POLS 6386 MEASUREMENT THEORY
Ninth Assignment
Due 1 April 2003


  1. The aim of this homework is to continue our analysis of the 1968 and 2000 two-dimensional thermometer scalings in question 3 of homework 7 and question 2 of homework 8 respectively. Recall that the first 20 lines of the coordinate output file for the 1968 scaling were:
    
     WALLACE          1.2646    0.5154  217.4823    0.5541 1242.0000
     HUMPHREY        -0.5559    0.3738  114.7892    0.6968 1252.0000
     NIXON            0.1480   -0.5415  123.2209    0.5319 1250.0000
     MCCARTHY        -0.6251   -0.4938  151.8926    0.3854 1204.0000
     REAGAN           0.3080   -0.8895  131.8091    0.4380 1212.0000
     ROCKEFELLER     -0.5579   -0.5995  148.1413    0.3724 1229.0000
     LBJ             -0.5223    0.4905  147.0334    0.5573 1253.0000
     ROMNEY          -0.4736   -0.7866  111.3147    0.3434 1167.0000
     R.KENNEDY       -0.4245    0.2351  148.8571    0.5418 1242.0000
     MUSKIE          -0.6611    0.1660  126.0836    0.4862 1177.0000
     AGNEW            0.2341   -0.8706  114.1418    0.4675 1180.0000
     LEMAY            1.1901    0.4267  174.3242    0.4601 1188.0000
     1681            -0.0285    0.2555    0.7918    0.6824   12.0000
     1124            -0.1768    0.2692    1.4788    0.6992   12.0000
       78             0.5707   -0.1514    3.5611    0.2141   12.0000
      553             0.1376    0.1064    0.1597    0.7047    9.0000
        7             0.2542    0.1235    1.2634    0.0116   12.0000
      412             0.2781    0.0867    0.1024    0.6197   12.0000
      631             0.5017    0.1088    1.1196    0.0742   12.0000
     1316             0.2175   -0.5842    1.1568    0.8577   12.0000
                           etc etc etc
                           etc etc etc
    
    And the first 20 lines of the coordinate output file for the 2000 election were:
    
     CLINTON         -0.7879   -0.0317  153.1404    0.7198 1477.0000
     GORE            -0.7133   -0.1701  112.1776    0.7061 1468.0000
     BUSH             0.8234   -0.2492  149.4325    0.5889 1458.0000
     BUCHANAN         0.4576    1.0536  178.0645    0.3114 1246.0000
     NADER           -0.2737    0.7599  174.6307    0.2645 1094.0000
     MCCAIN           0.2850   -0.6498  122.5794    0.3691 1182.0000
     BRADLEY         -0.0780   -0.7509  106.1498    0.3689 1088.0000
     LIEBERMAN       -0.3428   -0.6394  107.1314    0.4758 1096.0000
     CHENEY           0.7002   -0.4687  107.9753    0.5099 1147.0000
     HILLARY         -0.8617    0.0625  203.7540    0.6459 1466.0000
     DEMPARTY        -0.6788   -0.1713  112.8208    0.6861 1453.0000
     REPUBPARTY       0.8235   -0.3286  142.8395    0.5546 1447.0000
     REFORMPTY        0.1644    1.0398  132.9094    0.3140 1128.0000
     PARTIES          0.1949   -0.7946  158.0865    0.2290 1413.0000
        1             0.3666   -0.0534    1.2943    0.3584   12.0000
        2            -0.2740    0.6767    2.5447    0.5465   12.0000
        4             0.0094    0.0645    0.8008    0.0000   14.0000
        5             0.5073   -0.0010    1.3888    0.6249   14.0000
        7             0.2719    0.0294    0.3600    0.5458   14.0000
        8            -0.6582   -0.2931    1.8168    0.7683   14.0000
                                 etc etc etc
                                 etc etc etc
    1. Make a two-dimensional plot of the 1968 coordinates showing both the 12 politicians and the voters. Interpret the plot -- does in make sense? Why? Why not? Limit your answer to no more than two paragraphs.

    2. Make a two-dimensional plot of the 2000 coordinates showing both the 14 politicians/parties and the voters. Interpret the plot -- does in make sense? Why? Why not? Limit your answer to no more than two paragraphs.

