Document ID: EPA-HQ-OW-2008-0465-0909
Agency: epa
Document Type: Supporting & Related Material
Title: 
Posted Date: 2009-01-06T05:00Z

The SAS System         11:04 Friday, November 14, 2008   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 1202 1207 1226 
                                              1245 1246 1251 1252 1254 1262 
                                              1278 1287 1295 1310 1311 1312 
                                              1317 1395 1405 1423 1445 1461 
                                              1472 1512 1553 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       115.36292651                
                             1              4       115.36292651      0.00000000

                                            The SAS System         11:04 Friday, November 14, 2008   2

                                         The Mixed Procedure

                                      Convergence criteria met.                    

                                    Covariance Parameter Estimates
 
                                   Cov Parm     Subject    Estimate

                                   UN(1,1)      auth_id    5.21E-19
                                   Residual                  0.1597

                                           Fit Statistics

                                -2 Log Likelihood               115.4
                                AIC (smaller is better)         171.4
                                AICC (smaller is better)        190.2
                                BIC (smaller is better)         221.9

                                   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             5.8982      0.5566      25      10.60      <.0001
               year_indx           -0.05899     0.01755      63      -3.36      0.0013
               discrete             -0.1530      0.1673      63      -0.91      0.3638
               volunt               -1.2937      0.1550      63      -8.35      <.0001
               nonparam             -0.6919      0.1122      63      -6.16      <.0001
               INCOME               -6.1E-7    3.348E-6      63      -0.18      0.8561
               ladder_study         -0.3709      0.2076      63      -1.79      0.0789
               OUTLIER_BIDS         -0.7108      0.2133      63      -3.33      0.0014
               single_river         -0.2250      0.1162      63      -1.94      0.0572
               single_lake          -0.1391      0.2161      63      -0.64      0.5223
               multiple_river       -1.4485      0.3086      63      -4.69      <.0001
               regional_fresh        0.2698      0.1290      63       2.09      0.0405
               salt_pond             1.2163      0.3181      63       3.82      0.0003
               num_rivers_ponds      0.1104     0.02346      63       4.71      <.0001
               mr                   -0.8014      0.1226      63      -6.54      <.0001
               mp                    1.3534      0.2042      63       6.63      <.0001
               nonusers             -0.4512      0.1278      63      -3.53      0.0008
               allmult              -0.4073      0.1189      63      -3.43      0.0011
               nonspec              -0.2419      0.1550      63      -1.56      0.1237
               quality_ch           0.03405    0.006313      63       5.39      <.0001
               fish_use             -0.4505     0.08377      63      -5.38      <.0001

                                            The SAS System         11:04 Friday, November 14, 2008   3

                                         The Mixed Procedure

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

               fishplus              0.3781      0.1108      63       3.41      0.0011
               Index_Base_Low      0.005770    0.003655      63       1.58      0.1195
               mail                 -0.3450      0.1199      63      -2.88      0.0055
               lump_sum              0.7039      0.1728      63       4.07      0.0001
               non_reviewed         -0.4007      0.1205      63      -3.32      0.0015
               median_WTP           -0.4399      0.1986      63      -2.21      0.0304

                                     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    1202              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           .       .        .         .    

                                            The SAS System         11:04 Friday, November 14, 2008   4

                                         The Mixed Procedure

                                     Solution for Random Effects
 
                                                  Std Err
             Effect       auth_id    Estimate        Pred      DF    t Value    Pr > |t|

             Intercept    1445              0           .       .        .         .    
             Intercept    1461              0           .       .        .         .    
             Intercept    1472              0           .       .        .         .    
             Intercept    1512              0           .       .        .         .    
             Intercept    1553              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      11.30    0.0013
                        discrete               1      63       0.84    0.3638
                        volunt                 1      63      69.69    <.0001
                        nonparam               1      63      38.01    <.0001
                        INCOME                 1      63       0.03    0.8561
                        ladder_study           1      63       3.19    0.0789
                        OUTLIER_BIDS           1      63      11.10    0.0014
                        single_river           1      63       3.75    0.0572
                        single_lake            1      63       0.41    0.5223
                        multiple_river         1      63      22.04    <.0001
                        regional_fresh         1      63       4.37    0.0405
                        salt_pond              1      63      14.62    0.0003
                        num_rivers_ponds       1      63      22.15    <.0001
                        mr                     1      63      42.72    <.0001
                        mp                     1      63      43.91    <.0001
                        nonusers               1      63      12.46    0.0008
                        allmult                1      63      11.74    0.0011
                        nonspec                1      63       2.43    0.1237
                        quality_ch             1      63      29.10    <.0001
                        fish_use               1      63      28.93    <.0001
                        fishplus               1      63      11.65    0.0011
                        Index_Base_Low         1      63       2.49    0.1195
                        mail                   1      63       8.27    0.0055
                        lump_sum               1      63      16.59    0.0001
                        non_reviewed           1      63      11.05    0.0015
                        median_WTP             1      63       4.91    0.0304