Document ID: EPA-HQ-OW-2008-0465-1867
Agency: epa
Document Type: Supporting & Related Material
Title: 
Posted Date: 2009-12-07T05:00Z

The SAS System        11:19 Monday, November 23, 2009   1

                                        The Mixed Procedure

                                        Model Information

                      Data Set                     NEWMETA.ROBCON
                      Dependent Variable           lnWTP
                      Covariance Structure         Unstructured
                      Subject Effect               auth_id
                      Estimation Method            ML
                      Residual Variance Method     Profile
                      Fixed Effects SE Method      Empirical
                      Degrees of Freedom Method    Containment

                                      Class Level Information

                        Class      Levels    Values

                        auth_id        45    1004 1017 1031 1041 1063 1070
                                             1085 1097 1100 1114 1128 1145
                                             1160 1168 1177 1207 1226 1245
                                             1246 1251 1252 1254 1262 1278
                                             1287 1295 1310 1311 1312 1317
                                             1395 1405 1423 1445 1461 1472
                                             1512 1553 1554 1787 1922 2000
                                             2001 2002 2003

                                            Dimensions

                                Covariance Parameters             2
                                Columns in X                     27
                                Columns in Z Per Subject          1
                                Subjects                         45
                                Max Obs Per Subject              12

                                      Number of Observations

                            Number of Observations Read             120
                            Number of Observations Used             115
                            Number of Observations Not Used           5

                                         Iteration History

                    Iteration    Evaluations        -2 Log Like       Criterion

                            0              1       133.92578882
                            1              4       133.92578882      0.00000000
                                          The SAS System        11:19 Monday, November 23, 2009   2

                                        The Mixed Procedure

                                    Convergence criteria met.

                                  Covariance Parameter Estimates

                                 Cov Parm     Subject    Estimate

                                 UN(1,1)      auth_id     6.1E-20
                                 Residual                  0.1876

                                          Fit Statistics

                               -2 Log Likelihood               133.9
                               AIC (smaller is better)         189.9
                               AICC (smaller is better)        208.8
                               BIC (smaller is better)         240.5

                                 Null Model Likelihood Ratio Test

                                   DF    Chi-Square      Pr > ChiSq

                                    0          0.00          1.0000

                                    Solution for Fixed Effects

                                              Standard
              Effect              Estimate       Error      DF    t Value    Pr > |t|

              Intercept             5.7109      0.9352      25       6.11      <.0001
              year_indx           -0.08043     0.01482      63      -5.43      <.0001
              discrete             -0.1248      0.2230      63      -0.56      0.5776
              volunt               -1.3233      0.1653      63      -8.01      <.0001
              nonparam             -0.6698      0.1434      63      -4.67      <.0001
              INCOME              2.698E-6    3.902E-6      63       0.69      0.4919
              ladder_study         -0.3275      0.2692      63      -1.22      0.2284
              OUTLIER_BIDS         -0.8837      0.2855      63      -3.10      0.0029
              single_river         -0.4279      0.1412      63      -3.03      0.0035
              single_lake         -0.06316      0.2386      63      -0.26      0.7921
              multiple_river       -1.4752      0.3540      63      -4.17      <.0001
              regional_fresh        0.1588      0.1505      63       1.06      0.2955
              salt_pond             0.9849      0.3580      63       2.75      0.0078
              num_rivers_ponds      0.1173     0.02806      63       4.18      <.0001
              mr                   -0.8846      0.1832      63      -4.83      <.0001
              mp                    1.6337      0.2980      63       5.48      <.0001
              nonusers             -0.4036      0.1314      63      -3.07      0.0031
              allmult              -0.3728      0.1644      63      -2.27      0.0268
              nonspec              -0.4042      0.1731      63      -2.34      0.0227
              lnquality_ch          0.4065      0.1488      63       2.73      0.0082
              fish_use             -0.3317      0.1291      63      -2.57      0.0126
                                          The SAS System        11:19 Monday, November 23, 2009   3

                                        The Mixed Procedure

                                    Solution for Fixed Effects

                                              Standard
              Effect              Estimate       Error      DF    t Value    Pr > |t|

              fishplus              0.4432      0.1820      63       2.43      0.0177
              lnbase               0.02610      0.1183      63       0.22      0.8261
              mail                 -0.2013      0.1466      63      -1.37      0.1746
              lump_sum              0.5569      0.2387      63       2.33      0.0228
              non_reviewed         -0.2718      0.1625      63      -1.67      0.0993
              median_WTP           -0.5358      0.1875      63      -2.86      0.0058

                                    Solution for Random Effects

                                                 Std Err
            Effect       auth_id    Estimate        Pred      DF    t Value    Pr > |t|

