W-NOMINATE Program Page

W-NOMINATE Program


W-NOMINATE is a scaling procedure that performs parametric unfolding of binary choice data. Given a matrix of binary choices by individuals (for example, Yes or No) over a series of Parliamentary votes, W-NOMINATE produces a configuration of legislators and outcome points for the Yea and Nay alternatives for each roll call using a probabilistic model of choice. It is discussed in detail in:

    Spatial Models of Parliamentary Voting, by Keith T. Poole. New York: Cambridge University Press, 2005.
    Congress: A Political-Economic History of Roll Call Voting, by Keith T. Poole and Howard Rosenthal. New York: Oxford University Press, 1997.
    "Patterns of Congressional Voting." American Journal of Political Science, 35, 1991, 228-78, by Keith T. Poole and Howard Rosenthal.
    "A Spatial Model For Legislative Roll Call Analysis." American Journal of Political Science, May 1985, 357-384, by Keith T. Poole and Howard Rosenthal.
Download wnominate: W-NOMINATE Roll Call Analysis Software for R

W-NOMINATE in R Examples (R programs and datasets)

Download W-NOMINATE scores on the Data Download page


    Examples

    107th Senate (Detailed Discussion of Input and Output Files)
    96th House


      Example One: The 107th Senate.

      To see how W-NOMINATE works, download the program (WNOM9707.EXE), the "control card" file (NOMSTART.DAT), and the 107th Senate Roll Call data files below:

      W-NOMINATE Scaling Program Executable (Compiled For WINTEL Machines -- WNOM9707.EXE)

      W-NOMINATE Program Source Code (FORTRAN -- WNOM9707.FOR)

      Control Card File (NOMSTART.DAT)

      107th Senate Roll Call Data (SEN107KH.ORD)

      and place them in the same folder on a WINTEL machine. NOMSTRT.DAT looks like this:
      
      SEN107KH.ORD               Data File Name -- can include path statement
      NOMINAL MULTIDIMENSIONAL UNFOLDING OF 107th SENATE  Title of Run
        633   10   18            Number RCs, Left on 1st, Up on 2nd
          2   36                 Number Dimensions, Number Characters to Read From Header
       15.0000  0.5000           Starting Values for BETA and WEIGHT
        0.0250   20              RC Min. Cutoff, Number RCs for Legislator
      (36A1,3600I1)              Format for Roll Call File
      (1X,I4,36A1,1X,4I4,51F7.3) Format for Legislator Coordinate File -- NOM31.DAT
      (1X,I4,36A1,1X,51F7.3)     Format for W-NOMINATE, H-S, and Metric Coordinate File -- NOM36.DAT
      
      • The first line is the name of the roll call data file -- this can also include the path to the file. For example:

        C:\DATAFILES\MYROLLCALLS.TXT
        where MYROLLCALLS.TXT is your roll call matrix.
      • The second line is the title of the scaling.
      • The third line, in order, is the number of roll calls, the record number of a Senator/Legislator that you believe is on the "Left" of the first dimension (this just sets "liberal" on the left and "conservative" on the right of the first dimension), and the record number of a Senator/Legislator that you want to be "Up" on the second dimension (this feature is handy if you want, for example, Southern Democrats to be "Up" or positive on the second dimension -- in other countries, this could be another salient division such as religion). In the 107th 10 is Senator Boxer (D-CA) and 18 is Senator Graham (D-FL).
      • The fourth line, in order, is the number of dimensions and the number of characters to read of the front of each legislator's record ("36" for the 107th Senate). This number can be set as high as 99 depending upon how you have organized your data -- contact me KPoole@ucsd.edu if you have questions about how to do this.

