IFA to IRT

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IFA to IRT Powered By Docstoc
					                               Binary Example
Item                                        0=needs help   1=no help
       1                                            0.36          0.64
       2                                            0.16          0.84
       3                                            0.23          0.77
       4                                            0.34          0.66
       5                                            0.35          0.65
       6                                            0.27          0.73
       7                                            0.06          0.94



                             Polytomous Example
Item       0=Can't Do It 1=Big Problems 2=Some Problems 3=Can Do It
       1            0.09             0.08            0.26      0.58
       2            0.07             0.04            0.12      0.77
       3            0.09             0.05            0.15      0.72
       4            0.10             0.09            0.19      0.62
       5            0.06             0.16            0.21      0.57
       6            0.06             0.08            0.12      0.74
       7            0.01             0.03            0.08      0.88
                                    Binary Example

                  IFA      IFA                Pred       Pred        Logit
  Item                             Theta
               Intercept Loading              Logit      Prob       to Prob
           1         1.629   4.328     0         1.629      0.836         0.836
           7         5.962   3.283     0         5.962      0.997         0.997

                                              Pred       Pred        Logit
  Item          IRT b       IRT a     Theta
                                              Logit      Prob       to Prob
           1       -0.376     2.546       0      1.627      0.836         0.836
           7       -1.816     1.931       0      5.961      0.997         0.997



                             Polytmous GRM Example

                  IFA      IFA                Pred       Pred        Logit
 Item 1                            Theta
               Intercept Loading              Logit      Prob       to Prob
0 vs 123             9.808   6.846      0        9.808    0.99994       0.99994
01 vs 23             6.460   6.846      0        6.460    0.99844       0.99844
012 vs 3             1.238   6.846      0        1.238    0.77522       0.77522
0 vs 123             9.808   6.846     -1        2.962    0.95083       0.95083
01 vs 23             6.460   6.846     -1       -0.386    0.40468       0.40468
012 vs 3             1.238   6.846     -1       -5.608    0.00365       0.00365
                  FILL IN                                                 CALCULATED
Factor Mean                         0
Factor Variance                     1
Link Transformation               1.7
Error Variance                   3.29

                           Example for Binary Model (was estimated in ML logit)

                             Unstandardized            Calculated IRT            Calculated STDYX
Item                        Loading Thresh            pred a    pred b        Loading Thresh    R2
DIA1                           4.328    -1.629          2.546    -0.376         0.922 -0.347    0.851
DIA2                           4.978    -5.202          2.928    -1.045         0.940 -0.982    0.883
DIA3                           4.323    -3.462          2.543    -0.801         0.922 -0.738    0.850
DIA4                           7.511    -3.120          4.418    -0.415         0.972 -0.404    0.945
DIA5                           4.248    -1.833          2.499    -0.431         0.920 -0.397    0.846
DIA6                           3.451    -2.442          2.030    -0.708         0.885 -0.626    0.784
DIA7                           3.283    -5.962          1.931    -1.816         0.875 -1.590    0.766



                  FILL IN                                                 CALCULATED
Factor Mean                         0
Factor Variance                     1
Link Transformation               1.7
Error Variance                   3.29
           Example for 4-Category Graded Response Model (was estiamted in ML logit)
                             Unstandardized            Calculated IRT              Calculated STDYX
Item                        Loading Thresh            pred a    pred b        Loading Thresh      R2
CIA1                           6.846                    4.027                     0.967           0.934
                      $1                -9.808                   -1.433                   -1.385
                      $2                -6.460                   -0.944                   -0.912
                      $3                -1.238                   -0.181                   -0.175
CIA2                           5.200                    3.059                     0.944           0.892
                      $1                -8.145                   -1.566                   -1.479
                      $2                -6.313                   -1.214                   -1.146
                      $3                -3.737                   -0.719                   -0.679
CIA3                           4.613                    2.714                     0.931           0.866
                      $1                -6.841                   -1.483                   -1.380
                      $2                -5.194                   -1.126                   -1.048
                      $3                -2.572                   -0.558                   -0.519
CIA4                           5.701                    3.354                     0.953           0.908
                      $1                -7.454                   -1.307                   -1.246
                      $2                -4.635                   -0.813                   -0.775
                      $3                -1.426                   -0.250                   -0.238
CIA5                           3.556                    2.092                     0.891           0.794
                      $1                -6.578                   -1.850                   -1.648
                      $2                -3.041                   -0.855                   -0.762
                      $3                  -0.681                     -0.192                   -0.171
CIA6                            2.897                      1.704                     0.848                 0.718
                      $1                  -5.538                     -1.912                   -1.620
                      $2                  -3.583                     -1.237                   -1.048
                      $3                  -2.044                     -0.706                   -0.598
CIA7                            1.778                      1.046                     0.700                 0.490
                      $1                  -5.810                     -3.268                   -2.287
                      $2                  -4.398                     -2.474                   -1.732
                      $3                  -2.951                     -1.660                   -1.162