            Intercept    1004              0           .       .        .         .
            Intercept    1017              0           .       .        .         .
            Intercept    1031              0           .       .        .         .
            Intercept    1041              0           .       .        .         .
            Intercept    1063              0           .       .        .         .
            Intercept    1070              0           .       .        .         .
            Intercept    1085              0           .       .        .         .
            Intercept    1097              0           .       .        .         .
            Intercept    1100              0           .       .        .         .
            Intercept    1114              0           .       .        .         .
            Intercept    1128              0           .       .        .         .
            Intercept    1145              0           .       .        .         .
            Intercept    1160              0           .       .        .         .
            Intercept    1168              0           .       .        .         .
            Intercept    1177              0           .       .        .         .
            Intercept    1207              0           .       .        .         .
            Intercept    1226              0           .       .        .         .
            Intercept    1245              0           .       .        .         .
            Intercept    1246              0           .       .        .         .
            Intercept    1251              0           .       .        .         .
            Intercept    1252              0           .       .        .         .
            Intercept    1254              0           .       .        .         .
            Intercept    1262              0           .       .        .         .
            Intercept    1278              0           .       .        .         .
            Intercept    1287              0           .       .        .         .
            Intercept    1295              0           .       .        .         .
            Intercept    1310              0           .       .        .         .
            Intercept    1311              0           .       .        .         .
            Intercept    1312              0           .       .        .         .
            Intercept    1317              0           .       .        .         .
            Intercept    1395              0           .       .        .         .
            Intercept    1405              0           .       .        .         .
            Intercept    1423              0           .       .        .         .
            Intercept    1445              0           .       .        .         .
                                          The SAS System        11:19 Monday, November 23, 2009   4

                                        The Mixed Procedure

                                    Solution for Random Effects

                                                 Std Err
            Effect       auth_id    Estimate        Pred      DF    t Value    Pr > |t|

            Intercept    1461              0           .       .        .         .
            Intercept    1472              0           .       .        .         .
            Intercept    1512              0           .       .        .         .
            Intercept    1553              0           .       .        .         .
            Intercept    1554              0           .       .        .         .
            Intercept    1787              0           .       .        .         .
            Intercept    1922              0           .       .        .         .
            Intercept    2000              0           .       .        .         .
            Intercept    2001              0           .       .        .         .
            Intercept    2002              0           .       .        .         .
            Intercept    2003              0           .       .        .         .

                                   Type 3 Tests of Fixed Effects

                                            Num     Den
                       Effect                DF      DF    F Value    Pr > F

                       year_indx              1      63      29.45    <.0001
                       discrete               1      63       0.31    0.5776
                       volunt                 1      63      64.09    <.0001
                       nonparam               1      63      21.82    <.0001
                       INCOME                 1      63       0.48    0.4919
                       ladder_study           1      63       1.48    0.2284
                       OUTLIER_BIDS           1      63       9.58    0.0029
                       single_river           1      63       9.19    0.0035
                       single_lake            1      63       0.07    0.7921
                       multiple_river         1      63      17.37    <.0001
                       regional_fresh         1      63       1.11    0.2955
                       salt_pond              1      63       7.57    0.0078
                       num_rivers_ponds       1      63      17.47    <.0001
                       mr                     1      63      23.31    <.0001
                       mp                     1      63      30.05    <.0001
                       nonusers               1      63       9.43    0.0031
                       allmult                1      63       5.14    0.0268
                       nonspec                1      63       5.45    0.0227
                       lnquality_ch           1      63       7.46    0.0082
                       fish_use               1      63       6.60    0.0126
                       fishplus               1      63       5.93    0.0177
                       lnbase                 1      63       0.05    0.8261
                       mail                   1      63       1.89    0.1746
                       lump_sum               1      63       5.45    0.0228
                       non_reviewed           1      63       2.80    0.0993
                       median_WTP             1      63       8.16    0.0058
                                          The SAS System        11:19 Monday, November 23, 2009   5

                                Obs    Effect              Estimate

                                  1    Intercept             5.7109
                                  2    year_indx           -0.08043
                                  3    discrete             -0.1248
                                  4    volunt               -1.3233
                                  5    nonparam             -0.6698
                                  6    INCOME              2.698E-6
                                  7    ladder_study         -0.3275
                                  8    OUTLIER_BIDS         -0.8837
                                  9    single_river         -0.4279
                                 10    single_lake         -0.06316
                                 11    multiple_river       -1.4752
                                 12    regional_fresh        0.1588
                                 13    salt_pond             0.9849
                                 14    num_rivers_ponds      0.1173
                                 15    mr                   -0.8846
                                 16    mp                    1.6337
                                 17    nonusers             -0.4036
                                 18    allmult              -0.3728
                                 19    nonspec              -0.4042
                                 20    lnquality_ch          0.4065
                                 21    fish_use             -0.3317
                                 22    fishplus              0.4432
                                 23    lnbase               0.02610
                                 24    mail                 -0.2013
                                 25    lump_sum              0.5569
                                 26    non_reviewed         -0.2718
                                 27    median_WTP           -0.5358
                                          The SAS System        11:19 Monday, November 23, 2009   6

