Error: cannot compute an improvement -- discontinuous region encountered

[Laura Cabeza]

Good night,

I am trying to perform a probit ordered model with panel data and the following error appears: cannot compute an improvement -- discontinuous region encountered

Do anybody know how to solve this error and what does it means?

Thanks!
Laura

[Jonathan Horowitz]

Unfortunately, it means your model won't converge. Maximum likelihood has failed. Errors of that type are frustrating because the thing that causes them is often different in different cases. You may need to simplify the model.

[Carlo Lazzaro]

Laura:
welcome to this forum.
Please note that, we such scant details, Jonathan's helpful reply is the best that we can get.
In this instance, the usual fix is to start from scratch, add one predictor at a time and see when Stata starts gasping.
Please follow the FAQ when posting and share what you typed and what Stata gave you back.
If you think (as some occasional posters do) that following the FAQ is time-consuming, please note that is much more time-consuming posting and reposting the same thread with increasing details reported in each new message due to the lack of positive replies. Thanks.

[Laura Cabeza]

Firstly, thanks to Jonathan and Carlo for your answers. I apologise myself for not using adequately the forum. As it was the first time using it and did not know how to proceed. Sorry. I hope to be more clear now. I have a model where the dependent variable measures a firm policty whose values rank from an inadequate policy (1) to exceptional policy (5).

I have used this model in Stata v15 and the error commented yesterday appears:

xtoprobit dependiente260nueva f1_eco_soc_tec_pol f2_env sector_ans260 sector_reverte answer245nueva answer359 answer338nueva size variacion_valor answer78 yr2013c-yr2016c

note: yr2016c omitted because of collinearity

Fitting comparison model:

Iteration 0: log likelihood = -8863.2782
Iteration 1: log likelihood = -7163.5615
Iteration 2: log likelihood = -7139.5889
Iteration 3: log likelihood = -7139.5392
Iteration 4: log likelihood = -7139.5392

Refining starting values:

Grid node 0: log likelihood = -6035.6631

Fitting full model:

Iteration 0: log likelihood = -6035.6631
cannot compute an improvement -- discontinuous region encountered
r(430);

end of do-file

Today, following your suggestion I have estimated models only considering the dependent variable and each explanatory variable separately as a first step. And in all cases, the same error appears. So, it is not possible to estimate anything even considering in a independent way each variable.


I only paste some examples, as with all variables happens the same:

xtoprobit dependiente260nueva f1_eco_soc_tec_pol

Fitting comparison model:

Iteration 0: log likelihood = -8863.2782
Iteration 1: log likelihood = -8861.5915
Iteration 2: log likelihood = -8861.5915

Refining starting values:

Grid node 0: log likelihood = -7481.1461

Fitting full model:

Iteration 0: log likelihood = -7481.1461
cannot compute an improvement -- discontinuous region encountered
r(430);

end of do-file

r(430);

. do "C:\Users\Usuario\AppData\Local\Temp\STD2210_0 0000 0.tmp"

. xtoprobit dependiente260nueva f2_env

Fitting comparison model:

Iteration 0: log likelihood = -8863.2782
Iteration 1: log likelihood = -8821.9803
Iteration 2: log likelihood = -8821.9719
Iteration 3: log likelihood = -8821.9719

Refining starting values:

Grid node 0: log likelihood = -7444.1152

Fitting full model:

Iteration 0: log likelihood = -7444.1152
cannot compute an improvement -- discontinuous region encountered
r(430);

end of do-file

r(430);

Something similar happens also if I used xtologit instead of xtoprobit.

Thanks in advance, and best regards,

[Carlo Lazzaro]

Laura:
could you please provide an example/excerpt of your dataset via -dataex- (see the FAQ)? Thanks.
That said, as you surmised, the problem seems to rest on the regressand.

[Laura Cabeza]

I have reading this point 12.2 What to say about your data of FAQ and type ssc install dataex in my Stata. And the write 'dataex dependiente260nueva' (dependiente260nueva is the dependent variable which seems to have the problem). I am not sure if you refer to this.

