Eyesight example: test symmetry                  1
                                  19:28 Wednesday, November 29, 2017

                         The FREQ Procedure

                          Table of r by l

       r         l

       Frequency|       1|       2|       3|       4|  Total
       ---------+--------+--------+--------+--------+
              1 |    492 |    179 |     82 |     36 |    789
       ---------+--------+--------+--------+--------+
              2 |    205 |   1772 |    362 |    117 |   2456
       ---------+--------+--------+--------+--------+
              3 |     78 |    432 |   1512 |    234 |   2256
       ---------+--------+--------+--------+--------+
              4 |     66 |    124 |    266 |   1520 |   1976
       ---------+--------+--------+--------+--------+
       Total         841     2507     2222     1907     7477


                   Statistics for Table of r by l

                          Test of Symmetry
                      ------------------------
                      Statistic (S)    19.1066
                      DF                     6
                      Pr > S            0.0040


                          Kappa Statistics
 
    Statistic          Value       ASE     95% Confidence Limits
    ------------------------------------------------------------
    Simple Kappa      0.5954    0.0073       0.5811       0.6097
    Weighted Kappa    0.6524    0.0071       0.6385       0.6662

                         Sample Size = 7477
                  Eyesight example: test symmetry                  2
                                  19:28 Wednesday, November 29, 2017

                         The FREQ Procedure

                        Table of w97 by w05

       w97       w05

       Frequency|
       Percent  |
       Row Pct  |
       Col Pct  |C       |L       |LD      |RU      |  Total
       ---------+--------+--------+--------+--------+
       C        |     12 |      0 |      0 |      0 |     12
                |  16.22 |   0.00 |   0.00 |   0.00 |  16.22
                | 100.00 |   0.00 |   0.00 |   0.00 |
                |  57.14 |   0.00 |   0.00 |   0.00 |
       ---------+--------+--------+--------+--------+
       L        |      9 |     44 |      2 |      1 |     56
                |  12.16 |  59.46 |   2.70 |   1.35 |  75.68
                |  16.07 |  78.57 |   3.57 |   1.79 |
                |  42.86 | 100.00 |  25.00 | 100.00 |
       ---------+--------+--------+--------+--------+
       LD       |      0 |      0 |      6 |      0 |      6
                |   0.00 |   0.00 |   8.11 |   0.00 |   8.11
                |   0.00 |   0.00 | 100.00 |   0.00 |
                |   0.00 |   0.00 |  75.00 |   0.00 |
       ---------+--------+--------+--------+--------+
       Total          21       44        8        1       74
                   28.38    59.46    10.81     1.35   100.00
                  Eyesight example: test symmetry                  3
                                  19:28 Wednesday, November 29, 2017

                         The FREQ Procedure

                        Table of w97 by w05c

            w97       w05c

            Frequency|
            Percent  |
            Row Pct  |
            Col Pct  |C       |L       |LD      |  Total
            ---------+--------+--------+--------+
            C        |     12 |      0 |      0 |     12
                     |  16.22 |   0.00 |   0.00 |  16.22
                     | 100.00 |   0.00 |   0.00 |
                     |  57.14 |   0.00 |   0.00 |
            ---------+--------+--------+--------+
            L        |      9 |     45 |      2 |     56
                     |  12.16 |  60.81 |   2.70 |  75.68
                     |  16.07 |  80.36 |   3.57 |
                     |  42.86 | 100.00 |  25.00 |
            ---------+--------+--------+--------+
            LD       |      0 |      0 |      6 |      6
                     |   0.00 |   0.00 |   8.11 |   8.11
                     |   0.00 |   0.00 | 100.00 |
                     |   0.00 |   0.00 |  75.00 |
            ---------+--------+--------+--------+
            Total          21       45        8       74
                        28.38    60.81    10.81   100.00


                Statistics for Table of w97 by w05c

                          Test of Symmetry
                      ------------------------
                      Statistic (S)    11.0000
                      DF                     3
                      Pr > S            0.0117