  2. In this problem we are going to use my Optimal Classification (OC) and quadratic-normal (QN) programs to analyze the thermometer scores as roll call votes! Feeling thermometer data is technically not binary choice however, it can be interpreted as rank order data and that can be converted to binary choice. For example, using the 1968 Thermometers, suppose a respondent gave ratings of 30, 80, and 55 to Wallace (W), Humphrey (H), and Nixon (N) respectively. With respect to these three candidates, the rank order is H > N > W. Now suppose a second respondent gave ratings of 45, 65, and 95, respectively, for a rank order of N > H > W. These rank orders can be converted to binary choice data by treating each pair of candidates as a roll call vote. For example, consider the pair of Wallace and Humphrey. If a respondent rates Wallace higher than Humphrey make that Yea, and if Humphrey is rated higher than Wallace, make that Nay. Doing this consistently across respondents creates a roll call vote where the outcomes are Wallace and Humphrey, respectively. Doing this for every unique pair of candidates creates the same number of roll call votes. For 1968 this produces (12*11)/2 = 66 roll calls and in 2000 this produces (14*13)/2 = 91 roll calls. This process is discussed in more detail in the assigned reading Non-Parametric Analysis of Binary Choice Data.

    We are going to analyze these "roll call" matrices with the Optimal Classification (OC) and quadratic-normal (QN) programs. Download the programs, "control card" files, and two data files below:

    Maximum Classification Scaling Program (PERFL)

    Quadratic-Normal Scaling Program (Updated QUADMD00 -- Use this version!!)

    1968 Thermometer-Roll-Call File (VOTE_THERM_1968.ORD, 1335 records)

    2000 Thermometer-Roll-Call File (VOTE_THERM_2000.ORD, 1463 records)

    The Variables in the 1968 and 2000 Files are:
    
