Document ID: EPA-HQ-OW-2008-0465-1862
Agency: epa
Document Type: Supporting & Related Material
Title: 
Posted Date: 2009-12-07T05:00Z

The SAS System         15:22 Monday, November 9, 2009   1

                                        The Mixed Procedure

                                        Model Information

                      Data Set                     WORK.META2               
                      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       115.53686060                
                            1              4       115.53686060      0.00000000
                                          The SAS System         15:22 Monday, November 9, 2009   2

                                        The Mixed Procedure

                                    Convergence criteria met.                    

                                  Covariance Parameter Estimates
 
                                 Cov Parm     Subject    Estimate

                                 UN(1,1)      auth_id           0
                                 Residual                  0.1599

                                          Fit Statistics

                               -2 Log Likelihood               115.5
                               AIC (smaller is better)         171.5
                               AICC (smaller is better)        190.4
                               BIC (smaller is better)         222.1

                                 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             6.0946      0.5127      25      11.89      <.0001
              year_indx           -0.06707     0.01430      63      -4.69      <.0001
              discrete             -0.1696      0.1735      63      -0.98      0.3319
              volunt               -1.3049      0.1661      63      -7.86      <.0001
              nonparam             -0.6892      0.1164      63      -5.92      <.0001
              INCOME              -1.16E-7    3.328E-6      63      -0.03      0.9723
              ladder_study         -0.3631      0.2096      63      -1.73      0.0881
              OUTLIER_BIDS         -0.7829      0.2164      63      -3.62      0.0006
              single_river         -0.2724      0.1222      63      -2.23      0.0294
              single_lake          -0.1268      0.2223      63      -0.57      0.5704
              multiple_river       -1.5054      0.3184      63      -4.73      <.0001
              regional_fresh        0.2219      0.1168      63       1.90      0.0620
              salt_pond             1.1357      0.3142      63       3.61      0.0006
              num_rivers_ponds      0.1145     0.02510      63       4.56      <.0001
              mr                   -0.7932      0.1343      63      -5.91      <.0001
              mp                    1.5168      0.2574      63       5.89      <.0001
              nonusers             -0.4451      0.1301      63      -3.42      0.0011
              allmult              -0.4044      0.1266      63      -3.20      0.0022
              nonspec              -0.2988      0.1351      63      -2.21      0.0306
              quality_ch           0.03208    0.006337      63       5.06      <.0001
              fish_use             -0.4480      0.1034      63      -4.33      <.0001
                                          The SAS System         15:22 Monday, November 9, 2009   3

                                        The Mixed Procedure

                                    Solution for Fixed Effects
 
                                              Standard
              Effect              Estimate       Error      DF    t Value    Pr > |t|

              fishplus              0.4017      0.1217      63       3.30      0.0016
              Index_Base_Low      0.005205    0.003739      63       1.39      0.1688
              mail                 -0.3073      0.1155      63      -2.66      0.0099
              lump_sum              0.7188      0.1873      63       3.84      0.0003
              non_reviewed         -0.3744      0.1234      63      -3.03      0.0035
              median_WTP           -0.4675      0.1898      63      -2.46      0.0165

                                    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         15:22 Monday, November 9, 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      22.01    <.0001
                       discrete               1      63       0.96    0.3319
                       volunt                 1      63      61.73    <.0001
                       nonparam               1      63      35.07    <.0001
                       INCOME                 1      63       0.00    0.9723
                       ladder_study           1      63       3.00    0.0881
                       OUTLIER_BIDS           1      63      13.09    0.0006
                       single_river           1      63       4.97    0.0294
                       single_lake            1      63       0.33    0.5704
                       multiple_river         1      63      22.36    <.0001
                       regional_fresh         1      63       3.61    0.0620
                       salt_pond              1      63      13.07    0.0006
                       num_rivers_ponds       1      63      20.80    <.0001
                       mr                     1      63      34.91    <.0001
                       mp                     1      63      34.74    <.0001
                       nonusers               1      63      11.71    0.0011
                       allmult                1      63      10.21    0.0022
                       nonspec                1      63       4.89    0.0306
                       quality_ch             1      63      25.62    <.0001
                       fish_use               1      63      18.77    <.0001
                       fishplus               1      63      10.89    0.0016
                       Index_Base_Low         1      63       1.94    0.1688
                       mail                   1      63       7.08    0.0099
                       lump_sum               1      63      14.72    0.0003
                       non_reviewed           1      63       9.21    0.0035
                       median_WTP             1      63       6.06    0.0165