                          Kappa Statistics
 
    Statistic          Value       ASE     95% Confidence Limits
    ------------------------------------------------------------
    Simple Kappa      0.6935    0.0829       0.5311       0.8560
    Weighted Kappa    0.7172    0.0789       0.5625       0.8719

                          Sample Size = 74
             Eyesight example: fit symmetry via genmod             4
                                  19:28 Wednesday, November 29, 2017

                        The GENMOD Procedure

                         Model Information

                 Data Set              WORK.NEWEYES
                 Distribution               Poisson
                 Link Function                  Log
                 Dependent Variable           count


              Number of Observations Read          16
              Number of Observations Used          16


                      Class Level Information
 
        Class      Levels    Values

        md             10    -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 


               Criteria For Assessing Goodness Of Fit
 
  Criterion                     DF           Value        Value/DF

  Deviance                       6         19.2492          3.2082
  Scaled Deviance                6         19.2492          3.2082
  Pearson Chi-Square             6         19.1065          3.1844
  Scaled Pearson X2              6         19.1065          3.1844
  Log Likelihood                        42820.6478                
  Full Log Likelihood                     -68.3141                
  AIC (smaller is better)                 156.6282                
  AICC (smaller is better)                200.6282                
  BIC (smaller is better)                 164.3541                


Algorithm converged.                                                


         Analysis Of Maximum Likelihood Parameter Estimates
 
                                    Standard   Wald 95% Confidence
  Parameter         DF   Estimate      Error          Limits

  Intercept          0     0.0000     0.0000     0.0000     0.0000
  md          -10    1     5.5215     0.0447     5.4338     5.6091
  md          -9     1     4.7916     0.0644     4.6654     4.9179
  md          -8     1     5.9839     0.0355     5.9144     6.0535
  md          -7     1     3.9318     0.0990     3.7378     4.1259
  md          -6     1     4.3820     0.0791     4.2271     4.5370
  md          -5     1     5.2575     0.0510     5.1575     5.3575
  md          -4     1     7.3265     0.0256     7.2762     7.3767
  md          -3     1     7.3212     0.0257     7.2708     7.3716
  md          -2     1     7.4799     0.0238     7.4333     7.5264
  md          -1     1     6.1985     0.0451     6.1101     6.2868
  Scale              0     1.0000     0.0000     1.0000     1.0000

                   Analysis Of Maximum Likelihood
                        Parameter Estimates
 
                                     Wald
             Parameter         Chi-Square    Pr > ChiSq

             Intercept                .           .    
             md          -10      15243.3        <.0001
             md          -9       5533.34        <.0001
             md          -8       28431.1        <.0001
             md          -7       1576.84        <.0001
             md          -6       3072.35        <.0001
             md          -5       10614.2        <.0001
             md          -4       81589.2        <.0001
             md          -3       81042.9        <.0001
             md          -2       99140.5        <.0001
             md          -1       18903.2        <.0001
             Scale                                     

NOTE: The scale parameter was held fixed.


                   Lagrange Multiplier Statistics
 
               Parameter     Chi-Square    Pr > ChiSq

               Intercept          .             .    
             Eyesight example: fit symmetry via genmod             5
                                  19:28 Wednesday, November 29, 2017

              Obs    r    l    count     md    outpred

                1    4    4     1520     -4    1520.00
                2    4    3      266    -10     250.00
                3    4    2      124     -9     120.50
                4    4    1       66     -7      51.00
                5    3    4      234    -10     250.00
                6    3    3     1512     -3    1512.00
                7    3    2      432     -8     397.00
                8    3    1       78     -6      80.00
                9    2    4      117     -9     120.50
               10    2    3      362     -8     397.00
               11    2    2     1772     -2    1772.00
               12    2    1      205     -5     192.00
               13    1    4       36     -7      51.00
               14    1    3       82     -6      80.00
               15    1    2      179     -5     192.00
               16    1    1      492     -1     492.00
         Eyesight example: fit sat. model to test symmetry         6
                                  19:28 Wednesday, November 29, 2017