    idno          Respondent ID Number
    partyid       strength of party id -- 0 to 6
    income        raw income category
    race          0 = white, 1 = black, 2 and above, other
    sex           0 = male, 1 = female
    south         0 = north, 1 = south
    education     1 = HS, 2 = SC, 3 = College
    age           age in years
    married       0 = Not Married, 1 = Married
    voted         1 = Voted, 5 = Not Voted
    ---------------------------------------
    voted for 1968 1 = Humphrey, 2 = Nixon, 3 = Wallace
    66 "roll calls" -- wallace-humphrey, wallace-nixon,  ... ,
    muskie-agnew, muskie-lemay, agnew-lemay.  Yea = first
    thermometer of a pair is higher than the second; Nay = first
    thermometer of a pair lower than the second; if tied, treated
    as non-voting
    ---------------------------------------
    voted for 2000 1 = Gore, 2 = Bush, 3 = Other
    91 "roll calls" -- clinton-gore, clinton-bush,  ... ,
    repubpparty-reformpty, repubparty-parties, reformpty-parties.
    Yea = first thermometer of a pair is higher than the second;
    Nay = first thermometer of a pair lower than the second; if tied,
    treated as non-voting
    1. Run the 1968 data through PERFL (be sure to rename PERFSTRT.1968 to PERFSTRT.DAT!). Your PERF21.DAT for the 1968 data should look something this:
       22 MARCH     2003  17.02.59.18.
       RANDOM NUMBER SEED     65400
      VOTE_THERM_1968.ORD                                    
      NON-PARAMETRIC MULTIDIMENSIONAL UNFOLDING OF THERMOMETER DATA   
          2   66   20   40    1
      (40A1,3900I1)                                                   
      (I5,1X,40A1,2I5,50F8.3)                                         
       ******************************************************************************
        1 ROLL CALLS   2    9923   65406  0.15171  0.84829  0.48009           0.00000
          LEGISLATORS  2    7419   65406  0.11343  0.88657  0.61129  0.00000
        2 ROLL CALLS   2    7412   65406  0.11332  0.88668  0.61165           0.99993
          LEGISLATORS  2    7347   65406  0.11233  0.88767  0.61506  0.99009
        3 ROLL CALLS   2    7345   65406  0.11230  0.88770  0.61516           0.99998
          LEGISLATORS  2    7308   65406  0.11173  0.88827  0.61710  0.99161
        4 ROLL CALLS   2    7304   65406  0.11167  0.88833  0.61731           0.99996
          LEGISLATORS  2    7279   65406  0.11129  0.88871  0.61862  0.99528
        5 ROLL CALLS   2    7276   65406  0.11124  0.88876  0.61878           0.99999
          LEGISLATORS  2    7265   65406  0.11108  0.88892  0.61935  0.99521
        6 ROLL CALLS   2    7263   65406  0.11104  0.88896  0.61946           0.99999
          LEGISLATORS  2    7264   65406  0.11106  0.88894  0.61941  0.99734
        7 ROLL CALLS   2    7262   65406  0.11103  0.88897  0.61951           0.99999
          LEGISLATORS  2    7253   65406  0.11089  0.88911  0.61998  0.99750
        8 ROLL CALLS   2    7250   65406  0.11085  0.88915  0.62014           0.99999
          LEGISLATORS  2    7252   65406  0.11088  0.88912  0.62004  0.99801
        9 ROLL CALLS   2    7248   65406  0.11082  0.88918  0.62025           1.00000
          LEGISLATORS  2    7248   65406  0.11082  0.88918  0.62025  0.99811
       10 ROLL CALLS   2    7243   65406  0.11074  0.88926  0.62051           0.99999
          LEGISLATORS  2    7253   65406  0.11089  0.88911  0.61998  0.99745
       11 ROLL CALLS   2    7245   65406  0.11077  0.88923  0.62040           1.00000
          LEGISLATORS  2    7243   65406  0.11074  0.88926  0.62051  0.99787
       12 ROLL CALLS   2    7236   65406  0.11063  0.88937  0.62087           1.00000
          LEGISLATORS  2    7245   65406  0.11077  0.88923  0.62040  0.99743
       13 ROLL CALLS   2    7239   65406  0.11068  0.88932  0.62072           1.00000
          LEGISLATORS  2    7237   65406  0.11065  0.88935  0.62082  0.99712
       14 ROLL CALLS   2    7233   65406  0.11059  0.88941  0.62103           1.00000
          LEGISLATORS  2    7235   65406  0.11062  0.88938  0.62093  0.99859
       15 ROLL CALLS   2    7232   65406  0.11057  0.88943  0.62108           1.00000
          LEGISLATORS  2    7239   65406  0.11068  0.88932  0.62072  0.99763
       16 ROLL CALLS   2    7237   65406  0.11065  0.88935  0.62082           1.00000
          LEGISLATORS  2    7237   65406  0.11065  0.88935  0.62082  0.99795
       17 ROLL CALLS   2    7233   65406  0.11059  0.88941  0.62103           1.00000
          LEGISLATORS  2    7234   65406  0.11060  0.88940  0.62098  0.99795
       18 ROLL CALLS   2    7232   65406  0.11057  0.88943  0.62108           0.99999
          LEGISLATORS  2    7237   65406  0.11065  0.88935  0.62082  0.99730
       19 ROLL CALLS   2    7233   65406  0.11059  0.88941  0.62103           1.00000
          LEGISLATORS  2    7229   65406  0.11053  0.88947  0.62124  0.99833
       20 ROLL CALLS   2    7224   65406  0.11045  0.88955  0.62150           0.99970
          LEGISLATORS  2    7204   65406  0.11014  0.88986  0.62255  0.99259
       MEAN VOLUME LEG.   0.1519   0.1530 150.9721 153.1920   0.2291
       MACHINE PREC.   2    7159   65406   0.10945   0.89055
                            17.02.59.21.
       ELAPSED TIME OF JOB  17.10.06.59.
      
      Turn in a copy of PERF21.DAT.