Note: For items with more than 3 thresholds, you will need to insert rows within each set of thresholds.
                        Note: It is your job to keep track of whether LL should go up or down!
                                       These formulas work with absolute values.
                                     FILL IN                                                     CALCULATED

                                               Model       # Free                   Abs Value      DF
                    Model                                                LL*-2
                                               H0 LL       Parms                    -2*LL Diff     Diff

Binary 2PL                                     -1454.634            14   2909.268
Binary 1PL                                     -1464.457             8   2928.914
   vs. Binary 2PL                                                                      19.646             6

Categorical 2PL (GRM)                          -2523.585            28   5047.170
Categorical 1PL (Rasch GRM)                    -2591.310            22   5182.620
   vs. Categorical 2PL                                                                135.450             6

Binary 2PL NLMIXED                                                  14   2907.400
Binary 1PL NLMIXED                                                   8   2927.900
   vs. Binary 2PL                                                                      20.500             6

Categorical 2PL (GRM) NLMIXED                                       28   5045.400
Categorical 1PL (Rasch GRM) NLMIXED                                 22   5182.400
   vs. Categorical 2PL                                                                137.000             6
n!


 CALCULATED

              Exact p
               Value




              0.0032010




              0.0000000




              0.0022551




              0.0000000
                Binary Model
        Item            Model   Difficulty Threshold p(y=1) if Theta = 0
1. Housework         0 vs 1          -0.376    -1.629                0.84                            Item Difficulty
2. Bedmaking         1 vs 1          -1.045    -5.202                0.99                           0.0
3. Cooking           2 vs 1          -0.801    -3.462                0.97                          -0.2
4. Shopping          3 vs 1          -0.415    -1.833                0.86                          -0.4




                                                                                 Item Difficulty
5. Getting around    4 vs 1          -0.432    -2.442                0.92                          -0.6
6. Banking           5 vs 1          -0.708    -3.120                0.96                          -0.8
7. Telephone         6 vs 1          -1.816    -5.962                1.00
                                                                                                   -1.0
                                                                                                   -1.2
                                                                                                   -1.4
                                                                                                   -1.6
                                                                                                   -1.8
                                                                                                   -2.0
                                                                                                          1. Housework




0=Can't Do It
1=Big Problems
2=Some Problems
3=Can Do It


                    Polytomous Graded Response Model
        Item         Submodel Difficulty Threshold p(y=1) if Theta = 0                             0.0
1. Housework        0 vs 123       -1.433     -9.808               1.00
2. Bedmaking        0 vs 123       -1.566     -8.145               1.00                       -0.5
3. Cooking          0 vs 123       -1.483     -6.841               1.00
4. Shopping         0 vs 123       -1.307     -7.454               1.00                       -1.0
                                                                            Item Difficulty

5. Getting around   0 vs 123       -1.850     -6.578               1.00
6. Banking          0 vs 123       -1.912     -5.538               1.00                       -1.5
7. Telephone        0 vs 123       -3.268     -5.810               1.00
                                                                                              -2.0
1. Housework        01 vs 23       -0.944     -6.460               1.00
2. Bedmaking        01 vs 23       -1.214     -6.313               1.00
                                                                                              -2.5
3. Cooking          01 vs 23       -1.126     -5.194               0.99
4. Shopping         01 vs 23       -0.813     -4.635               0.99
                                                                                              -3.0
5. Getting around   01 vs 23       -0.855     -3.041               0.95
6. Banking          01 vs 23       -1.237     -3.583               0.97                       -3.5
7. Telephone        01 vs 23       -2.474     -4.398               0.99
1. Housework        012 vs 3       -0.181     -1.238               0.78
2. Bedmaking        012 vs 3       -0.719     -3.737               0.98
3. Cooking          012 vs 3       -0.558     -2.572               0.93
4. Shopping         012 vs 3       -0.250     -1.426               0.81
5. Getting around   012 vs 3       -0.192     -0.681               0.66
6. Banking     012 vs 3   -0.706   -2.044   0.89
7. Telephone   012 vs 3   -1.660   -2.951   0.95
Item Difficulty -- these are the Theta values at which prob(y=1) = .50                                     Item Thresholds -- these are the logits of