        Technically, the computer "sees" the third and fourth lines as:
        006330001000018
        and
        0000200036
        This spacing must not be changed! If you want to analyze 1221 roll calls in 3 dimensions with everything else the same the two lines must look like this:
        012210001000018
        0000300036

        or with the zeroes removed

        1221 10 18
        3 36
      • The Fifth line, in order, is the starting value for Beta and the starting value for Weight for the first dimension. Most users should leave these set at these values! The program just uses them as starts in any event!
      • The Sixth Line, in order, is the cutoff criteria for roll calls in terms of the minimum proportion on the minority side for the roll call to be included; and the cutoff criteria for the Senators/Legislators in terms of the minimum number of roll call votes cast to be included. For the 107th these are set to 0.0250 (2.5% or better on the minority side of the roll call call -- this variable is XVMIN in the FORTRAN source code) and 20 roll calls for a legislator to be included in the scaling (this variable is KVMIN in the FORTRAN source code). Note that the program sees this line as:
        000.025000020
        If you change these criteria to 5% for the roll calls and 10 for the legislators, then the line must look like this:
        000.050000010
        or
        0.0500 10
        or
        0.05 10
      • The seventh line is the format for the roll call vote file -- SEN107KH.ORD in this example. The "36A1" is the number of characters before the first roll call vote. Note that the only thing you should ever have to change in this line is the "36". That number must match the "36" in line four. The "3600I1" allows up to 3,600 roll call votes to be read in. The program expects each roll call vote to be only one digit with no spaces between roll calls. For example, the first three lines of SEN107KH.ORD look like this:
        
        
        1079991099 0USA     200  BUSH       111111111999119999999999999991999999999....etc.
        1074970041 0ALABAMA 20001SESSIONS   111111111111111611111611111111166661611....etc.
        1079465941 0ALABAMA 20001SHELBY     111111111111111611111611111111166611611....etc.
        There are 36 columns before the first roll call and then each roll call is only one digit in width.

      • The eighth line is the format for the Legislator Coordinate Output file -- NOM31.DAT. The only thing you will ever have to change in this line is the "36". That number must match the "36" in line four. If you have 41 characters on the front of a legislator's record, then this format will look like this:
        
        (1X,I4,41A1,1X,4I4,51F7.3)
      • The ninth line is the format for a Legislator Coordinate Output file -- NOM36.DAT -- that contains the W-NOMINATE coordinates, the Heckman-Snyder coordinates, and the metric scaling coordinates (see below). The only thing you will ever have to change in this line is the "36". That number must match the "36" in line four. If you have 41 characters on the front of a legislator's record, then this format will look like this:
        
        (1X,I4,41A1,1X,51F7.3)
      At the command prompt type:

      WNOM9707

      and you will get five output files: NOM21.DAT, NOM23.DAT, NOM31.DAT, NOM33.DAT, and NOM36.DAT

      1. NOM21.DAT


      2. The NOM21.DAT file contains the basic measures of fit and it should look something like this (click on the links to see detailed explanations of some of the lines of the file):
        SEN107KH.ORD
        NOMINAL MULTIDIMENSIONAL UNFOLDING OF 107th SENATE
        633 10 18
        The lines in red simply echo back 2 36 the corresponding lines in NOMSTART.DAT 15.0000 0.5000
        0.0250 20
        (36A1,3600I1)
        (1x,I4,36A1,1X,4i4,51f7.3)
        (1x,I4,36A1,1X,51f7.3)