                        The GENMOD Procedure

                         Model Information

                 Data Set              WORK.NEWEYES
                 Distribution               Poisson
                 Link Function                  Log
                 Dependent Variable           count


              Number of Observations Read          16
              Number of Observations Used          16


                      Class Level Information
 
                   Class      Levels    Values

                   r               4    1 2 3 4 
                   l               4    1 2 3 4 


                       Parameter Information
 
                Parameter       Effect       r    l

                Prm1            Intercept          
                Prm2            r*l          1    1
                Prm3            r*l          1    2
                Prm4            r*l          1    3
                Prm5            r*l          1    4
                Prm6            r*l          2    1
                Prm7            r*l          2    2
                Prm8            r*l          2    3
                Prm9            r*l          2    4
                Prm10           r*l          3    1
                Prm11           r*l          3    2
                Prm12           r*l          3    3
                Prm13           r*l          3    4
                Prm14           r*l          4    1
                Prm15           r*l          4    2
                Prm16           r*l          4    3
                Prm17           r*l          4    4


               Criteria For Assessing Goodness Of Fit
 
  Criterion                     DF           Value        Value/DF

  Deviance                       0          0.0000           .    
  Scaled Deviance                0          0.0000           .    
  Pearson Chi-Square             .          0.0000           .    
  Scaled Pearson X2              .          0.0000           .    
  Log Likelihood                        42830.2723                
  Full Log Likelihood                     -58.6895                
  AIC (smaller is better)                 149.3790                
  AICC (smaller is better)                   .                    
  BIC (smaller is better)                 161.7405                


Algorithm converged.                                                


         Analysis Of Maximum Likelihood Parameter Estimates
 
                                     Standard   Wald 95% Confidence
 Parameter           DF   Estimate      Error          Limits

 Intercept            0     0.0000     0.0000     0.0000     0.0000
 r*l         1   1    1     6.1985     0.0451     6.1101     6.2868
 r*l         1   2    1     5.1874     0.0747     5.0409     5.3339
 r*l         1   3    1     4.4067     0.1104     4.1903     4.6232
 r*l         1   4    1     3.5835     0.1667     3.2569     3.9102
 r*l         2   1    1     5.3230     0.0698     5.1861     5.4599
 r*l         2   2    1     7.4799     0.0238     7.4333     7.5264
 r*l         2   3    1     5.8916     0.0526     5.7886     5.9947
 r*l         2   4    1     4.7622     0.0925     4.5810     4.9434
 r*l         3   1    1     4.3567     0.1132     4.1348     4.5786
 r*l         3   2    1     6.0684     0.0481     5.9741     6.1627
 r*l         3   3    1     7.3212     0.0257     7.2708     7.3716
 r*l         3   4    1     5.4553     0.0654     5.3272     5.5834
 r*l         4   1    1     4.1897     0.1231     3.9484     4.4309
 r*l         4   2    1     4.8203     0.0898     4.6443     4.9963
 r*l         4   3    1     5.5835     0.0613     5.4633     5.7037
 r*l         4   4    1     7.3265     0.0256     7.2762     7.3767
 Scale                0     1.0000     0.0000     1.0000     1.0000

                   Analysis Of Maximum Likelihood
                        Parameter Estimates
 
                                      Wald
            Parameter           Chi-Square    Pr > ChiSq

            Intercept                  .           .    
            r*l         1   1      18903.2        <.0001
            r*l         1   2      4816.71        <.0001
            r*l         1   3      1592.37        <.0001
            r*l         1   4       462.30        <.0001
            r*l         2   1      5808.56        <.0001
            r*l         2   2      99140.5        <.0001
            r*l         2   3      12565.6        <.0001
            r*l         2   4      2653.36        <.0001
            r*l         3   1      1480.51        <.0001
            r*l         3   2      15908.7        <.0001
            r*l         3   3      81042.9        <.0001
            r*l         3   4      6963.96        <.0001
            r*l         4   1      1158.51        <.0001
            r*l         4   2      2881.15        <.0001
            r*l         4   3      8292.66        <.0001
            r*l         4   4      81589.2        <.0001
            Scale                                       

NOTE: The scale parameter was held fixed.


