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W-NOMINATE Parametric Bootstrap Program


Jeff Lewis and Keith Poole


(Updated 24 October 2006)


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:


Please read the documentation on how to use the W-NOMINATE program on the W-NOMINATE page before continuing below. The Parametric Bootstrap program is a slightly modified version of W-NOMINATE and the input and output files are, with two minor exceptions, exactly the same. The documentation below concentrates on the two differences and complements the discussion on the W-NOMINATE page.


Examples

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


  1. Example One: The 107th Senate.
  2. To see how Parametric Bootstrap W-NOMINATE works, download the program (WNOMJLEWIS_NO_OC.EXE), the "control card" file (NOMSTART_JLEWIS.DAT), and the 107th Senate Roll Call data files below:

    W-NOMINATE Parametric Bootstrap Scaling Program Executable (Compiled For WINTEL Machines -- WNOMJLEWIS_NO_OC.EXE)

    W-NOMINATE Parametric Bootstrap Program Source Code (FORTRAN -- WNOMJLEWIS_NO_OC.FOR)

    Control Card File (NOMSTART_JLEWIS.DAT)

    107th Senate Roll Call Data (SEN107KH.ORD)

    Plot_Boostrap_S107.R -- R Program to plot legislator output (see figure below)

    and place them in the same folder on a WINTEL machine. NOMSTART_JLEWIS.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 1001            Number Dimensions, Number Characters to Read From Header, Number of Bootstrap Trials
     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,I4,36A1,80F10.4)       Format for W-NOMINATE, H-S, and Metric Coordinate File -- NOM36.DAT -- 
                               and FORT.26 -- The Parametric Bootstrap Legislator Coordinates and Standard Errors
    
    At the command prompt type:

    WNOMJLEWIS_NO_OC

    and you will get six output files: NOM21.DAT, NOM23.DAT, NOM31.DAT, NOM33.DAT, and NOM36.DAT, and FORT.26.

    1. NOM21.DAT, NOM23.DAT, NOM31.DAT, NOM33.DAT, and NOM36.DAT

      The format of these files is explained in detail on the W-NOMINATE Program page. However, each file has all the bootstrap runs stacked upon one another. For example, the NOM21.DAT file as the initial output exactly like W-NOMINATE. This output is then repeated for each of the bootstrap trials.

      For example, for the legislator coordinate output file -- NOM31.DAT -- if there are 102 Senators and 1001 bootstrap trials, then there will be 102,102 lines in the file.

    2. FORT.26

      FORT.26 has the W-NOMINATE legislator coordinates and the bootstrapped standard errors. If the number of trials is set to 1001, then the number of bootstrap draws is 1000 (or always one less than the number). The extra "1" is the inital W-NOMINATE scaling to obtain the choice probabilities for the parametric bootstrap trials (see our Political Analysis articles for the details).

      The file with the bootstrapped standard errors for the 107th Senate looks something like this (these are random draws so your results may be slightly different):
      
         1 1079991099 0USA     20000BUSH           0.7605    0.1849    0.8266    0.1409    0.1312    0.3363    1.0000   -0.0440   -0.0440    1.0000
         2 1074970041 0ALABAMA 20001SESSIONS       0.6413   -0.4361    0.6926   -0.4954    0.0758    0.1152    1.0000    0.0533    0.0533    1.0000
         3 1079465941 0ALABAMA 20001SHELBY         0.5048   -0.1749    0.5646   -0.2032    0.0784    0.1246    1.0000    0.0532    0.0532    1.0000
         4 1071490781 0ALASKA  20001MURKOWSKI      0.6319    0.4609    0.6786    0.4407    0.0707    0.1546    1.0000    0.0646    0.0646    1.0000
         5 1071210981 0ALASKA  20001STEVENS        0.5176    0.3038    0.5899    0.3249    0.0887    0.1598    1.0000    0.0395    0.0395    1.0000
                                        etc 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 columns in Turquoise are the W-NOMINATE Coordinates. 
               The columns in Purple are the Mean Coordinate Values For the 1000 Trials
               The columns in Green are the Parametric Bootstrapped Standard Errors
               The last four columns are the Pearson Correlation Matrix between the two dimensions.  The column
                 in Deeppink is the Pearson Correlation Between the First and
                        Second Dimension Coordinate estimates across the 1000 Bootstrap Trials
                        This can be used to obtain the corresponding covariance term
                                        etc etc etc
        98 1071492256 0WEST VI 10001ROCKEFELLER   -0.7407   -0.1129   -0.7197   -0.1616    0.0551    0.1440    1.0000   -0.0500   -0.0500    1.0000
        99 1074930925 0WISCONS 10001FEINGOLD      -0.7206   -0.6933   -0.7128   -0.6586    0.0497    0.0739    1.0000   -0.3755   -0.3755    1.0000
       100 1071570325 0WISCONS 10001KOHL          -0.5807    0.1534   -0.5395    0.0984    0.0638    0.1491    1.0000    0.0402    0.0402    1.0000
       101 1074970668 0WYOMING 20001ENZI           0.7769    0.3826    0.7873    0.3420    0.0529    0.1471    1.0000    0.1047    0.1047    1.0000
       102 1071563368 0WYOMING 20001THOMAS         0.8422    0.3621    0.8374    0.3115    0.0555    0.1420    1.0000    0.0080    0.0080    1.0000
    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. The vertical and horizontal lines through each senator's ideal point show the 95 percent confidence intervals for each coordinate of that senator's position. Confidence ellipses are shown for senators whose first-dimension and second-dimension coordinates have a correlation coefficient greater than 0.15 in absolute value.