        DATA 0 0 Read in Data: Total CPU time, CPU time of Read CLEAN 0 0 Throw out Unscalable RCs and Legislators: Total CPU time, CPU time of Clean STARTS 1 1 Generate Legislator Starts: Total CPU time, CPU time of Starts RECODE 1 0 Generate Roll Call Starts: Total CPU time, CPU time of Recode 1 47 6 1.000 -1.000 1.000 PERCENT CLASSIFIED= 89.134 AGGREGATE PRE= 0.687 1 1 1 6 5 -12229.7295 0.7610 0.6352 0.6621 1 2 2 6 0 -11498.9316 0.7735 0.9959 1 3 0 7 1 -11493.0479 0.7736 0.6785 15.2322 0.5296 PERCENT CLASSIFIED= 89.266 AGGREGATE PRE= 0.691 1 4 1 11 4 -11986.9141 0.7651 0.9957 0.9939 1 5 2 11 0 -11385.1641 0.7755 0.9990 1 6 0 12 1 -11375.5322 0.7756 0.9955 15.9184 0.5307 PERCENT CLASSIFIED= 89.270 AGGREGATE PRE= 0.691 1 7 1 15 3 -11947.9150 0.7658 0.9937 0.9996 1 8 2 16 1 -11350.7012 0.7761 0.9999 1 9 0 17 1 -11342.5059 0.7762 0.9955 16.7035 0.5276 PERCENT CLASSIFIED= 89.286 AGGREGATE PRE= 0.692 1 10 1 20 3 -11946.8047 0.7658 0.9983 0.9997 SAG IN RECOVERED LEGISLATOR COORDINATES 110729142 5 0RHODE I 10001REED 294 20 6 136 -1.000 11071303952 0MARYLAN 10001SARBANES 304 11 5 137 -1.000 11071501171 0CALIFOR 10001BOXER 281 22 8 131 -1.000 11071410547 0NORTH C 20001HELMS 115 15 10 188 0.931 11071462849 0TEXAS 20001GRAMM, PHIL 171 24 13 233 0.984 11071542961 0ARIZONA 20001KYL 171 33 9 242 1.000 CONSTRAINED UNCONSTRAINED OFF OPPOSITE OFF SAME 42 74 341 2 7 36 1.633 -1.528 1.000 PERCENT CLASSIFIED= 89.172 AGGREGATE PRE= 0.688 2 11 1 21 1 -10584.7471 0.7895 0.0000 0.0027 2 12 2 22 1 -10520.0684 0.7906 0.0009 2 13 -1 23 1 -10643.2773 0.7884 0.0025 16.7035 0.5189 PERCENT CLASSIFIED= 90.007 AGGREGATE PRE= 0.712 2 14 1 24 1 -10577.8984 0.7896 0.8803 0.7860 2 15 2 25 1 -10493.7646 0.7911 0.9689 2 16 -1 25 0 -10552.6006 0.7900 0.8437 16.7035 0.5397 PERCENT CLASSIFIED= 90.074 AGGREGATE PRE= 0.714 2 17 1 27 2 -10521.1230 0.7906 0.9449 0.8791 2 18 2 27 0 -10455.6855 0.7917 0.9891 2 19 -1 28 1 -10507.5830 0.7908 0.9190 16.7035 0.5620 PERCENT CLASSIFIED= 90.099 AGGREGATE PRE= 0.715 2 20 1 29 1 -10500.7441 0.7909 0.9883 0.9301 SAG IN RECOVERED LEGISLATOR COORDINATES 110714240 6 0VERMONT 20001JEFFORDS 63 14 6 57 -0.999 11071503961 0ARIZONA 20001MCCAIN 173 43 57 169 -0.953 110749905 5 0RHODE I 20001CHAFEE 212 43 48 153 -0.891 11071420364 0MONTANA 10001BAUCUS 266 48 17 114 0.931 11071305645 0LOUISIA 10001BREAUX 272 32 28 120 0.989 11074010335 0NEBRASK 10001NELSON, BEN 275 30 22 129 0.992 CONSTRAINED UNCONSTRAINED OFF OPPOSITE OFF SAME 92 62 303 11.37.52.28. ELAPSED TIME OF JOB 11.38.21.96.
      3. NOM23.DAT


