各位大神，求教个问题，在用广义倾向得分匹配（GPS）分析时，老是出现两个问题：1. The assumption of Normality is not statistically satisfied at .05 level
It is advisable to try a different trasformation of the treatment variable
2. 1 group found, 2 required

对于第一个问题，我依次尝试了ln, lnskew0, bcskew0,boxcox几种不同形式，还是出现这种提示。
求教对这两个问题应该如何解决，万分感谢！！

回归结果如下：
qui generate cut=20 if cen<=20

. . qui replace cut=40 if cen>20 & cen<=40

. . qui replace cut=60 if cen>40 & cen<=60

. . qui replace cut=80 if cen>60

. . qui replace cut=100 if cen>80

. matrix define tp=(10\20\30\40\50\60\70\80\90\100)

. doseresponse lnta , outcome(lntotal) t(cen) gpscore(pscore) predict(hat_treat) sigma(sd) cutpoints(cut) index(p50) nq_gps(5) t _transf(boxcox) dose_response(dose_response) tpoints(tp) delta(1) reg_type_t(quadratic) reg_type_gps(quadratic) interaction(1) bootstrap(yes) boot_reps(100) filename("output") analysis(yes) graph("graph_output") detail

********************************************
ESTIMATE OF THE GENERALIZED PROPENSITY SCORE
********************************************

Generalized Propensity Score

******************************************************
Algorithm to estimate the generalized propensity score
******************************************************



Estimation of the propensity score

The BoxCox transformation of the treatment variable cen is used

                              T
-------------------------------------------------------------
      Percentiles      Smallest
1%     1.166742       1.166742
5%     1.179652       1.166742
10%     1.179652       1.166742       Obs              22,231
25%     1.219498       1.166742       Sum of Wgt.      22,231

50%     1.252957                      Mean            1.26956
                        Largest       Std. Dev.      .0656851
75%     1.340244       1.384281
90%     1.360923       1.384766       Variance       .0043145
95%     1.368533       1.384929       Skewness       .2122693
99%     1.376733       1.384948       Kurtosis       1.628219

initial:       log likelihood =     -<inf>  (could not be evaluated)
feasible:      log likelihood = -31542.819
rescale:       log likelihood = -21284.562
rescale eq:    log likelihood = -3300.4439
Iteration 0:   log likelihood = -3300.4439  (not concave)
Iteration 1:   log likelihood =  14393.478  (not concave)
Iteration 2:   log likelihood =  27857.065  
Iteration 3:   log likelihood =  28702.593  
Iteration 4:   log likelihood =  29035.453  
Iteration 5:   log likelihood =  29039.052  
Iteration 6:   log likelihood =  29039.053  

                                                Number of obs     =     22,231
                                                Wald chi2(1)      =     101.38
Log likelihood =  29039.053                     Prob > chi2       =     0.0000

------------------------------------------------------------------------------
           T |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
eq1          |
        lnta |   .0032904   .0003268    10.07   0.000     .0026499    .0039309
       _cons |   1.198379   .0070833   169.18   0.000     1.184496    1.212261
-------------+----------------------------------------------------------------
eq2          |
       _cons |   .0655344   .0003108   210.86   0.000     .0649253    .0661436
------------------------------------------------------------------------------

Test for normality of the disturbances

Kolmogorov-Smirnov equality-of-distributions test
Normal Distribution of the disturbances

One-sample Kolmogorov-Smirnov test against theoretical distribution
           normal((res_etreat - r(mean))/sqrt(r(Var)))

Smaller group       D       P-value  Corrected
----------------------------------------------
res_etreat:         0.1579    0.000
Cumulative:        -0.1224    0.000
Combined K-S:       0.1579    0.000      0.000

Note: Ties exist in dataset;
      there are 22224 unique values out of 22231 observations.

The assumption of Normality is not statistically satisfied at .05 level
It is advisable to try a different trasformation of the treatment variable

           Estimated generalized propensity score
-------------------------------------------------------------
      Percentiles      Smallest
1%     1.569283       1.146247
5%     1.821294       1.226061
10%     2.006727       1.228207       Obs              22,231
25%     2.664825       1.238576       Sum of Wgt.      22,231

50%     4.133582                      Mean           3.962133
                        Largest       Std. Dev.      1.381247
75%     5.111096       6.087499
90%     5.848306       6.087522       Variance       1.907842
95%     5.929101       6.087524       Skewness      -.1122427
99%     6.018518       6.087524       Kurtosis       1.696721

********************************************
End of the algorithm to estimate the gpscore
********************************************

******************************************************************************
The set of the potential treatment values is divided into 6 intervals

The values of the gpscore evaluated at the representative point of each
treatment interval are divided into 5 intervals
******************************************************************************

***********************************************************
Summary statistics of the distribution of the GPS evaluated
at the representative point of each treatment interval
***********************************************************

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
       gps_1 |     22,231    4.543274     .237251   2.885289   5.826589

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
       gps_2 |     22,231    4.774775    .2135613   3.095474   5.918881

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
       gps_3 |     22,231    3.037522    .2429328   1.566484   4.691811

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
       gps_4 |     22,231    2.071809    .2117767   .9311559   3.648537

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
       gps_5 |     22,231    1.608863    .1853206   .6689561   3.050296

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
       gps_6 |     22,231    1.301614     .163156   .5098148    2.61117


************************************************************************************
Test that the conditional mean of the pre-treatment variables given the generalized
propensity score is not different between units who belong to a particular treatment
interval and units who belong to all other treatment intervals
************************************************************************************
1 group found, 2 required