                                                                                                           0.0
                                                                                                           -1.0




                                                                                          Item Threshold
                                                                                                           -2.0
                                                                                                           -3.0
                                                                                                           -4.0
                                                                                                           -5.0
                                                                                                           -6.0
                                                                                                           -7.0
  1. Housework           3. Cooking          5. Getting around   7. Telephone                                     1. Housework         3. Cooking




                  0 vs 123        01 vs 23         012 vs 3                                                                       0 vs 123
                                                                                                      0.0
                                                                                                  -1.0
                                                                                                  -2.0
                                                                                                  -3.0
                                                                                Item Threshold




                                                                                                  -4.0
                                                                                                  -5.0
                                                                                                  -6.0
                                                                                                  -7.0
                                                                                                  -8.0
                                                                                                  -9.0
                                                                                           -10.0
these are the logits of (y=0) for someone with Theta = 0                                                 These are the implied probabilities of (y = 1) for some

                                                                                                         1.00




                                                                     Probability of y = 1 if Theta = 0
                                                                                                         0.95

                                                                                                         0.90

                                                                                                         0.85

                                                                                                         0.80

                                                                                                         0.75
        3. Cooking          5. Getting around   7. Telephone




   0 vs 123          01 vs 23       012 vs 3                                                                                  0 vs 123        01 vs 23
                                                                                                         1.00

                                                                                                         0.95
                                                               Probability of y = 1 if Theta = 0




                                                                                                         0.90

                                                                                                         0.85

                                                                                                         0.80

                                                                                                         0.75

                                                                                                         0.70

                                                                                                         0.65

                                                                                                         0.60
lities of (y = 1) for someone with Theta = 0




      01 vs 23        012 vs 3
Theta      Item 1    Item 2    Item 3    Item 4    Item 5    Item 6    Item 7
     -3.00     0.000     0.000     0.000     0.000     0.000     0.000     0.020
     -2.80     0.000     0.000     0.000     0.000     0.000     0.001     0.038
     -2.60     0.000     0.000     0.000     0.000     0.000     0.001     0.071
     -2.40     0.000     0.001     0.001     0.000     0.000     0.003     0.128                       1.0
     -2.20     0.000     0.003     0.002     0.000     0.001     0.006     0.221                       0.9
     -2.00     0.001     0.009     0.006     0.000     0.001     0.011     0.353                       0.8
     -1.80     0.002     0.023     0.013     0.000     0.003     0.023     0.513




                                                                                   Probability (y=1)
                                                                                                       0.7
     -1.60     0.005     0.059     0.031     0.000     0.007     0.044     0.670
                                                                                                       0.6
     -1.40     0.012     0.146     0.070     0.001     0.016     0.084     0.797
     -1.20     0.028     0.316     0.151     0.003     0.037     0.155     0.883                       0.5
     -1.00     0.063     0.556     0.297     0.012     0.082     0.267     0.936                       0.4
     -0.80     0.138     0.772     0.501     0.053     0.173     0.421     0.966                       0.3
     -0.60     0.275     0.902     0.704     0.200     0.328     0.592     0.982                       0.2
     -0.40     0.474     0.961     0.850     0.529     0.533     0.743     0.991
                                                                                                       0.1
     -0.20     0.682     0.985     0.931     0.834     0.728     0.852     0.995
      0.00     0.836     0.995     0.970     0.958     0.862     0.920     0.997                       0.0
      0.20     0.924     0.998     0.987     0.990     0.936     0.958     0.999                             -3.0
      0.40     0.966     0.999     0.994     0.998     0.972     0.979     0.999
      0.60     0.986     1.000     0.998     1.000     0.988     0.989     1.000
      0.80     0.994     1.000     0.999     1.000     0.995     0.995     1.000
      1.00     0.997     1.000     1.000     1.000     0.998     0.997     1.000
      1.20     0.999     1.000     1.000     1.000     0.999     0.999     1.000
      1.40     1.000     1.000     1.000     1.000     1.000     0.999     1.000
      1.60     1.000     1.000     1.000     1.000     1.000     1.000     1.000
      1.80     1.000     1.000     1.000     1.000     1.000     1.000     1.000
      2.00     1.000     1.000     1.000     1.000     1.000     1.000     1.000
      2.20     1.000     1.000     1.000     1.000     1.000     1.000     1.000
      2.40     1.000     1.000     1.000     1.000     1.000     1.000     1.000
      2.60     1.000     1.000     1.000     1.000     1.000     1.000     1.000
      2.80     1.000     1.000     1.000     1.000     1.000     1.000     1.000
      Item Characteristic Curves (not parallel for 2PL)