      4. NOM23.DAT shows various intermediate output of W-NOMINATE which is useful for diagnostic purposes. The information below tells you how many roll calls and legislators the program has read and how many have been discarded using the cutoff criteria specified in line six of NOMSTART.DAT. Typically, the cutoff criteria for roll calls is set to 0.0250 (2.5% or better on the minority side of the roll call call -- this variable is XVMIN in the FORTRAN source code) and 20 roll calls for a legislator to be included in the scaling (this variable is KVMIN in the FORTRAN source code). It also shows the distribution of roll call margins for those roll calls meeting the cutoff criteria.
        NOMINAL MULTIDIMENSIONAL UNFOLDING OF 107th SENATE
        ROLL-CALLS READ= 633 NUMBER REJECTED= 176 NUMBER ACCEPTED= 457 CUTOFF= 0.025
        LEGISLATORS READ= 103 NUMBER REJECTED= 1 NUMBER ACCEPTED= 102 CUTOFF= 20
        DISTRIBUTION OF SCALABLE ROLL CALLS
        1 50 - 55 128 0.280
        2 56 - 60 98 0.214
        3 61 - 65 51 0.112
        4 66 - 70 44 0.096
        5 71 - 75 30 0.066
        6 76 - 80 27 0.059
        7 81 - 85 18 0.039
        8 86 - 90 21 0.046
        9 91 - 95 26 0.057
        10 96 - 99.5 14 0.031
        This is the output for an eigenvalue-eigenvector decomposition of the double-centered, symmetric, legislator by legislator agreement score matrix and the Heckman-Snyder covariance matrix. The 2nd column shows the eigenvalues of the double-centered agreement score matrix, the third column is the percent variation explained, and the fourth is the total variation explained. Columns 5-7 are for the decomposition of the H-S covariance matrix.
         PERFORMANCE INDEX EIGENVALUE/VECTOR ROUTINE=    2  102    0     0
        PERFORMANCE INDEX EIGENVALUE/VECTOR ROUTINE= 2 102 0 0
        1 10.7676 70.3183 70.3183 12.4941 58.0379 58.0379
        2 0.3445 2.2495 72.5677 0.7742 3.5965 61.6344
        3 0.3141 2.0512 74.6189 0.5320 2.4711 64.1055
        4 0.2055 1.3420 75.9609 0.4132 1.9195 66.0251
        5 0.1794 1.1717 77.1326 0.3487 1.6197 67.6447
        6 0.1542 1.0068 78.1394 0.2972 1.3807 69.0254
        7 0.1458 0.9523 79.0917 0.2747 1.2761 70.3015
        8 0.1209 0.7894 79.8810 0.2413 1.1207 71.4223
        9 0.1071 0.6996 80.5807 0.2141 0.9944 72.4167
        10 0.0929 0.6064 81.1871 0.2071 0.9620 73.3787
        11 0.0887 0.5791 81.7662 0.1954 0.9076 74.2864
        12 0.0813 0.5313 82.2974 0.1777 0.8253 75.1116
        13 0.0773 0.5048 82.8023 0.1684 0.7821 75.8937
        14 0.0691 0.4514 83.2537 0.1655 0.7687 76.6624
        15 0.0627 0.4096 83.6633 0.1553 0.7216 77.3840
        16 0.0585 0.3822 84.0455 0.1523 0.7076 78.0916
        17 0.0542 0.3541 84.3996 0.1491 0.6925 78.7841
        18 0.0513 0.3352 84.7348 0.1441 0.6695 79.4536
        19 0.0482 0.3151 85.0498 0.1400 0.6505 80.1040
        20 0.0451 0.2944 85.3442 0.1315 0.6110 80.7150
        The eigenvalues of the double-centered agreement score matrix are very useful for making a Skree plot like the one below. The "elbow" gives the user a pretty good indication of the dimensionality of the data.



