Measurement Theory: Fifth Assignment Page

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POLS 6386 MEASUREMENT THEORY
Fifth Assignment
Due 7 March 2001

The aim of this problem is to reproduce the classic results of Weisberg and Rusk in their 1970 APSR article "Dimensions of Candidate Evaluation." Below is the correlation matrix for the 1968 NES thermometer scores. These correlations are slightly different than the matrix in their article because respondents with missing data on other variables in the OLS68B.DAT file were discarded.


WALLACE       1  1.0000
HUMPHREY      2 -0.3108  1.0000
NIXON         3  0.0169 -0.2011  1.0000
MCCARTHY      4 -0.1283  0.2449  0.0779  1.0000
REAGAN        5  0.2054 -0.1824  0.4331  0.1073  1.0000
ROCKEFELLER   6 -0.1517  0.1614  0.1232  0.3304  0.1941  1.0000
LBJ           7 -0.2290  0.7251 -0.1248  0.1276 -0.1089  0.1621  1.0000
ROMNEY        8 -0.0568  0.1755  0.2419  0.3390  0.3120  0.3361  0.2386  1.0000
R.KENNEDY     9 -0.2427  0.5658 -0.1629  0.3371 -0.1193  0.2323  0.5035  0.2582  1.0000
MUSKIE       10 -0.2546  0.5791 -0.1093  0.2955 -0.0717  0.2759  0.4676  0.2537  0.4349  1.0000
AGNEW        11  0.1514 -0.1168  0.6153  0.1299  0.4522  0.1323 -0.0492  0.3432 -0.0302 -0.0374  1.0000
LEMAY        12  0.6731 -0.2144  0.1604 -0.0203  0.2822 -0.0477 -0.0887  0.1077 -0.1269 -0.1643  0.3328  1.0000

Run the correlation matrix through KYST in one, two, and three dimensions and report the STRESS values. Plot the one and two dimensional solutions using SPSS.

In this problem we are going to use my optimal classification program -- PERFL_2006 -- to study dimensionality. Download the 90^th Senate roll call matrix from my website and place it in the same directory as PERFL_2006 and PERFSTRT_2006.DAT.

90^th Senate Roll Call Matrix
1. First, run PERFL_2006 in one dimension. Your PERFSTRT_2006.DAT file should look like this:
```
SEN90KH.ORD
NON-PARAMETRIC MULTIDIMENSIONAL UNFOLDING
    1  596   10   19    1    4   20 0.025    3
(3X,9A1,7X,4A1,2X,6A1,5X,1600I1)
(I5,1X,19A1,2I5,50F8.3)
```
  The "1" in the 3^rd row is the number of dimensions. In the output file PERF23.DAT you will find the eigenvalues of the double-centered squared distance matrix formed from the agreement scores. Below is what these look like for the 100^th Senate. The column headed by "6.1684" are the eigenvalues. Graph these in the same fashion using Excel as you did for homework 3.
```
 PERFORMANCE INDEX EIGENVALUE/VECTOR ROUTINE=    1  102    0     0
 PERFORMANCE INDEX EIGENVALUE/VECTOR ROUTINE=    1  102    0     0
   1    6.1684   50.0408   50.0408    6.3530   35.4969   35.4969
   2    0.7269    5.8968   55.9376    1.1253    6.2875   41.7844
   3    0.4319    3.5042   59.4418    0.6667    3.7250   45.5093
   4    0.3564    2.8912   62.3330    0.4909    2.7431   48.2524
   5    0.2792    2.2650   64.5980    0.4092    2.2866   50.5390
   6    0.2445    1.9831   66.5812    0.3824    2.1369   52.6759
   7    0.2015    1.6349   68.2160    0.3442    1.9233   54.5991
   8    0.1705    1.3833   69.5994    0.3012    1.6827   56.2819
   9    0.1254    1.0173   70.6166    0.2887    1.6131   57.8950
  10    0.1151    0.9341   71.5507    0.2622    1.4650   59.3599
```
2. Use Excel to graph the estimated rank ordering of the Senators against the proportion of roll call choices that are correctly classified. These are the last two columns of PERF25.DAT (see the example in homework 3). The graph for the 100^th Senate is below. Save the one dimensional output files!

Run PERFL_2006 in two dimensions. In PERFSTRT_2006.DAT simply change the "1" to "2" and it will estimate two dimensions. PERF25.DAT contains the two dimensional coordinates for the legislators at the top of the file and the roll call coordinates below. For example, here are the first few lines of PERF25.DAT for the 100^th Senate:
```
  
 27 FEBRUARY  2001  13.27.23.43.
    1 9990799 0 200REAGAN   10  122   0.918   0.009   0.813   0.560
    2 1465941 0 100SHELBY   52  625   0.917   0.002  -0.012  -0.705
    3 1470541 0 100HEFLIN   47  628   0.925   0.002   0.054  -0.822
    4 1490781 0 200MURKOW   69  578   0.881   0.005   0.345   0.132
    5 1210981 0 200STEVEN   90  600   0.850   0.002   0.225   0.204
    6 1503961 0 200MCCAIN   78  598   0.870   0.010   0.387   0.101
    7 1450261 0 100DECONC   92  620   0.852   0.002  -0.110  -0.448
    8 1079142 0 100PRYOR,   42  603   0.930   0.002  -0.255  -0.185
    9 1430042 0 100BUMPER   55  605   0.909   0.003  -0.283  -0.146
   10 1491571 0 200WILSON   96  583   0.835   0.002   0.324   0.232
                          etc.   etc.   
```
The column headed by "0.918" is the proportion correctly classified. Note that this is computed from the two columns just preceding it:
([122-10]/122=0.918).

Use Epsilon to place the proportion correctly classified in two dimensions into the one dimensional output file. Graph the difference between the two and one dimensional correct classifications against the rank ordering in one dimension and interpret the results. Who are the Senators that get the biggest increase in fit from adding a 2^nd dimension and is there some relationship between their spatial location and this increase in fit?
The last two columns in PERF25.DAT are the estimated two dimensional coordinates for the Senators. Make a two dimensional plot of the Senators using SPSS.

Use HOUSYM3 to get an agreement score matrix for the 90^th Senate. Run this agreement score through KYST. Report the one, two, and three dimensional STRESS values and use Excel to compute the correlations between the two dimensional coordinates from KYST with those from PERFL_2006. Report the correlations one dimension at a time for each dimensionality using the format below:



      One Dimension Scalings
          PERF 1d    KYST 1d         WNOM 1d
------------------------------------------------
PERF 1d  1		
KYST 1d	-0.92682	1	
WNOM 1d	-0.95408	0.990908	1


      Two Dimensional Scalings
 	1 PERF 2d	1 KYST 2d	1 WNOM 2d
-------------------------------------------------
1 PERF 2d	1		
1 KYST 2d	0.99034	1	
1 WNOM 2d	1	0.99034 	1

 	2 PERF 2d	2 KYST 2d	2 WNOM 2d
-------------------------------------------------
2 PERF 2d	1		
2 KYST 2d	0.592688	1	
2 WNOM 2d	1	0.592688	1

              etc.