                           year_                                      ladder_ OUTLIER_  single_
 Obs  _NAME_  Intercept     indx discrete   volunt nonparam   INCOME    study   BIDS      river

  1  Estimate   5.7109  -0.08043  -0.1248  -1.3233  -0.6698 2.698E-6  -0.3275  -0.8837  -0.4279

      single_  multiple_  regional_     salt_  num_rivers_
 Obs     lake    river      fresh        pond     ponds           mr        mp  nonusers   allmult

  1  -0.06316   -1.4752     0.1588     0.9849     0.1173     -0.8846    1.6337   -0.4036   -0.3728

               lnquality_                                                      non_     median_
 Obs  nonspec      ch      fish_use  fishplus    lnbase      mail  lump_sum  reviewed       WTP

  1   -0.4042     0.4065    -0.3317    0.4432   0.02610   -0.2013    0.5569   -0.2718   -0.5358
                                          The SAS System        11:19 Monday, November 23, 2009   7

                  year_                                      ladder_ OUTLIER_  single_  single_
 Obs Intercept     indx discrete   volunt nonparam   INCOME    study   BIDS      river     lake

  1    5.7109  -0.08043  -0.1248  -1.3233  -0.6698 2.698E-6  -0.3275  -0.8837  -0.4279 -0.06316

     multiple_  regional_     salt_  num_rivers_
 Obs   river      fresh        pond     ponds           mr        mp  nonusers   allmult   nonspec

  1   -1.4752     0.1588     0.9849     0.1173     -0.8846    1.6337   -0.4036   -0.3728   -0.4042

     lnquality_                                                            non_      median_
 Obs     ch       fish_use   fishplus     lnbase       mail   lump_sum   reviewed        WTP

  1     0.4065     -0.3317     0.4432    0.02610    -0.2013     0.5569    -0.2718    -0.5358
                                          The SAS System        11:19 Monday, November 23, 2009   8

                                        The Mixed Procedure

                                        Model Information

                      Data Set                     NEWMETA.ROBCON_2
                      Dependent Variable           lnWTP
                      Covariance Structure         Unstructured
                      Subject Effect               auth_id
                      Estimation Method            ML
                      Residual Variance Method     Profile
                      Fixed Effects SE Method      Empirical
                      Degrees of Freedom Method    Containment

                                      Class Level Information

                        Class      Levels    Values

                        auth_id        45    1004 1017 1031 1041 1063 1070
                                             1085 1097 1100 1114 1128 1145
                                             1160 1168 1177 1207 1226 1245
                                             1246 1251 1252 1254 1262 1278
                                             1287 1295 1310 1311 1312 1317
                                             1395 1405 1423 1445 1461 1472
                                             1512 1553 1554 1787 1922 2000
                                             2001 2002 2003

                                            Dimensions

                                Covariance Parameters             2
                                Columns in X                     27
                                Columns in Z Per Subject          1
                                Subjects                         45
                                Max Obs Per Subject              12

                                      Number of Observations

                            Number of Observations Read             120
                            Number of Observations Used             115
                            Number of Observations Not Used           5

                                         Iteration History

                    Iteration    Evaluations        -2 Log Like       Criterion

                            0              1       133.92578882
                            1              4       133.92578882      0.00000000
                                          The SAS System        11:19 Monday, November 23, 2009   9

                                        The Mixed Procedure

                                    Convergence criteria met.

                                  Covariance Parameter Estimates

                                 Cov Parm     Subject    Estimate

                                 UN(1,1)      auth_id     6.1E-20
                                 Residual                  0.1876

                             Asymptotic Covariance Matrix of Estimates

                              Row    Cov Parm        CovP1       CovP2

                                1    UN(1,1)
                                2    Residual                 0.000612

                                          Fit Statistics

                               -2 Log Likelihood               133.9
                               AIC (smaller is better)         189.9
                               AICC (smaller is better)        208.8
                               BIC (smaller is better)         240.5

                                 Null Model Likelihood Ratio Test

                                   DF    Chi-Square      Pr > ChiSq

                                    0          0.00          1.0000

                                    Solution for Fixed Effects

                                              Standard
              Effect              Estimate       Error      DF    t Value    Pr > |t|

