**
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
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*APSR***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**.

- Run the correlation matrix through
- 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

- First, run
**PERFL_2006**in one dimension. Your**PERFSTRT_2006.DAT**file should look like this:

The "1" in the 3**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)**^{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** - 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!**

- First, run

- 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:

The column headed by "0.918" is the proportion correctly classified. Note that this is computed from the two columns just preceding it:**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.**

([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.**