                   Lagrange Multiplier Statistics
 
               Parameter     Chi-Square    Pr > ChiSq

               Intercept          .             .    


                         Contrast Results
 
                               Chi-
      Contrast        DF     Square    Pr > ChiSq    Type

      r0               6      19.25        0.0038    LR      
         Eyesight example: fit sat. model to test quasisym.        7
                                  19:28 Wednesday, November 29, 2017

                        The GENMOD Procedure

                         Model Information

                 Data Set              WORK.NEWEYES
                 Distribution               Poisson
                 Link Function                  Log
                 Dependent Variable           count


              Number of Observations Read          16
              Number of Observations Used          16


                      Class Level Information
 
                   Class      Levels    Values

                   r               4    1 2 3 4 
                   l               4    1 2 3 4 


                       Parameter Information
 
                Parameter       Effect       r    l

                Prm1            Intercept          
                Prm2            r*l          1    1
                Prm3            r*l          1    2
                Prm4            r*l          1    3
                Prm5            r*l          1    4
                Prm6            r*l          2    1
                Prm7            r*l          2    2
                Prm8            r*l          2    3
                Prm9            r*l          2    4
                Prm10           r*l          3    1
                Prm11           r*l          3    2
                Prm12           r*l          3    3
                Prm13           r*l          3    4
                Prm14           r*l          4    1
                Prm15           r*l          4    2
                Prm16           r*l          4    3
                Prm17           r*l          4    4


               Criteria For Assessing Goodness Of Fit
 
  Criterion                     DF           Value        Value/DF

  Deviance                       0          0.0000           .    
  Scaled Deviance                0          0.0000           .    
  Pearson Chi-Square             .          0.0000           .    
  Scaled Pearson X2              .          0.0000           .    
  Log Likelihood                        42830.2723                
  Full Log Likelihood                     -58.6895                
  AIC (smaller is better)                 149.3790                
  AICC (smaller is better)                   .                    
  BIC (smaller is better)                 161.7405                


Algorithm converged.                                                


         Analysis Of Maximum Likelihood Parameter Estimates
 
                                     Standard   Wald 95% Confidence
 Parameter           DF   Estimate      Error          Limits

 Intercept            0     0.0000     0.0000     0.0000     0.0000
 r*l         1   1    1     6.1985     0.0451     6.1101     6.2868
 r*l         1   2    1     5.1874     0.0747     5.0409     5.3339
 r*l         1   3    1     4.4067     0.1104     4.1903     4.6232
 r*l         1   4    1     3.5835     0.1667     3.2569     3.9102
 r*l         2   1    1     5.3230     0.0698     5.1861     5.4599
 r*l         2   2    1     7.4799     0.0238     7.4333     7.5264
 r*l         2   3    1     5.8916     0.0526     5.7886     5.9947
 r*l         2   4    1     4.7622     0.0925     4.5810     4.9434
 r*l         3   1    1     4.3567     0.1132     4.1348     4.5786
 r*l         3   2    1     6.0684     0.0481     5.9741     6.1627
 r*l         3   3    1     7.3212     0.0257     7.2708     7.3716
 r*l         3   4    1     5.4553     0.0654     5.3272     5.5834
 r*l         4   1    1     4.1897     0.1231     3.9484     4.4309
 r*l         4   2    1     4.8203     0.0898     4.6443     4.9963
 r*l         4   3    1     5.5835     0.0613     5.4633     5.7037
 r*l         4   4    1     7.3265     0.0256     7.2762     7.3767
 Scale                0     1.0000     0.0000     1.0000     1.0000