                                                                Item 1
                                                                Item 2
                                                                Item 3
                                                                Item 4
                                                                Item 5
                                                                Item 6
                                                                Item 7


3.0     -2.2     -1.4    -0.6      0.2      1.0           1.8       2.6
               Theta (Mean = 0, Variance = 1)
                                                                                              BINARY ITEMS
Theta   Test Information Theta Standard Error
   -4.0              0.01               10.88
   -3.8              0.02                7.83
   -3.6              0.03                5.64                                               Test Information
   -3.4              0.06                4.07                             Info 30 =
                                                                   28     Reliability .97
   -3.2              0.12                2.94                                                                  The test has NO
   -3.0              0.22                2.13                      24
                                                                                                               information at al




                                                Test Information
   -2.8              0.41                1.56                      20                                          past Theta
   -2.6              0.75                1.16
   -2.4              1.29                0.88                      16
   -2.2              2.06                0.70                      12
   -2.0              2.95                0.58
                                                                   8
   -1.8              3.84                0.51
   -1.6              5.05                0.45                      4
   -1.4              7.50                0.37                      0
   -1.2            11.72                 0.29
                                                                          -2.0 -1.6 -1.2 -0.8 -0.4 0.0 0.4 0.8
   -1.0            16.15                 0.25
   -0.8            19.92                 0.22                                           Theta (Mean = 0, Variance = 1)
   -0.6            25.90                 0.20
   -0.4            28.90                 0.19
   -0.2            18.55                 0.23
    0.0              8.59                0.34                 Info        Reliability
    0.2              3.73                0.52                        28      0.9655
    0.4              1.61                0.79                        24      0.9600
    0.6              0.70                1.20                        20      0.9524
    0.8              0.30                1.82                        16      0.9412
    1.0              0.13                2.74                        10      0.9091
    1.2              0.06                4.12                         9      0.9000
    1.4              0.03                6.18                         6      0.8571
    1.6              0.01                9.22                         5      0.8333
    1.8              0.01               13.72                         4      0.8000
    2.0              0.00               20.33
    2.2              0.00               30.02
    2.4              0.00               44.28
    2.6              0.00               64.55
    2.8              0.00               95.35
    3.0              0.00              141.42
    3.2              0.00              182.57
    3.4              0.00              316.23
    3.6              0.00              316.23
EMS
                                                                                                                     Theta
                                                                                                                        -4.0
                                                                                                                        -3.8
                                                                         Theta Standard Error                           -3.6
                                                            2.0                                                         -3.4
                                                            1.8     SE = 1 /SQRT(info)                                  -3.2
         The test has NO
         information at all
                                                            1.6                                                         -3.0