              Intercept             5.7109      0.9352      25       6.11      <.0001
              year_indx           -0.08043     0.01482      63      -5.43      <.0001
              discrete             -0.1248      0.2230      63      -0.56      0.5776
              volunt               -1.3233      0.1653      63      -8.01      <.0001
              nonparam             -0.6698      0.1434      63      -4.67      <.0001
              INCOME              2.698E-6    3.902E-6      63       0.69      0.4919
              ladder_study         -0.3275      0.2692      63      -1.22      0.2284
              OUTLIER_BIDS         -0.8837      0.2855      63      -3.10      0.0029
              single_river         -0.4279      0.1412      63      -3.03      0.0035
              single_lake         -0.06316      0.2386      63      -0.26      0.7921
              multiple_river       -1.4752      0.3540      63      -4.17      <.0001
              regional_fresh        0.1588      0.1505      63       1.06      0.2955
              salt_pond             0.9849      0.3580      63       2.75      0.0078
                                          The SAS System        11:19 Monday, November 23, 2009  10

                                        The Mixed Procedure

                                    Solution for Fixed Effects

                                              Standard
              Effect              Estimate       Error      DF    t Value    Pr > |t|

              num_rivers_ponds      0.1173     0.02806      63       4.18      <.0001
              mr                   -0.8846      0.1832      63      -4.83      <.0001
              mp                    1.6337      0.2980      63       5.48      <.0001
              nonusers             -0.4036      0.1314      63      -3.07      0.0031
              allmult              -0.3728      0.1644      63      -2.27      0.0268
              nonspec              -0.4042      0.1731      63      -2.34      0.0227
              lnquality_ch          0.4065      0.1488      63       2.73      0.0082
              fish_use             -0.3317      0.1291      63      -2.57      0.0126
              fishplus              0.4432      0.1820      63       2.43      0.0177
              lnbase               0.02610      0.1183      63       0.22      0.8261
              mail                 -0.2013      0.1466      63      -1.37      0.1746
              lump_sum              0.5569      0.2387      63       2.33      0.0228
              non_reviewed         -0.2718      0.1625      63      -1.67      0.0993
              median_WTP           -0.5358      0.1875      63      -2.86      0.0058

                           Empirical Covariance Matrix for Fixed Effects

    Row  Effect                Col1      Col2      Col3      Col4      Col5      Col6      Col7

      1  Intercept           0.8746  -0.00890  -0.03518  -0.00819  -0.05908  -1.83E-6   -0.1944

                           Empirical Covariance Matrix for Fixed Effects

   Row      Col8      Col9     Col10     Col11     Col12     Col13     Col14     Col15     Col16

     1  -0.06113  0.000725   0.01692  -0.07074  -0.03642    0.1565  0.001285    0.1105   0.01600

                           Empirical Covariance Matrix for Fixed Effects

   Row     Col17     Col18     Col19     Col20     Col21     Col22     Col23     Col24     Col25

     1  -0.00653  -0.00082   0.02250  -0.08039   0.04699  -0.01592  -0.09461  -0.00279   0.02461

                                       Empirical Covariance
                                     Matrix for Fixed Effects

                                     Row     Col26       Col27

                                       1   0.03740    -0.04969
                                          The SAS System        11:19 Monday, November 23, 2009  11

                                        The Mixed Procedure

                           Empirical Covariance Matrix for Fixed Effects

    Row  Effect                Col1      Col2      Col3      Col4      Col5      Col6      Col7

      2  year_indx         -0.00890  0.000220  -0.00016  0.000542  0.001055  1.804E-8  0.003094
      3  discrete          -0.03518  -0.00016   0.04972  0.005891   0.01346  1.045E-7   0.02268
      4  volunt            -0.00819  0.000542  0.005891   0.02732  0.009303  -1.37E-7   0.01037
      5  nonparam          -0.05908  0.001055   0.01346  0.009303   0.02056  2.162E-7   0.02669
      6  INCOME            -1.83E-6  1.804E-8  1.045E-7  -1.37E-7  2.162E-7  1.52E-11  5.743E-7
      7  ladder_study       -0.1944  0.003094   0.02268   0.01037   0.02669  5.743E-7   0.07249
      8  OUTLIER_BIDS      -0.06113  -0.00007   0.01580  -0.00931  0.001179  1.897E-7  0.005147
      9  single_river      0.000725  -0.00034  -0.00924  -0.00712  -0.01070  -3.23E-8  -0.01175
     10  single_lake        0.01692  -0.00079  0.005332  0.006631  0.000258  1.949E-8  -0.00862
     11  multiple_river    -0.07074  0.002157  0.005516   0.02436   0.01879  1.353E-7   0.03160
     12  regional_fresh    -0.03642  -0.00057  -0.00919  -0.00353  -0.00745  -5.77E-8  -0.01068
     13  salt_pond           0.1565  -0.00237  -0.02161  0.001859  -0.03525  -9.44E-7  -0.07015
     14  num_rivers_ponds  0.001285  -0.00007  0.001031  -0.00154  -0.00028  1.424E-8  0.000102
     15  mr                  0.1105  -0.00133  -0.00482  0.001373  -0.01179  -4.16E-7  -0.03073
     16  mp                 0.01600  -0.00022  -0.03722  0.006135  -0.00385  -1.56E-8  -0.00616
     17  nonusers          -0.00653  -0.00040  -0.00158  -0.00221  -0.00604  1.383E-7  -0.00197
     18  allmult           -0.00082  -0.00001  0.001745  0.006629  0.002742  -9.17E-8  0.000094
     19  nonspec            0.02250  -0.00039  -0.01789  0.002578  -0.01465  -2.37E-7  -0.01729
     20  lnquality_ch      -0.08039  0.000613  -0.00138  -0.00071  0.000117  -5.61E-8  0.009886
     21  fish_use           0.04699  -0.00041  -0.00922  0.002351  -0.00340  -9.98E-8  -0.00913
     22  fishplus          -0.01592  0.000541  0.003278  -0.00037  0.002432  7.098E-9   0.01069
     23  lnbase            -0.09461  0.000976  0.005062  0.003360  0.008472  1.885E-7   0.02178
     24  mail              -0.00279  -0.00012  0.004501  -0.00458  0.004975  1.268E-7  0.009529
     25  lump_sum           0.02461  -0.00064  -0.02965  -0.00826  -0.01691  -1.06E-7  -0.02637
     26  non_reviewed       0.03740  -0.00043  -0.02153  -0.00117  -0.01064  -9.03E-8  -0.01271
     27  median_WTP        -0.04969  0.001701  -0.00561  0.003406  0.006125  7.882E-8   0.02208