                   Analysis Of Maximum Likelihood
                        Parameter Estimates
 
                                      Wald
            Parameter           Chi-Square    Pr > ChiSq

            Intercept                  .           .    
            r*l         1   1      18903.2        <.0001
            r*l         1   2      4816.71        <.0001
            r*l         1   3      1592.37        <.0001
            r*l         1   4       462.30        <.0001
            r*l         2   1      5808.56        <.0001
            r*l         2   2      99140.5        <.0001
            r*l         2   3      12565.6        <.0001
            r*l         2   4      2653.36        <.0001
            r*l         3   1      1480.51        <.0001
            r*l         3   2      15908.7        <.0001
            r*l         3   3      81042.9        <.0001
            r*l         3   4      6963.96        <.0001
            r*l         4   1      1158.51        <.0001
            r*l         4   2      2881.15        <.0001
            r*l         4   3      8292.66        <.0001
            r*l         4   4      81589.2        <.0001
            Scale                                       

NOTE: The scale parameter was held fixed.


                   Lagrange Multiplier Statistics
 
               Parameter     Chi-Square    Pr > ChiSq

               Intercept          .             .    


                         Contrast Results
 
                               Chi-
      Contrast        DF     Square    Pr > ChiSq    Type

      r0               3       7.27        0.0638    LR      
                      Quasisymmetry via CATMOD                     8
                                  19:28 Wednesday, November 29, 2017

                        The CATMOD Procedure

                            Data Summary

        Response           r*l         Response Levels    16
        Weight Variable    count       Populations         1
        Data Set           NEWEYES     Total Frequency  7477
        Frequency Missing  0           Observations       16


                        Population Profiles
 
                       Sample    Sample Size
                       ---------------------
                           1            7477


                         Response Profiles
 
                         Response    r    l
                         ------------------
                             1       1    1
                             2       1    2
                             3       1    3
                             4       1    4
                             5       2    1
                             6       2    2
                             7       2    3
                             8       2    4
                             9       3    1
                            10       3    2
                            11       3    3
                            12       3    4
                            13       4    1
                            14       4    2
                            15       4    3
                            16       4    4


                        Analysis of Variance
 
             Source       DF   Chi-Square    Pr > ChiSq
             ------------------------------------------
             Residual      3         7.22        0.0651
                    Marginal symmetry via CATMOD                   9
                                  19:28 Wednesday, November 29, 2017

                        The CATMOD Procedure

                            Data Summary

        Response           r*l         Response Levels    16
        Weight Variable    count       Populations         1
        Data Set           NEWEYES     Total Frequency  7477
        Frequency Missing  0           Observations       16


                        Population Profiles
 
                       Sample    Sample Size
                       ---------------------
                           1            7477


                         Response Profiles
 
                         Response    r    l
                         ------------------
                             1       1    1
                             2       1    2
                             3       1    3
                             4       1    4
                             5       2    1
                             6       2    2
                             7       2    3
                             8       2    4
                             9       3    1
                            10       3    2
                            11       3    3
                            12       3    4
                            13       4    1
                            14       4    2
                            15       4    3
                            16       4    4


                        Analysis of Variance
 
             Source       DF   Chi-Square    Pr > ChiSq
             ------------------------------------------
             Residual      3        11.98        0.0075
                    Quasiindependence via GENMOD                  10
                                  19:28 Wednesday, November 29, 2017

                        The GENMOD Procedure

                         Model Information

                 Data Set              WORK.NEWEYES
                 Distribution               Poisson
                 Link Function                  Log
                 Dependent Variable           count


              Number of Observations Read          16
              Number of Observations Used          16


                      Class Level Information
 
                  Class      Levels    Values

                  l               4    1 2 3 4   
                  r               4    1 2 3 4   
                  d               5    1 2 3 4 5 