    2. The file PERF25.DAT contains the coordinates for the respondents and the cutting lines for the Thermometer "roll calls". The two are stacked upon each other. The file for the 1968 data should look something like this:
       22 MARCH     2003  17.02.59.18.
          1         1  6 14  0  0  0  3 28  0  1  2     3   55   0.945   0.018  -0.131   0.362
          2         2  1 15  0  0  0  3 25  0  1  1     2   60   0.967   0.314   0.404   0.558
          3         4  3 13  0  0  1  1 25  1  5  0    17   54   0.685   0.265   0.210   0.010
          4         5  5 21  0  0  1  1 42  1  5  0     3   42   0.929   0.111  -0.534   0.717
          5         7  1 10  0  1  1  1 83  0  1  3     8   49   0.837   0.091  -0.101  -0.369
          6         8  4 20  0  1  1  1 54  1  5  0     1   30   0.967   0.125   0.018  -0.471
          7         9  4 13  0  1  0  1 69  1  1  2    11   56   0.804   0.014  -0.099  -0.147
          8        10  0 20  0  0  1  1 55  1  1  1    10   59   0.831   0.033   0.110   0.034
          9        11  4 11  0  0  1  2 50  1  5  0    12   57   0.789   0.026   0.224   0.270
         10        16  3 14  0  0  0  2 23  1  5  0     7   57   0.877   0.315   0.344   0.080
                                            etc etc etc
                                            etc etc etc
       1245      2100  0 20  1  1  0  1 35  0  1  1     1   58   0.983   0.252   0.441  -0.147
       1246      2103  2 11  1  1  0  1 52  0  5  0     3   48   0.938   0.111   0.179  -0.270
       1247      2104  0 23  1  1  0  1 43  0  1  1     2   57   0.965   0.015   0.421   0.605
       1248      2105  0 20  1  1  1  1 31  1  1  1     1   51   0.980   0.343   0.361   0.114
       1249      2106  0 14  1  1  1  1 44  1  1  1     3   61   0.951   0.461   0.563  -0.091
       1250      2110  0 13  1  1  1  1 32  1  5  0     0   52   1.000   0.273   0.142   0.000
       1251      2113  0 21  1  0  1  2 32  1  1  1     3   61   0.951   0.283   0.144  -0.074
       1252      2114  1 20  1  0  0  1 25  0  1  1     1   58   0.983   0.501   0.286   0.264
       1253      2901  0 13  1  1  0  1 30  0  1  1     2   61   0.967   0.332   0.447   0.052
       1254      2904  1 20  1  1  1  1 22  1  5  0     2   49   0.959   0.501   0.318   0.012
          1    1 240 942  21 996 258  0.913  0.171 -0.901 -0.433
          2    2 1751003  34 1941060  0.806 -0.256  0.375  0.927
          3    3 258 849  34 930 324  0.868  0.109 -0.645 -0.764
          4    4 246 830  43 326 928  0.825 -0.108  0.368  0.930
          5    5 258 860  32 273 981  0.876 -0.165  0.679  0.734
                               etc etc etc
         62   62 826 243 111 2181036  0.543 -0.238  0.954 -0.300
         63   63 973 152  46 1341120  0.697 -0.326  0.965  0.263
         64   64 566 246  98 534 720  0.602 -0.033  0.938 -0.347
         65   65 806 157  531100 154  0.662  0.297 -0.912 -0.410
         66   66 707 173  65 2101044  0.624 -0.228  0.312  0.950
      Remove the last 66 lines from PERF25.DAT (be sure to save them!) and make plots using R of the Humphrey Voters, Nixon Voters, and Wallace Voters. These plots should look like those you did for question 3 of homework 7.

    3. Run the 2000 data through PERFL (be sure to rename PERFSTRT.2000 to PERFSTRT.DAT!). Turn in a copy of the PERF21.DAT file.

    4. Make plots using R of the Gore Voters and Bush Voters. These plots should look like those you did for question 2 of homework 8.