  3. Example Two: The 96th House.
  4. Control Card File for 96th House (NOMSTART_JLEWIS.H96) (Rename this to NOMSTART_JLEWIS.DAT)

    96th House Roll Call Data (HOU96KH.ORD)

    Plot_Boostrap_H96.R -- R Program to plot legislator output (see figure below)

    NOMSTART_JLEWIS.H96 looks like this:
    
    HOU96KH.ORD                Data File Name -- can include path statement
     NOMINAL MULTIDIMENSIONAL UNFOLDING OF 96TH HOUSE   Title of Run
     1276    1    4            Number RCs, Left on 1st, Up on 2nd
        2   36 1001            Number Dimensions, Number Characters to Read From Header, Number of Bootstrap Trials
     15.0000  0.5000           Starting Values for BETA and WEIGHT
      0.0250   20              RC Min. Cutoff, Number RCs for Legislator
    (36A1,15000I1)             Format for Roll Call File
    (1x,I4,36A1,1X,4i4,51f7.3) Format for Legislator Coordinate File -- NOM31.DAT
    (I4,1X,36A1,80F10.4)       Format for W-NOMINATE, H-S, and Metric Coordinate File -- NOM36.DAT -- 
                               and FORT.26 -- The Parametric Bootstrap Legislator Coordinates and Standard Errors
    
    The file with the bootstrapped standard errors for the 96th House looks something like this (these are random draws so your results may be slightly different):
    
       1  969990699 0USA     10000CARTER        -0.5675    0.3060   -0.5532    0.2532    0.0613    0.1204    1.0000    0.0202    0.0202    1.0000
       2  961072141 1ALABAMA 20001EDWARDS J      0.2690    0.1142    0.2553    0.1208    0.0352    0.0650    1.0000   -0.0539   -0.0539    1.0000
       3  961071741 2ALABAMA 20001DICKINSON      0.5833    0.2121    0.5709    0.2402    0.0376    0.0787    1.0000    0.0011    0.0011    1.0000
       4  961103741 3ALABAMA 10001NICHOLS        0.1722    0.8014    0.1331    0.8823    0.0536    0.1140    1.0000    0.2858    0.2858    1.0000
       5  961100041 4ALABAMA 10001BEVILL  T     -0.0197    0.9998   -0.0387    0.9896    0.0404    0.0288    1.0000    0.0220    0.0220    1.0000
                                      etc 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 columns in Turquoise are the W-NOMINATE Coordinates. 
             The columns in Purple are the Mean Coordinate Values For the 1000 Trials
             The columns in Green are the Parametric Bootstrapped Standard Errors
             The last four columns are the Pearson Correlation Matrix between the two dimensions.  The column
               in Deeppink is the Pearson Correlation Between the First and
                      Second Dimension Coordinate estimates across the 1000 Bootstrap Trials
                      This can be used to obtain the corresponding covariance term
                                      etc etc etc
     436  961467525 6WISCONS 20002PETRI          0.3170   -0.7953    0.3135   -0.8778    0.0364    0.1007    1.0000   -0.2289   -0.2289    1.0000
     437  961203625 7WISCONS 10001OBEY  D       -0.6867   -0.3093   -0.7381   -0.3129    0.0691    0.0635    1.0000   -0.0703   -0.0703    1.0000
     438  961465525 8WISCONS 20001ROTH  T        0.5172   -0.3872    0.5164   -0.4095    0.0351    0.0735    1.0000   -0.0470   -0.0470    1.0000
     439  961465725 9WISCONS 20001SENSENBRENN    0.6537   -0.6186    0.6562   -0.6479    0.0394    0.0712    1.0000   -0.1445   -0.1445    1.0000
     440  961461168 1WYOMING 20001CHENEY  R      0.5594   -0.1952    0.5585   -0.1939    0.0352    0.0710    1.0000   -0.0249   -0.0249    1.0000
Below is a plot of the member 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. The vertical and horizontal lines through each representative's ideal point show the 95 percent confidence intervals for each coordinate of that representative's position. Confidence ellipses are shown for representatives whose first-dimension and second-dimension coordinates have a correlation coefficient greater than 0.30 in absolute value.