        Below is the output for a metric multidimensional scaling of the agreement score matrix. The scaling will be done in whatever dimensionality is set by the User in NOMSTART.DAT. The 2nd column is the sum of squared error, the third column is the Pearson r-square, the fourth column is a stopping criteria, and the fifth column is the number of agreement scores. For information on how this scaling works, see "Least Squares Metric, Unidimensional Unfolding." Psychometrika, 1984, pp.311-323, by Keith T. Poole; and "Least Squares Metric, Unidimensional Scaling of Multivariate Linear Models." Psychometrika, 1990, pp.123-149, by Keith T. Poole.
           0  1371.27405     0.97102     0.00000    5151
        1 128.96994 0.96999 0.90595 5151
        2 63.48307 0.97747 0.50777 5151
        3 52.60210 0.98008 0.17140 5151
        4 47.91137 0.98065 0.08917 5151
        5 45.17076 0.98066 0.05720 5151
        6 43.43190 0.98053 0.03850 5151
        7 42.26067 0.98041 0.02697 5151
        8 41.43574 0.98032 0.01952 5151
        9 40.83847 0.98028 0.01441 5151
        10 40.39579 0.98027 0.01084 5151
        The Starting values of the Legislator coordinates are adjusted so that the furthest left individual is set to -1 and the furthest right is set to +1. The estimated coordinates are reported before the adjustment is made. Note that this is a simple linear transformation.
         NUMBER LEGISLATORS= 102 FURTHEST LEFT=   -0.6087 FURTHEST RIGHT=    0.6125
        POSITIONS: LEFT= 47 RIGHT= 6
        After each roll call phase, the cross-tabulation of the classifications is reported.
         TOTAL VOTES PREDICTED FOR  457 ROLL-CALLS
        ACTUAL
        YEA NAY
        YEA 24229 2781
        NAY 2084 15678
        After each legislator phase, the cross-tabulation of the classifications is reported.
         TOTAL VOTES PREDICTED FOR  102 LEGISLATORS
        ACTUAL
        YEA NAY
        YEA 24182 2728
        NAY 2131 15731
        Numerous other diagnostics are reported in the file but these are really useful for de-bugging purposes only. If you wish any information about them just send e-mail to me at KPoole@ucsd.edu and I would be happy to answer any questions that you may have.

      5. NOM31.DAT


      6. NOM31.DAT is the coordinate output file for the legislators. The format of this output file is controlled by the user. The format statement is the 8th line of NOMSTART.DAT. In the case of the 107th Senate the format is:
        (1X,I4,36A1,1X,4I4,51F7.3)
        The "1X,I4" tells W-NOMINATE to write out a simple integer counter from 1 to the number of scaled legislators. The "36A1" is the number of characters on each line of the roll call data file before the roll calls begin. Most users only need to change the "36" wherever it appears in NOMSTART.DAT. The "4I4" handles the cross-classifications and the "51F7.3" handles the coordinates and measures of fit. If you have problems with the formatting of files please send me an e-mail at KPoole@ucsd.edu and I would be happy to answer any questions that you may have.

        Here is what the NOM31.DAT file looks like:
        
            11079991099 0USA     200  BUSH          32   0   1  20  0.922  0.761  0.208  0.296  2.503
            21074970041 0ALABAMA 20001SESSIONS     172  27  32 213  0.785  0.641 -0.437  0.037  0.097
            31079465941 0ALABAMA 20001SHELBY       195  33  33 186  0.739  0.505 -0.158  0.031  0.095
            41071490781 0ALASKA  20001MURKOWSKI    198  15  13 194  0.828  0.632  0.464  0.039  0.169
            51071210981 0ALASKA  20001STEVENS      210  18  21 163  0.781  0.518  0.307  0.036  0.138
                                          etc etc
                 The first column is an integer counter
                 The column in red is the Congress number
        The column in blue is the ICPSR ID Number
        The column in Magenta is the ICPSR State Code
        The column of zeroes will show the two digit Congressional District Number for House Roll Call Matrices
        The column in Coral is the first seven letters of the State Name
        The column in Midnightblue is the party code -- see the Party Codes Page for a complete listing
        The column in Firebrick are the ICPSR Occupancy and Election Codes
        Name of Senator/Representative
        The cross classification is in Turquoise.
        The second and third columns are classification errors -- predicted yes voted no and predicted
        no voted yes. So for Bush
        correct classification = (32+20)/(32+20+0+1) = 98.1%
        The column in Purple is the Geometric Mean Probability
        The two columns in Green are the Legislator coordinates
        The last two columns in Deeppink are the Conditional Standard Errors
        etc etc
        981071492256 0WEST VI 10001ROCKEFELLER 298 21 18 117 0.821 -0.741 -0.096 0.039 0.127 991074930925 0WISCONS 10001FEINGOLD 240 75 20 122 0.697 -0.727 -0.686 0.031 0.119 1001071570325 0WISCONS 10001KOHL 300 20 21 104 0.801 -0.581 0.155 0.035 0.139 1011074970668 0WYOMING 20001ENZI 187 30 9 219 0.821 0.777 0.397 0.039 0.183 1021071563368 0WYOMING 20001THOMAS 190 22 8 228 0.845 0.842 0.313 0.049 0.199
        The Conditional Standard Errors are known to under-report the true uncertainty in the legislator coordinates (see the Appendix to Congress: A Political-Economic History of Roll Call Voting). Jeff Lewis and I have computed 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:

        The computer program that computes these bootstrapped standard errors for W-NOMINATE is posted on the Parametric Bootstrap Program Page.

        Below is a plot of the Senator coordinates. The R tokens are Republicans, the S tokens are Southern Democrats (11 states of the Confederacy plus Kentucky and Oklahoma), the D tokens are Northern (Non-Southern) Democrats, and the P is President Bush.



      7. NOM33.DAT


      8. NOM33.DAT is the coordinate output file for the roll call coordinates.
          
        1 6 0 69 4 7 20 0.770 0.542 -0.774 -0.715 0.084 0.035 0.303 0.053 0.088 0.501 2 8 0 53 0 6 42 0.865 0.857 -0.694 -0.331 0.284 0.123 0.264 0.134 0.090 0.201 3 15 0 53 1 3 43 0.897 0.909 -1.207 -0.327 0.024 0.266 0.600 0.068 0.098 1.484 4 16 0 31 6 3 59 0.813 0.735 0.878 -0.557 -0.186 0.148 0.383 0.047 0.100 0.288 5 17 0 51 2 7 39 0.826 0.780 -0.736 -0.373 0.013 -0.598 0.322 0.075 0.052 1.321 etc etc The first column is an integer counter The column in red is position of the roll call in the file
        The column in blue indicates if the roll call is constrained:
        0 = unconstrained
        1 = Zmid at the rim of the unit hypersphere
        If this Variable is 1, the standard errors in the last four columns are meaningless
        The cross classification is in Turquoise. For the First Vote:

        ACTUAL
        Yea Nay
        Yea 69 4
        PREDICTED or 89/100 = 89% correct
        Nay 7 20

        The column in Purple is the Geometric Mean Probability
        The column in Firebrick is the Proportional Reduction in Error (PRE)
        [PRE = (number voting in minority - classification errors)/number voting in minority]
        For the first vote this is (24 - 11)/24 = .542
        The columns in Coral are in order:
        Spread First Dimension
        Midpoint First Dimension
        Spread Second Dimension
        Midpoint Second Dimension
        The columns in Midnightblue are the corresponding Conditional Standard Errors
        etc etc
        453 628 1 78 6 4 10 0.801 0.375 -1.189 -0.813 -0.007 0.582 0.600 0.045 0.056 1.114 454 629 1 90 9 0 0 0.810 0.000 -0.690 -1.000 0.000 0.000 0.388 0.120 0.067 1.760 455 630 0 50 0 6 43 0.847 0.860 -0.708 -0.291 0.166 0.212 0.271 0.114 0.092 0.300 456 631 0 83 8 1 4 0.794 0.250 0.769 0.829 -0.004 0.524 0.484 0.089 0.073 1.856 457 632 0 86 8 0 3 0.801 0.273 0.780 0.858 0.029 0.006 0.536 0.087 0.093 2.377
      9. NOM36.DAT