    5. Run the quadratic-normal (QN) scaling program on the 1968 data. Your QUAD0021.DAT file should look something like this:
       23 MARCH     2003  15.42.21.90.
      \OLDTIME\VOTE_THERM_1968.ORD                                    
      QUADRATIC-NORMAL MULTIDIMENSIONAL UNFOLDING                     
          2   66   10   40    1
      (40A1,3600I1)                                                   
      (I5,1X,40A1,2I5,50F8.3)                                         
      (I5,1X,40A1,2I5,F8.3,F12.3,50F8.3)                              
       ******************************************************************************
       RC  CLASSIFICATION ERROR    1  2    9791   65406   0.14970   0.85030
       LEG CLASSIFICATION ERROR    1  2    7300   65406   0.11161   0.88839
       RC  CLASSIFICATION ERROR    2  2    7293   65406   0.11150   0.88850
       LEG CLASSIFICATION ERROR    2  2    7177   65406   0.10973   0.89027
       RC  CLASSIFICATION ERROR    3  2    7175   65406   0.10970   0.89030
       LEG CLASSIFICATION ERROR    3  2    7155   65406   0.10939   0.89061
       RC  CLASSIFICATION ERROR    4  2    7153   65406   0.10936   0.89064
       LEG CLASSIFICATION ERROR    4  2    7145   65406   0.10924   0.89076
       RC  CLASSIFICATION ERROR    5  2    7141   65406   0.10918   0.89082
       LEG CLASSIFICATION ERROR    5  2    7129   65406   0.10900   0.89100
       LOG-LIKELIHOOD 2D/SIGMA PHASE              65406    -26107.14650  0.67089
       LOG-LIKELIHOOD SIGMAi PHASE                65406    -21123.06640  0.72401
       LOG-LIKELIHOOD 2D/SIGMA PHASE              65406    -20819.13480  0.72738
       LOG-LIKELIHOOD SIGMAi PHASE                65406    -20727.87300  0.72840
       LOG-LIKELIHOOD & CLASS LEG PHASE    9170   65406    -19280.11910  0.74470
       LOG-LIKELIHOOD & CLASS RC PHASE     9152   65406    -18870.81450  0.74937
       LOG-L & CLASS N-VECTOR PHASE        8937   65406    -18560.91990  0.75293
       LOG-LIKELIHOOD 2D/SIGMA PHASE              65406    -18421.78520  0.75454
       LOG-LIKELIHOOD SIGMAi PHASE                65406    -18103.96290  0.75821
       LOG-LIKELIHOOD 2D/SIGMA PHASE              65406    -18088.63480  0.75839
       LOG-LIKELIHOOD SIGMAi PHASE                65406    -18083.92380  0.75844
       LOG-LIKELIHOOD & CLASS LEG PHASE    8895   65406    -17836.66990  0.76132
       LOG-LIKELIHOOD & CLASS RC PHASE     8901   65406    -17800.70700  0.76173
       LOG-L & CLASS N-VECTOR PHASE        8917   65406    -17753.82620  0.76228
       LOG-LIKELIHOOD 2D/SIGMA PHASE              65406    -17718.52150  0.76269
       LOG-LIKELIHOOD SIGMAi PHASE                65406    -17637.39260  0.76364
       LOG-LIKELIHOOD 2D/SIGMA PHASE              65406    -17633.59570  0.76368
       LOG-LIKELIHOOD SIGMAi PHASE                65406    -17631.32030  0.76371
       LOG-LIKELIHOOD & CLASS LEG PHASE    8902   65406    -17548.90040  0.76467
       LOG-LIKELIHOOD & CLASS RC PHASE     8904   65406    -17540.12300  0.76478
       LOG-L & CLASS N-VECTOR PHASE        8876   65406    -17524.01760  0.76496
       CLASSIFICATION CHECK AT CONVERGENCE
        56530   8876  65406  19086  0.8643  0.5349
       LEGS: Rs BTWN STARTS & ESTIMATES    1 1254  0.9342  0.8855
       LEGS: Rs BTWN STARTS & ESTIMATES    2 1254  0.8158  0.8232
                            15.42.21.90.
       ELAPSED TIME OF JOB  15.47.46.67.
      Turn in a copy of this file.

    6. The 1968 respondent coordinates are in the output file QUAD0048.DAT. The first ten lines look like this:
      
          1         1  6 14  0  0  0  3 28  0  1  2    52    3   0.945      -6.545   0.888  -0.049   0.439   0.276   0.054   0.130
          2         2  1 15  0  0  0  3 25  0  1  1    60    0   1.000      -1.257   0.979   0.283   0.516   0.164   0.204   0.193
          3         4  3 13  0  0  1  1 25  1  5  0    34   20   0.630     -32.655   0.546   0.129   0.157   3.333   0.100   0.245
          4         5  5 21  0  0  1  1 42  1  5  0    37    5   0.881      -8.306   0.821  -0.610   0.783   1.250   0.210   0.352
          5         7  1 10  0  1  1  1 83  0  1  3    39   10   0.796     -24.752   0.603   0.078  -0.649   2.381   0.123   0.156
          6         8  4 20  0  1  1  1 54  1  5  0    29    1   0.967      -1.750   0.943   0.121  -0.557   0.205   0.172   0.204
          7         9  4 13  0  1  0  1 69  1  1  2    49    7   0.875     -20.582   0.692  -0.072  -0.164   0.463   0.030   0.035
          8        10  0 20  0  0  1  1 55  1  1  1    47   12   0.797     -17.032   0.749   0.118  -0.056   0.610   0.049   0.121
          9        11  4 11  0  0  1  2 50  1  5  0    46   11   0.807     -23.638   0.661   0.232   0.365   1.515   0.088   0.159
         10        16  3 14  0  0  0  2 23  1  5  0    49    8   0.860     -15.413   0.763   0.423   0.301   1.020   0.135   0.183
      The estimated two-dimensional coordinates are the fourth and fifth colums after the columns of integers. Respondent 1's (the ID number is the second column) two dimensional coordinates are -0.049 0.439. Note that this output file has all the variables from VOTE_THERM_1968.ORD file so that you can select the voters and non-voters. Make plots using R of the Humphrey Voters, Nixon Voters, and Wallace Voters. These plots should look like those you did for question 3 of homework 7.