               Criteria For Assessing Goodness Of Fit
 
  Criterion                     DF           Value        Value/DF

  Deviance                       5        199.1062         39.8212
  Scaled Deviance                5        199.1062         39.8212
  Pearson Chi-Square             5        198.0094         39.6019
  Scaled Pearson X2              5        198.0094         39.6019
  Log Likelihood                        42730.7193                
  Full Log Likelihood                    -158.2426                
  AIC (smaller is better)                 338.4852                
  AICC (smaller is better)                404.4852                
  BIC (smaller is better)                 346.9837                


Algorithm converged.                                                


         Analysis Of Maximum Likelihood Parameter Estimates
 
                            Standard       Wald 95%             Wald
Parameter     DF  Estimate     Error   Confidence Limits  Chi-Square

Intercept      1    4.3884    0.0745    4.2423    4.5345     3465.63
r          1   1   -0.4570    0.0755   -0.6050   -0.3090       36.62
r          2   1    0.6872    0.0647    0.5604    0.8140      112.83
r          3   1    0.7818    0.0641    0.6561    0.9074      148.78
r          4   0    0.0000    0.0000    0.0000    0.0000         .  
l          1   1   -0.1769    0.0748   -0.3235   -0.0303        5.59
l          2   1    0.8716    0.0669    0.7405    1.0027      169.77
l          3   1    0.8900    0.0679    0.7569    1.0230      171.87
l          4   0    0.0000    0.0000    0.0000    0.0000         .  
d          1   1    2.4439    0.0946    2.2586    2.6293      668.01
d          2   1    1.5326    0.0700    1.3954    1.6698      479.57
d          3   1    1.2610    0.0704    1.1230    1.3990      320.69
d          4   1    2.9381    0.0788    2.7835    3.0926     1388.97
d          5   0    0.0000    0.0000    0.0000    0.0000         .  
Scale          0    1.0000    0.0000    1.0000    1.0000            

                        Analysis Of Maximum
                        Likelihood Parameter
                             Estimates
 
                      Parameter     Pr > ChiSq

                      Intercept         <.0001
                      r          1      <.0001
                      r          2      <.0001
                      r          3      <.0001
                      r          4       .    
                      l          1      0.0181
                      l          2      <.0001
                      l          3      <.0001
                      l          4       .    
                      d          1      <.0001
                      d          2      <.0001
                      d          3      <.0001
                      d          4      <.0001
                      d          5       .    
                      Scale                   

NOTE: The scale parameter was held fixed.


                 LR Statistics For Type 3 Analysis
 
                                      Chi-
            Source           DF     Square    Pr > ChiSq

            r                 3     464.77        <.0001
            l                 3     453.16        <.0001
            d                 4    6472.41        <.0001
                    Quasiindependence via GENMOD                  11
                                  19:28 Wednesday, November 29, 2017

                         The FREQ Procedure

                   Statistics for Table of r by l

       Statistic                              Value       ASE
       ------------------------------------------------------
       Gamma                                 0.7982    0.0080
       Kendall's Tau-b                       0.6583    0.0080
       Stuart's Tau-c                        0.6327    0.0079

       Somers' D C|R                         0.6590    0.0080
       Somers' D R|C                         0.6576    0.0080

       Pearson Correlation                   0.7027    0.0084
       Spearman Correlation                  0.7064    0.0082
       Polychoric Correlation                0.7797    0.0060

       Lambda Asymmetric C|R                 0.5612    0.0087
       Lambda Asymmetric R|C                 0.5656    0.0085
       Lambda Symmetric                      0.5634    0.0084

       Uncertainty Coefficient C|R           0.3377    0.0075
       Uncertainty Coefficient R|C           0.3390    0.0075
       Uncertainty Coefficient Symmetric     0.3383    0.0075

                         Sample Size = 7477