                           Empirical Covariance Matrix for Fixed Effects

   Row      Col8      Col9     Col10     Col11     Col12     Col13     Col14     Col15     Col16

     2  -0.00007  -0.00034  -0.00079  0.002157  -0.00057  -0.00237  -0.00007  -0.00133  -0.00022
     3   0.01580  -0.00924  0.005332  0.005516  -0.00919  -0.02161  0.001031  -0.00482  -0.03722
     4  -0.00931  -0.00712  0.006631   0.02436  -0.00353  0.001859  -0.00154  0.001373  0.006135
     5  0.001179  -0.01070  0.000258   0.01879  -0.00745  -0.03525  -0.00028  -0.01179  -0.00385
     6  1.897E-7  -3.23E-8  1.949E-8  1.353E-7  -5.77E-8  -9.44E-7  1.424E-8  -4.16E-7  -1.56E-8
     7  0.005147  -0.01175  -0.00862   0.03160  -0.01068  -0.07015  0.000102  -0.03073  -0.00616
     8   0.08151  -0.00164  -0.00875  -0.01236  0.003785  -0.01163  0.002141  -0.01797  -0.02075
     9  -0.00164   0.01993  0.005106  0.001981   0.01088   0.02258  -0.00048  0.003902  -0.01129
    10  -0.00875  0.005106   0.05694  0.009107  0.008208   0.01621  -0.00069  0.005361  -0.02705
    11  -0.01236  0.001981  0.009107    0.1253  -0.00696  -0.00284  -0.00848  -0.00503  -0.01067
    12  0.003785   0.01088  0.008208  -0.00696   0.02265   0.01801  -0.00007  -0.00564  0.006653
    13  -0.01163   0.02258   0.01621  -0.00284   0.01801    0.1282  -0.00223   0.04110  -0.01084
    14  0.002141  -0.00048  -0.00069  -0.00848  -0.00007  -0.00223  0.000788  -0.00090  -0.00079
    15  -0.01797  0.003902  0.005361  -0.00503  -0.00564   0.04110  -0.00090   0.03357  -0.00114
    16  -0.02075  -0.01129  -0.02705  -0.01067  0.006653  -0.01084  -0.00079  -0.00114   0.08882
                                          The SAS System        11:19 Monday, November 23, 2009  12

                                        The Mixed Procedure

                           Empirical Covariance Matrix for Fixed Effects

   Row      Col8      Col9     Col10     Col11     Col12     Col13     Col14     Col15     Col16

    17  0.003909  0.002059  -0.00427  -0.00994  0.001972  -0.00109  0.000073  0.001087   0.01286
    18  0.003401  -0.00520   0.02080   0.01114  0.001235  0.009171  -0.00055  0.003855  -0.01119
    19  -0.01309  0.002421  0.000843  -0.00439  0.006796   0.03376  -0.00121   0.01607   0.02308
    20  -0.01309  0.006443  0.001246  0.006652  0.007537  0.006278  -0.00089  0.001009  -0.00591
    21  -0.00464  -0.00623  -0.00670  -0.00051  -0.00158  0.006384  -0.00017  0.006032   0.02280
    22  -0.00266  -0.01262  0.001739   0.01482  -0.00395  -0.00223  -0.00060  0.000848  0.006369
    23  0.004247  -0.00198  -0.00100  0.005347  0.004785  -0.02117  -0.00011  -0.01671  0.000124
    24  0.005563  -0.00735  -0.01232  -0.01394  -0.00544  -0.02714  0.001446  -0.00070   0.01512
    25  0.009165   0.01384  -0.02400  -0.01517   0.01176   0.03446  0.000177  0.006683   0.02847
    26  -0.02307  0.004441  0.001097  0.001512  0.005410   0.01220  -0.00137  0.009492   0.02839
    27  -0.02408  0.001138  -0.00425   0.02212  -0.00937  -0.01272  -0.00145  -0.00135  -0.00232

