignment of American Politics*

For all practical purposes, the coordinates estimated by DW-NOMINATE are identical to the original D-NOMINATE coordinates for the 1^{st}to the 99^{th}Congresses. For the 2-dimensional, dynamic model, the Pearson correlations between the two sets of coordinates for the House were .977 for the first dimension and .923 for the second dimension (n = 31,306). The corresponding correlations for the Senate were .974 and .901 respectively (n = 7619).

Note that the*average*DW-NOMINATE coordinate for every legislator is constrained to lie within the unit hypersphere. However, some members may have large linear terms so that for some Congresses their coordinates can be greater than +1/-1. Also note that the weight on the 2^{nd}dimension is about .3 for both the House and the Senate [see(joint with Nolan McCarty, 1997, AEI Press) for further details]. To reiterate the warning above, because these coordinates were estimated using a weighted utility model,*Income Redistribution and the Realignment of American Politics*in any analyses using the distances.*if distances are computed between legislators, this weighting must be taken into account*

- KREH01.ORD to KREH99.ORD and KRES01.ORD to KRES99.ORD are D-NOMINATE coordinates.
The format of the D-NOMINATE files is:

Note that if the 1st and 2nd dimension coordinates are exactly .000, then the Senator/Representative did not have enough roll call votes to be estimated in that Congress.**1. Congress Number 2. ICPSR ID Number: 5 digit code assigned by the ICPSR as corrected by Howard Rosenthal and myself. 3. ICPSR ID Number: original 5 digit ICPSR code (this field is usually blank). 4. State Code: 2 digit ICPSR State Code. 5. Congressional District Number (0 if Senate) 6. State Name 7. Party Code: 100 = Dem., 200 = Repub. (See PARTY3.DAT) 8. ICPSR Occupancy Code: See any ICPSR Roll Call Voting Codebook 9. ICPSR Office Code: See any ICPSR Roll Call Voting Codebook 10. Name 11. 1st Dimension Coordinate 12. 2nd Dimension Coordinate**

To download these files go to the D-NOMINATE Scores Page. - W-NOMINATE coordinates.

W-NOMINATE scores With Bootstrapped Standard Errors**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) 5. State Name 6. Party Code: 100 = Dem., 200 = Repub. (See PARTY3.DAT) 7. Name 8-11. The cross-classications for the legislator. The two middle numbers are the "errors". For example, in the 106**^{th}House Callahan's cross classification numbers are: CALLAHAN 494 50 20 278 or in table form ACTUAL Yea Nay Yea 494 50 PREDICTED Nay 20 278 12. Geometric Mean Probability 13. 1st Dimension Coordinate 14. 2nd Dimension Coordinate 15. 1st Dimension Standard Error 16. 2nd Dimension Standard Error

W-NOMINATE scores by year for 1939 - 1998

W-NOMINATE Program - BL75107.DAT are the Common Space coordinates -- W-NOMINATE coordinates for the 75th
through the 107th Houses and Senates adjusted so that the the House and Senate members
and the Presidents are in the same space. There is one record for each legislator
in each Congress for this time period (n=17,871, 1937-2002). For an explanation of
how this was done, see "Estimating a Basic Space From a Set of Issue Scales,"
pp. 954-993.*American Journal of Political Science*, 42 (July 1998),

The format for BL75107.DAT is:

To download these files go to the Common Space Page.**1. Congress Number 1 - 107 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. Congress District Number (Senate and President = 0) 5. Name of State 6. Party Code: 100 = Dem., 200 = Repub. (See PARTY3.DAT) 7. Name 8. 1st Dimension Coordinate 9. 2nd Dimension Coordinate 10. Indicator For Chamber 0 = House 1 = Senate 2 = President (83 - 107)** - H761939.DAT to H1051998.DAT and S861959.DAT to S1051998.DAT are yearly W-NOMINATE
coordinates.

The format of these files is the same as the D-NOMINATE and W-NOMINATE files.

W-NOMINATE scores by year for 1939 - 1998 - HL01107A1.DAT and SL01107A1.DAT are DW-NOMINATE legislator coordinates for the 1
^{st}to the 107^{th}Congresses. HC01107A1.DAT and SC01107A1.DAT are the corresponding roll call coordinates.

To download these files go to the DW-NOMINATE Page.**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) 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 Conditional Standard Error 11. 2nd Dimension Conditional Standard Error 12. Log-Likelihood 13. Number of Votes 14. Number of Classification Errors 15. Geometric Mean Probability The format of the roll call files is: 1. Congress Number 2 Roll Call Number 3. Spread on 1st Dimension -- if the roll call was not scaled, there 4. Midpoint on 1st Dimension -- are 0.000's in all four fields 5. Spread on 2nd Dimension -- 6 Midpoint on 2nd Dimension --**

The state, congressional district, and party codes correspond to Ken Martis's

The file PARTY3.DAT contains the dictionary for the party codes. Please cite Ken Martis's atlas as the original source if you use these codes in any way.

NOMINATE Data, Roll Call Data, and Software

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