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
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:
and
0000200036012210001000018
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)
WNOM9707
and you will get five output files: NOM21.DAT, NOM23.DAT, NOM31.DAT, NOM33.DAT, and NOM36.DAT
- NOM21.DAT
- NOM23.DAT
- NOM31.DAT
- NOM33.DAT
- NOM36.DAT
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.
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 SENATEThis 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.
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
PERFORMANCE INDEX EIGENVALUE/VECTOR ROUTINE= 2 102 0 0The 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.
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
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 5151The 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.
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
NUMBER LEGISLATORS= 102 FURTHEST LEFT= -0.6087 FURTHEST RIGHT= 0.6125After each roll call phase, the cross-tabulation of the classifications is reported.
POSITIONS: LEFT= 47 RIGHT= 6
TOTAL VOTES PREDICTED FOR 457 ROLL-CALLSAfter each legislator phase, the cross-tabulation of the classifications is reported.
ACTUAL
YEA NAY
YEA 24229 2781
NAY 2084 15678
TOTAL VOTES PREDICTED FOR 102 LEGISLATORSNumerous 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.
ACTUAL
YEA NAY
YEA 24182 2728
NAY 2131 15731
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:
"Measuring Bias and Uncertainty in Ideal Point
Estimates via the Parametric Bootstrap" by
Jeffrey B. Lewis and
Keith T. Poole. 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.
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
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.ORDThe 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.
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.
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.