                           Empirical Covariance Matrix for Fixed Effects

   Row     Col17     Col18     Col19     Col20     Col21     Col22     Col23     Col24     Col25

     2  -0.00040  -0.00001  -0.00039  0.000613  -0.00041  0.000541  0.000976  -0.00012  -0.00064
     3  -0.00158  0.001745  -0.01789  -0.00138  -0.00922  0.003278  0.005062  0.004501  -0.02965
     4  -0.00221  0.006629  0.002578  -0.00071  0.002351  -0.00037  0.003360  -0.00458  -0.00826
     5  -0.00604  0.002742  -0.01465  0.000117  -0.00340  0.002432  0.008472  0.004975  -0.01691
     6  1.383E-7  -9.17E-8  -2.37E-7  -5.61E-8  -9.98E-8  7.098E-9  1.885E-7  1.268E-7  -1.06E-7
     7  -0.00197  0.000094  -0.01729  0.009886  -0.00913   0.01069   0.02178  0.009529  -0.02637
     8  0.003909  0.003401  -0.01309  -0.01309  -0.00464  -0.00266  0.004247  0.005563  0.009165
     9  0.002059  -0.00520  0.002421  0.006443  -0.00623  -0.01262  -0.00198  -0.00735   0.01384
    10  -0.00427   0.02080  0.000843  0.001246  -0.00670  0.001739  -0.00100  -0.01232  -0.02400
    11  -0.00994   0.01114  -0.00439  0.006652  -0.00051   0.01482  0.005347  -0.01394  -0.01517
    12  0.001972  0.001235  0.006796  0.007537  -0.00158  -0.00395  0.004785  -0.00544   0.01176
    13  -0.00109  0.009171   0.03376  0.006278  0.006384  -0.00223  -0.02117  -0.02714   0.03446
    14  0.000073  -0.00055  -0.00121  -0.00089  -0.00017  -0.00060  -0.00011  0.001446  0.000177
    15  0.001087  0.003855   0.01607  0.001009  0.006032  0.000848  -0.01671  -0.00070  0.006683
    16   0.01286  -0.01119   0.02308  -0.00591   0.02280  0.006369  0.000124   0.01512   0.02847
    17   0.01727  -0.00547  0.007857  -0.00358  -0.00002  -0.00496  0.001589  0.002489  0.008550
    18  -0.00547   0.02703  0.007309  -0.00113  0.006869   0.01556  -0.00166  -0.00108  -0.01702
    19  0.007857  0.007309   0.02996  0.004119   0.01110   0.01018  -0.00510  -0.00292   0.01389
    20  -0.00358  -0.00113  0.004119   0.02215  -0.00700  0.000494  0.006536  -0.00471  0.001031
    21  -0.00002  0.006869   0.01110  -0.00700   0.01668   0.01145  -0.00737  0.007790  0.003223
    22  -0.00496   0.01556   0.01018  0.000494   0.01145   0.03313  -0.00192  0.003178  -0.01121
    23  0.001589  -0.00166  -0.00510  0.006536  -0.00737  -0.00192   0.01400  -0.00238  -0.00535
    24  0.002489  -0.00108  -0.00292  -0.00471  0.007790  0.003178  -0.00238   0.02149  -0.00559
    25  0.008550  -0.01702   0.01389  0.001031  0.003223  -0.01121  -0.00535  -0.00559   0.05695
    26  0.005107  0.000705   0.01702  0.001603   0.01092  0.004441  -0.00607  0.003279  0.003724
    27  -0.00279  -0.00392  -0.00063   0.01104  -0.00531  0.000972  0.005380  -0.00486  -0.00968

                                          The SAS System        11:19 Monday, November 23, 2009  13

                                        The Mixed Procedure

                                       Empirical Covariance
                                     Matrix for Fixed Effects

                                     Row     Col26       Col27

                                       2  -0.00043    0.001701
                                       3  -0.02153    -0.00561
                                       4  -0.00117    0.003406
                                       5  -0.01064    0.006125
                                       6  -9.03E-8    7.882E-8
                                       7  -0.01271     0.02208
                                       8  -0.02307    -0.02408
                                       9  0.004441    0.001138
                                      10  0.001097    -0.00425
                                      11  0.001512     0.02212
                                      12  0.005410    -0.00937
                                      13   0.01220    -0.01272
                                      14  -0.00137    -0.00145
                                      15  0.009492    -0.00135
                                      16   0.02839    -0.00232
                                      17  0.005107    -0.00279
                                      18  0.000705    -0.00392
                                      19   0.01702    -0.00063
                                      20  0.001603     0.01104
                                      21   0.01092    -0.00531
                                      22  0.004441    0.000972
                                      23  -0.00607    0.005380
                                      24  0.003279    -0.00486
                                      25  0.003724    -0.00968
                                      26   0.02639    0.003322
                                      27  0.003322     0.03517