                                     Theta Standard Error
         past Theta = 1!                                    1.4                                                         -2.8
                                                            1.2                                                         -2.6
                                                            1.0                                                         -2.4
                                                            0.8                                                         -2.2
             Info 4 =                                       0.6                                                         -2.0
             Reliability .80                                                                                            -1.8
                                                            0.4
                                                            0.2                                                         -1.6
                                                                                                                        -1.4
                                                            0.0
                                                                                                                        -1.2
            0.8 1.2     1.6    2.0                                -2.0 -1.6 -1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 1.6 2.0
                                                                                                                        -1.0
= 0, Variance = 1)                                                          Theta (Mean = 0, Variance = 1)              -0.8
                                                                                                                        -0.6
                                                                                                                        -0.4
                                                                                                                        -0.2
                                                                                                                         0.0
                                                                                                                         0.2
                                                                                                                         0.4
                                                                                                                         0.6
                                                                                                                         0.8
                                                                                                                         1.0
                                                                                                                         1.2
                                                                                                                         1.4
                                                                                                                         1.6
                                                                                                                         1.8
                                                                                                                         2.0
                                                                                                                         2.2
                                                                                                                         2.4
                                                                                                                         2.6
                                                                                                                         2.8
                                                                                                                         3.0
                                                                                                                         3.2
                                                                                                                         3.4
                                                                                                                         3.6
                                                                                                                         3.8
                                                                                    POLYTOMOUS ITEMS
            Theta
Test Information Standard Error
             0.09    3.31
             0.13    2.82                                                      Test Information
             0.17    2.41                                  Info 30 =
                                                     28    Reliability .97
             0.23    2.06
                                                                                                      The test has NO
             0.32    1.76                            24
                                                                                                      information at all




                                  Test Information
             0.45    1.49                            20                                               past Theta = 1!
             0.64    1.25
             0.92    1.04                            16
             1.35    0.86                            12
             2.02    0.70                                                                                 Info 4 =
             3.08    0.57                            8                                                    Reliability .80
             4.91    0.45                            4
             7.95    0.35
                                                     0
           11.40     0.30
                                                          -3.0    -2.4       -1.8 -1.2 -0.6 0.0         0.6      1.2        1.8
           14.56     0.26
           19.14     0.23                                                      Theta (Mean = 0, Variance = 1)
           22.48     0.21
           23.18     0.21
           24.68     0.20
           24.76     0.20
           16.16     0.25
             7.28    0.37
             3.00    0.58
             1.28    0.88
             0.58    1.31
             0.28    1.90
             0.14    2.69
             0.07    3.73
             0.04    5.09
             0.02    6.84
             0.01    9.07
             0.01   11.84
             0.00   15.27
             0.00   19.43
             0.00   24.47
             0.00   30.43
             0.00   37.53
             0.00   46.13
             0.00   56.80
             0.00   69.01
                                           Theta Standard Error
                             2.0
                             1.8     SE = 1 /SQRT(info)
                             1.6
      Theta Standard Error