    7. Run the 2000 data through QN (be sure to rename QUADSTRT.2000 to QUADSTRT.DAT!). Turn in a copy of the QUAD0021.DAT file.

    8. Make plots using R of the Gore Voters and Bush Voters. These plots should look like those you did for question 2 of homework 8.

    9. Compare the plots you made in 2.b and 2.f and compare the plots you made in 2.d with 2.h. Which set in each pair do you find the most intuitively appealing? Why? Why Not?

  3. In this problem we are going to use R to create STATA files that we can then use for some multivariate data analysis. To do this we are going to use the R programs that created the plots in 2.b and 2.d. Below is a partial listing of the R program I wrote to do the plots for 2.b. Note that I am reading all the variables from the PERF25.DAT file from the 1968 scaling:
    
    #
    # homework_9_plot_1968_1.r
    #
    # Reads in output from OC Applied to Thermometer "Roll Calls"
    #         and produces Simple Graphs of Voters and Non-Voters.
    #         Also outputs data as STATA file
    #
    #   DATA FILE
    #           -- 1st column: Counter 1 to 1254
    #           -- 2nd column: ID Number
    #           -- 3rd column: partyid -- 0 (SD) to 6 (SR)
    #           -- 4th column: income category
    #           -- 5th column: race, 0=white, 1=black, >2 = other
    #           -- 6th column: sex, 0=male, 1=female
    #           -- 7th column: 0= non-south, 1=south
    #           -- 8th column: education 1=HS, 2=SC, 3=College
    #           -- 9th column: age
    #           --10th column: 0= not married, 1 = married
    #           --11th column: Vote=1 Not Vote=5
    #           --12th column: 1=Humphrey, 2=Nixon, 3=Wallace, 0=Other/Not Vote
    #           --13th column: Classification Errors
    #           --14th column: Total Choices
    #           --15th column: Proportion Correctly Classified
    #           --16th column: Volume of Polytope
    #           --17th column: 1st dim. from Thermometers
    #           --18th column: 2nd dim. from Thermometers
    #
    library(MASS)         This is the easy way to call a library!
    library(foreign)      We need this library to do the STATA output
    T <- matrix(scan("D:/R_Files/oc_leg_1968_therm_full.dat",0),ncol=18,byrow=TRUE)
    TT <- T
    nrow <- length(T[,1])
    ncol <- length(T[1,])
    #
    # Change Sign on the Dimensions
    #
    T[,17] <- -T[,17]
    T[,18] <- -T[,18]
    #
     -- Your Plotting Commands Here --
    #
    outputdf <- as.data.frame(T)                    These two commands Tell STATA
    write.dta(outputdf,file="d:/k7moa/T_1968.DTA")  To Write Out The Entire T Matrix
    #                                               as a STATA FILE
    To enable this feature of R you must load the foreign package in the same way that you loaded the MASS package for Problem 1 of Homework 6 and Problem 1 of Homework 7.

    1. Turn in the R code that you write to create the plots with the STATA file creation feature for both the 1968 and 2000 files.

    2. Define the variables in STATA appropriately and turn in the results of the d and summ commands for both the 1968 and 2000 files.

    3. Run Ordered Probit using party id as the dependent variable with at least the two dimensions from the Thermometers. This simple ordered probit is done with the command:

      oprobit partyid dim1 dim2

      Experiment with specifications for both elections and turn in the table of results (neatly formatted!!) showing what you think is a reasonable specification. Explain in no more than two paragraphs why you chose your model. Do this for both the 1968 and 2000 files.