                                    Solution for Random Effects

                                                 Std Err
            Effect       auth_id    Estimate        Pred      DF    t Value    Pr > |t|

            Intercept    1004              0           .       .        .         .
            Intercept    1017              0           .       .        .         .
            Intercept    1031              0           .       .        .         .
            Intercept    1041              0           .       .        .         .
            Intercept    1063              0           .       .        .         .
            Intercept    1070              0           .       .        .         .
            Intercept    1085              0           .       .        .         .
            Intercept    1097              0           .       .        .         .
            Intercept    1100              0           .       .        .         .
            Intercept    1114              0           .       .        .         .
            Intercept    1128              0           .       .        .         .
            Intercept    1145              0           .       .        .         .
            Intercept    1160              0           .       .        .         .
            Intercept    1168              0           .       .        .         .
                                          The SAS System        11:19 Monday, November 23, 2009  14

                                        The Mixed Procedure

                                    Solution for Random Effects

                                                 Std Err
            Effect       auth_id    Estimate        Pred      DF    t Value    Pr > |t|

            Intercept    1177              0           .       .        .         .
            Intercept    1207              0           .       .        .         .
            Intercept    1226              0           .       .        .         .
            Intercept    1245              0           .       .        .         .
            Intercept    1246              0           .       .        .         .
            Intercept    1251              0           .       .        .         .
            Intercept    1252              0           .       .        .         .
            Intercept    1254              0           .       .        .         .
            Intercept    1262              0           .       .        .         .
            Intercept    1278              0           .       .        .         .
            Intercept    1287              0           .       .        .         .
            Intercept    1295              0           .       .        .         .
            Intercept    1310              0           .       .        .         .
            Intercept    1311              0           .       .        .         .
            Intercept    1312              0           .       .        .         .
            Intercept    1317              0           .       .        .         .
            Intercept    1395              0           .       .        .         .
            Intercept    1405              0           .       .        .         .
            Intercept    1423              0           .       .        .         .
            Intercept    1445              0           .       .        .         .
            Intercept    1461              0           .       .        .         .
            Intercept    1472              0           .       .        .         .
            Intercept    1512              0           .       .        .         .
            Intercept    1553              0           .       .        .         .
            Intercept    1554              0           .       .        .         .
            Intercept    1787              0           .       .        .         .
            Intercept    1922              0           .       .        .         .
            Intercept    2000              0           .       .        .         .
            Intercept    2001              0           .       .        .         .
            Intercept    2002              0           .       .        .         .
            Intercept    2003              0           .       .        .         .

                                   Type 3 Tests of Fixed Effects

                                            Num     Den
                       Effect                DF      DF    F Value    Pr > F

                       year_indx              1      63      29.45    <.0001
                       discrete               1      63       0.31    0.5776
                       volunt                 1      63      64.09    <.0001
                       nonparam               1      63      21.82    <.0001
                       INCOME                 1      63       0.48    0.4919
                       ladder_study           1      63       1.48    0.2284
                       OUTLIER_BIDS           1      63       9.58    0.0029
                       single_river           1      63       9.19    0.0035
                       single_lake            1      63       0.07    0.7921
                                          The SAS System        11:19 Monday, November 23, 2009  15

                                        The Mixed Procedure

                                   Type 3 Tests of Fixed Effects

                                            Num     Den
                       Effect                DF      DF    F Value    Pr > F

                       multiple_river         1      63      17.37    <.0001
                       regional_fresh         1      63       1.11    0.2955
                       salt_pond              1      63       7.57    0.0078
                       num_rivers_ponds       1      63      17.47    <.0001
                       mr                     1      63      23.31    <.0001
                       mp                     1      63      30.05    <.0001
                       nonusers               1      63       9.43    0.0031
                       allmult                1      63       5.14    0.0268
                       nonspec                1      63       5.45    0.0227
                       lnquality_ch           1      63       7.46    0.0082
                       fish_use               1      63       6.60    0.0126
                       fishplus               1      63       5.93    0.0177
                       lnbase                 1      63       0.05    0.8261
                       mail                   1      63       1.89    0.1746
                       lump_sum               1      63       5.45    0.0228
                       non_reviewed           1      63       2.80    0.0993
                       median_WTP             1      63       8.16    0.0058
                                          The SAS System        11:19 Monday, November 23, 2009  16

                  year_                                      ladder_ OUTLIER_  single_  single_
 Obs Intercept     indx discrete   volunt nonparam   INCOME    study   BIDS      river     lake