      10. NOM36.DAT is another Legislator coordinate output file that is very similar to NOM31.DAT. The format of this output file is controlled by the user. The format statement is the 9th line of NOMSTART.DAT. In the case of the 107th Senate the format is:
        (1X,I4,36A1,1X,51F7.3)
        The "1X,I4" tells W-NOMINATE to write out a simple integer counter from 1 to the number of scaled legislators. The "36A1" is the number of characters on each line of the roll call data file before the roll calls begin. Most users only need to change the "36" wherever it appears in NOMSTART.DAT. The "1X,51F7.3" handles the coordinates that are written to the file. This file is identical to NOM31.DAT through the name of the legislator. NOM36.DAT looks like this:
            11079991099 0USA     200  BUSH          0.761  0.208  0.973  0.090  0.544  0.108
            21074970041 0ALABAMA 20001SESSIONS      0.641 -0.437  0.790 -0.109  0.453 -0.423
            31079465941 0ALABAMA 20001SHELBY        0.505 -0.158  0.665 -0.028  0.361 -0.332
            41071490781 0ALASKA  20001MURKOWSKI     0.632  0.464  0.813 -0.009  0.464  0.316
            51071210981 0ALASKA  20001STEVENS       0.518  0.307  0.692  0.006  0.375  0.413
                                          etc etc
                 The columns in red are the W-NOMINATE Coordinates -- Same as NOM31.DAT
        The columns in blue are the Heckman-Snyder Coordinates rotated to best match the W-NOMINATE Coordinates
        The columns in magenta are the Metric Scaling Coordinates rotated to best match the W-NOMINATE Coordinates
        etc etc
        981071492256 0WEST VI 10001ROCKEFELLER -0.741 -0.096 -0.843 -0.030 -0.483 -0.035 991074930925 0WISCONS 10001FEINGOLD -0.727 -0.686 -0.746 -0.302 -0.519 -0.855 1001071570325 0WISCONS 10001KOHL -0.581 0.155 -0.702 0.180 -0.375 0.140 1011074970668 0WYOMING 20001ENZI 0.777 0.397 0.846 -0.139 0.529 0.039 1021071563368 0WYOMING 20001THOMAS 0.842 0.313 0.877 -0.192 0.552 0.052

      Example Two: The 96th House.

      Control Card File for 96th House (NOMSTART.H96) (Rename this to NOMSTART.DAT)

      96th House Roll Call Data (HOU96KH.ORD)