                             1.4
                             1.2
                             1.0
                             0.8
                             0.6
                             0.4
                             0.2
                             0.0
1.8                                -3.0 -2.4 -1.8 -1.2 -0.6 0.0 0.6 1.2       1.8
                                             Theta (Mean = 0, Variance = 1)
                          Saved from Mplus                                             Calculated Based on Mplus
Theta          Prob of 0 Prob of 1 Prob of 2 Prob of 3    Theta          Prob of 0 vs 123 Prob of 01 vs 23
        -4.0            1         0         0         0           -4.0               0.000             0.000
        -3.8            1         0         0         0           -3.8               0.000             0.000
        -3.6            1         0         0         0           -3.6               0.000             0.000
        -3.4            1         0         0         0           -3.4               0.000             0.000
        -3.2     0.99999 0.00001            0         0           -3.2               0.000             0.000
        -3.0     0.99998 0.00002            0         0           -3.0               0.000             0.000
        -2.8     0.99991 0.00008            0         0           -2.8               0.000             0.000
        -2.6     0.99966 0.00033 0.00001              0           -2.6               0.000             0.000
        -2.4     0.99867 0.00128 0.00005              0           -2.4               0.001             0.000
        -2.2      0.9948 0.00502 0.00018              0           -2.2               0.005             0.000
        -2.0     0.97985 0.01943 0.00072              0           -2.0               0.020             0.001
        -1.8     0.92517 0.07199 0.00282 0.00002                  -1.8               0.075             0.003
        -1.6     0.75871 0.23024       0.011 0.00006              -1.6               0.241             0.011
        -1.4     0.44433 0.51356 0.04187 0.00024                  -1.4               0.556             0.042
        -1.2     0.16899 0.68362 0.14646 0.00093                  -1.2               0.831             0.147
        -1.0     0.04917 0.54615 0.40103 0.00365                  -1.0               0.951             0.405
        -0.8     0.01298 0.25928 0.71352 0.01422                  -0.8               0.987             0.728
        -0.6     0.00333 0.08354 0.85945 0.05368                  -0.6               0.997             0.913
        -0.4     0.00085 0.02277 0.79401 0.18237                  -0.4               0.999             0.976
        -0.2     0.00022    0.0059 0.52664 0.46725                -0.2               1.000             0.994
         0.0     0.00006 0.00151 0.22322 0.77522                   0.0               1.000             0.998
         0.2     0.00001 0.00038 0.06828 0.93132                   0.2               1.000             1.000
         0.4            0   0.0001 0.01831 0.98159                 0.4               1.000             1.000
         0.6            0 0.00002 0.00472 0.99525                  0.6               1.000             1.000
         0.8            0 0.00001     0.0012 0.99879               0.8               1.000             1.000
         1.0            0         0 0.00031 0.99969                1.0               1.000             1.000
         1.2            0         0 0.00008 0.99992                1.2               1.000             1.000
         1.4            0         0 0.00002 0.99998                1.4               1.000             1.000
         1.6            0         0 0.00001 0.99999                1.6               1.000             1.000
         1.8            0         0         0         1            1.8               1.000             1.000
         2.0            0         0         0         1            2.0               1.000             1.000
         2.2            0         0         0         1            2.2               1.000             1.000
         2.4            0         0         0         1            2.4               1.000             1.000
         2.6            0         0         0         1            2.6               1.000             1.000
         2.8            0         0         0         1            2.8               1.000             1.000
         3.0            0         0         0         1            3.0               1.000             1.000
         3.2            0         0         0         1            3.2               1.000             1.000
         3.4            0         0         0         1            3.4               1.000             1.000
         3.6            0         0         0         1            3.6               1.000             1.000
         3.8            0         0         0         1            3.8               1.000             1.000
         4.0            0         0         0         1            4.0               1.000             1.000
d Based on Mplus                   4.027             -1.433           -0.944          -0.181
            Prob of 012 vs 3   Theta      Prob of 0 vs 123 Prob of 01 vs 23 Prob of 012 vs 3
                       0.000         -4.0             0.000            0.000           0.000
                       0.000         -3.8             0.000            0.000           0.000
                       0.000         -3.6             0.000            0.000           0.000
                       0.000         -3.4             0.000            0.000           0.000
                       0.000         -3.2             0.000            0.000           0.000
                       0.000         -3.0             0.000            0.000           0.000
                       0.000         -2.8             0.000            0.000           0.000
                       0.000         -2.6             0.000            0.000           0.000
                       0.000         -2.4             0.001            0.000           0.000
                       0.000         -2.2             0.005            0.000           0.000
                       0.000         -2.0             0.020            0.001           0.000
                       0.000         -1.8             0.075            0.003           0.000
                       0.000         -1.6             0.242            0.011           0.000
                       0.000         -1.4             0.556            0.042           0.000
                       0.001         -1.2             0.831            0.148           0.001
                       0.004         -1.0             0.951            0.405           0.004
                       0.014         -0.8             0.987            0.728           0.014
                       0.054         -0.6             0.997            0.913           0.054
                       0.182         -0.4             0.999            0.976           0.183
                       0.467         -0.2             1.000            0.994           0.468
                       0.775          0.0             1.000            0.998           0.775
                       0.931          0.2             1.000            1.000           0.931
                       0.982          0.4             1.000            1.000           0.982
                       0.995          0.6             1.000            1.000           0.995
                       0.999          0.8             1.000            1.000           0.999
                       1.000          1.0             1.000            1.000           1.000
                       1.000          1.2             1.000            1.000           1.000
                       1.000          1.4             1.000            1.000           1.000
                       1.000          1.6             1.000            1.000           1.000
                       1.000          1.8             1.000            1.000           1.000
                       1.000          2.0             1.000            1.000           1.000
                       1.000          2.2             1.000            1.000           1.000
                       1.000          2.4             1.000            1.000           1.000
                       1.000          2.6             1.000            1.000           1.000
                       1.000          2.8             1.000            1.000           1.000
                       1.000          3.0             1.000            1.000           1.000
                       1.000          3.2             1.000            1.000           1.000
                       1.000          3.4             1.000            1.000           1.000
                       1.000          3.6             1.000            1.000           1.000
                       1.000          3.8             1.000            1.000           1.000
                       1.000          4.0             1.000            1.000           1.000

				
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