  1    5.7109  -0.08043  -0.1248  -1.3233  -0.6698 2.698E-6  -0.3275  -0.8837  -0.4279 -0.06316

     multiple_  regional_     salt_  num_rivers_
 Obs   river      fresh        pond     ponds           mr        mp  nonusers   allmult   nonspec

  1   -1.4752     0.1588     0.9849     0.1173     -0.8846    1.6337   -0.4036   -0.3728   -0.4042

     lnquality_                                                            non_      median_
 Obs     ch       fish_use   fishplus     lnbase       mail   lump_sum   reviewed        WTP

  1     0.4065     -0.3317     0.4432    0.02610    -0.2013     0.5569    -0.2718    -0.5358
                                          The SAS System        11:19 Monday, November 23, 2009  17

                                        The MODEL Procedure

NOTE: Values for all of the 27 parameters in the model were read from the PARMSDATA=BOOT2TR data
      set.

                                        Parameter Settings

                                   intercept           5.710917
                                   year_indx           -0.08043
                                   discrete            -0.12483
                                   volunt              -1.32328
                                   nonparam            -0.66975
                                   income              2.698E-6
                                   ladder_study        -0.32749
                                   outlier_bids        -0.88372
                                   single_river        -0.42792
                                   single_lake         -0.06316
                                   multiple_river      -1.47521
                                   regional_fresh      0.158776
                                   salt_pond            0.98487
                                   num_rivers_ponds    0.117303
                                   mr                  -0.88457
                                   mp                  1.633701
                                   nonusers            -0.40363
                                   allmult             -0.37279
                                   nonspec             -0.40424
                                   lnquality_ch        0.406512
                                   fish_use            -0.33169
                                   fishplus            0.443232
                                   lnbase                0.0261
                                   mail                -0.20131
                                   lump_sum            0.556928
                                   non_reviewed        -0.27182
                                   median_WTP          -0.53575
                                          The SAS System        11:19 Monday, November 23, 2009  18

                                        The MODEL Procedure

                                          Model Summary

                                    Model Variables         27
                                    Parameters              27
                                    Equations               27
                                    Number of Statements    27

   Model Variables  a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13 a14 a15
                    a16 a17 a18 a19 a20 a21 a22 a23 a24 a25 a26 a27
 Parameters(Value)  intercept(5.7109172742) year_indx(-0.080432554) discrete(-0.124827951)
                    volunt(-1.323276929) nonparam(-0.669751797) income(2.6976685E-6)
                    ladder_study(-0.327490299) outlier_bids(-0.883717183)
                    single_river(-0.427917854) single_lake(-0.063159141)
                    multiple_river(-1.47521449) regional_fresh(0.1587758407)
                    salt_pond(0.9848700459) num_rivers_ponds(0.1173029891) mr(-0.884565067)
                    mp(1.633700551) nonusers(-0.403633614) allmult(-0.372786316)
                    nonspec(-0.404240487) lnquality_ch(0.4065123858) fish_use(-0.331694528)
                    fishplus(0.4432319802) lnbase(0.0260995136) mail(-0.201310504)
                    lump_sum(0.5569281118) non_reviewed(-0.271820763) median_WTP(-0.535754181)
         Equations  a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13 a14 a15
                    a16 a17 a18 a19 a20 a21 a22 a23 a24 a25 a26 a27
                                          The SAS System        11:19 Monday, November 23, 2009  19

                                        The MODEL Procedure
                                      Simultaneous Simulation

NOTE: Variables for only 26 of the 27 parameters were found in the ESTDATA=BOOTCOV3 data set.
The following parameters were found:
intercept
year_indx
discrete
volunt
nonparam
income
ladder_study
outlier_bids
single_river
single_lake
multiple_river
regional_fresh
salt_pond
num_rivers_ponds
mr
mp
nonusers
allmult
lnquality_ch
fish_use
fishplus
lnbase
mail
lump_sum
non_reviewed
median_WTP
                                          The SAS System        11:19 Monday, November 23, 2009  20

                                        The MODEL Procedure
                                      Simultaneous Simulation

                                         Data Set Options

                                       DATA=       ONEOBS
                                       ESTDATA=    BOOTCOV3
                                       OUT=        BOOTWTP

                                         Solution Summary

                                  Variables Solved             27
                                  Random Replications       10000
                                  Seed                        123
                                  Solution Method          NEWTON
                                  CONVERGE=                  1E-8
                                  Maximum CC             6.63E-15
                                  Maximum Iterations            1
                                  Total Iterations          10001
                                  Average Iterations            1

                                       Observations Processed

                                          Read          1
                                          Solved    10001

                                       Variables Solved For

a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13 a14 a15 a16 a17 a18 a19 a20 a21 a22 a23 a24 a25 a26 a27