      NOM21.DAT for the 96th House in two dimensions should look something like this:
      HOU96KH.ORD                           
      NOMINAL MULTIDIMENSIONAL UNFOLDING
      1276 1 4
      2 36
      15.0000 0.5000
      0.0250 20
      (36A1,3600I1)
      (1x,I4,36A1,1X,4i4,51f7.3)
      (1x,I4,36A1,1X,51f7.3)
      DATA 0 0
      CLEAN 0 0
      STARTS 35 35
      RECODE 35 0
      1 173 94 1.000 -1.000 1.000
      PERCENT CLASSIFIED= 84.034 AGGREGATE PRE= 0.464
      1 1 1 63 28 -153741.0310 0.6920 0.5634 0.4737
      1 2 2 71 8 -148005.8120 0.7016 0.9849
      1 3 0 91 20 -148009.2190 0.7015 0.5760 13.6244 0.5749
      PERCENT CLASSIFIED= 84.255 AGGREGATE PRE= 0.472
      1 4 1 111 20 -149193.2970 0.6996 0.9779 0.9350
      1 5 2 118 7 -146960.5000 0.7033 0.9972
      1 6 0 125 7 -146960.3120 0.7033 0.9618 13.5915 0.5879
      PERCENT CLASSIFIED= 84.282 AGGREGATE PRE= 0.473
      1 7 1 144 19 -148714.0940 0.7004 0.9939 0.9746
      1 8 2 150 6 -146809.5310 0.7036 0.9994
      1 9 0 162 12 -146801.5940 0.7036 0.9873 13.8950 0.5815
      PERCENT CLASSIFIED= 84.280 AGGREGATE PRE= 0.473
      1 10 1 181 19 -148866.5310 0.7001 0.9938 0.9626
      SAG IN RECOVERED LEGISLATOR COORDINATES
      1 96142691314NEW YOR 10001RICHMOND F 521 34 15 312 -1.000
      0 961303152 7MARYLAN 10001MITCHELL P 530 95 18 337 -1.000
      1 961301171 8CALIFOR 10001DELLUMS R 502 77 15 342 -1.000
      1 961073463 2IDAHO 20001HANSEN G 407 50 23 465 1.000
      0 961425244 7GEORGIA 10001MCDONALD L 404 90 32 508 1.000
      1 96142904922TEXAS 20001PAUL R 382 119 59 476 1.000
      CONSTRAINED UNCONSTRAINED
      OFF OPPOSITE OFF SAME
      29 165 873
      2 137 328 1.359 -1.230 1.000
      PERCENT CLASSIFIED= 84.235 AGGREGATE PRE= 0.471
      2 11 1 193 11 -136035.0780 0.7220 0.0015 0.0005
      2 12 2 203 10 -134958.9530 0.7238 0.0006
      2 13 -1 211 8 -135535.4530 0.7228 0.0002 13.8950 0.5071
      PERCENT CLASSIFIED= 85.875 AGGREGATE PRE= 0.526
      2 14 1 222 11 -135435.2030 0.7230 0.8735 0.7097
      2 15 2 228 6 -134953.3440 0.7238 0.9819
      2 16 -1 236 8 -135133.7660 0.7235 0.8729 13.8950 0.5152
      PERCENT CLASSIFIED= 85.840 AGGREGATE PRE= 0.525
      2 17 1 246 10 -135109.0160 0.7236 0.9260 0.8763
      2 18 2 252 6 -134867.3910 0.7240 0.9983
      2 19 -1 269 17 -135058.1720 0.7236 0.9442 13.8950 0.5232
      PERCENT CLASSIFIED= 85.826 AGGREGATE PRE= 0.524
      2 20 1 279 10 -135065.2030 0.7236 0.9884 0.9362
      SAG IN RECOVERED LEGISLATOR COORDINATES
      1 9614240 6 1VERMONT 20001JEFFORDS J 446 118 87 277 -1.000
      1 961422112 5NEW JER 20001FENWICK M 448 187 90 307 -0.997
      1 961405162 1COLORAD 10001SCHROEDER 429 158 97 300 -0.987
      1 96146744914TEXAS 10001WYATT J 598 66 88 226 0.991
      1 961078847 1NORTH C 10001JONES W 543 72 54 238 0.998
      1 961100041 4ALABAMA 10001BEVILL T 612 61 50 252 1.000
      CONSTRAINED UNCONSTRAINED
      OFF OPPOSITE OFF SAME
      93 129 845
      15.18.40.40.
      ELAPSED TIME OF JOB 15.23.20.51.
      The correct classification is 85.826% with an APRE of 0.524 and a geometric mean probability of .7236. The 96th (1979-80) House was part of the 3-Party period from the late 1930s to the mid-1980s when the Democratic Party was split into Northern and Southern blocs (see my book with Howard Rosenthal Congress: A Political-Economic History of Roll Call Voting, our paper D-NOMINATE After 10 Years: A Comparative Update to Congress: A Political-Economic History of Roll Call Voting [a version of this paper was published in Legislative Studies Quarterly, 26:5-29, 2001], and my monograph with Nolan McCarty and Howard Rosenthal Income Redistribution and the Realignment of American Politics, 1997, AEI Press. Congressional voting through this period was two dimensional.

      Below is a Skree Plot of the Eigenvalues of the Double-Centered agreement score matrix. In contrast to the Skree Plot for the 107th Senate, note that the "elbow" is not as sharp indicating the possible presence of a 2nd dimension:



      Below is a plot of the Representative coordinates. The R tokens are Republicans, the S tokens are Southern Democrats (11 states of the Confederacy plus Kentucky and Oklahoma), the D tokens are Northern (Non-Southern) Democrats, and the P is President Carter.





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