The following appear in stata:

dataex dependiente260nueva

----------------------- copy starting from the next line -----------------------

* Example generated by -dataex-. To install: ssc install dataex
clear
input float dependiente260nueva
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
2
4
4
4
3
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
5
5
5
5
4
4
4
4
4
4
4
4
4
4
4
1
1
4
4
4
4
5
5
5
5
4
4
4
4
4
4
4
4
5
4
4
4
4
4
4
4
3
3
3
3
4
4
4
4
4
4
4
4
4
4
4
4
end

------------------ copy up to and including the previous line ------------------

Listed 100 out of 6705 observations
Use the count() option to list more


*** And the same information by company:

dataex company_id dependiente260nueva

----------------------- copy starting from the next line -----------------------

* Example generated by -dataex-. To install: ssc install dataex
clear
input int company_id float dependiente260nueva
  3 4
  3 4
  3 4
  3 4
  6 4
  6 4
  6 4
  6 4
 13 4
 13 4
 13 4
 13 4
 16 4
 16 4
 16 4
 18 4
 18 4
 18 4
 18 4
 28 4
 28 4
 28 4
 28 4
 29 2
 29 4
 29 4
 29 4
 31 3
 31 4
 31 4
 31 4
 32 4
 32 4
 32 4
 32 4
 38 4
 38 4
 38 4
 38 4
 41 4
 41 4
 41 4
 41 4
 43 5
 43 5
 43 5
 43 5
 45 4
 45 4
 45 4
 53 4
 53 4
 53 4
 53 4
 78 4
 78 4
 78 4
 78 4
 80 1
 80 1
 93 4
 93 4
 93 4
 93 4
 96 5
 96 5
 96 5
 96 5
 98 4
 98 4
 98 4
 98 4
102 4
102 4
102 4
102 4
105 5
105 4
105 4
105 4
107 4
107 4
107 4
107 4
119 3
119 3
119 3
119 3
130 4
130 4
130 4
130 4
131 4
131 4
131 4
131 4
132 4
132 4
132 4
132 4
end

------------------ copy up to and including the previous line ------------------

Listed 100 out of 6705 observations
Use the count() option to list more

[Carlo Lazzaro]

Laura:
you're on the right track.
However, interested listers need at least a predictor.
Eventually, the -timevar- would not harm, too.
Thanks.

[Laura Cabeza]

Good morning, Carlo. I have run dataex with the company variable, the year variable, the dependent variable, and 2 predictors. Both are in lagged values and there is a possible endogeneity problem with them (for this reason for them no values in 2013 appears):

dataex company_id year dependiente260nueva sector_ans260_1 f2_env_1

----------------------- copy starting from the next line -----------------------

* Example generated by -dataex-. To install: ssc install dataex
clear
input int(company_id year) float(dependiente260nueva sector_ans260_1 f2_env_1)
  3 2013 4      .        .
  3 2014 4 2.4359  -.13596
  3 2015 4   2.25  -.12736
  3 2016 4  2.275  -.13341
  6 2013 4      .        .
  6 2014 4 2.1308  -.74878
  6 2015 4 2.1471  -.76785
  6 2016 4  2.049  -.95268
 13 2013 4      .        .
 13 2014 4 1.5192  -.13596
 13 2015 4  1.434  -.12736
 13 2016 4 1.6078  -.13341
 16 2013 4      .        .
 16 2014 4  2.086  -.13596
 16 2015 4 2.0805  -.12736
 18 2013 4      .        .
 18 2014 4  2.086  -.29758
 18 2015 4 2.0805  -.33368
 18 2016 4 2.1839  -.29843
 28 2013 4      .        .
 28 2014 4 1.7563  -.58434
 28 2015 4 1.6905  -.66139
 28 2016 4 1.6615    -.621
 29 2013 2      .        .
 29 2014 4 2.2647   -.3133
 29 2015 4    2.4  -.30741
 29 2016 4 2.4151  -.25386
 31 2013 3      .        .
 31 2014 4 2.0388  -.74878
 31 2015 4 1.9806  -.76785
 31 2016 4 1.8509  -.95268
 32 2013 4      .        .
 32 2014 4  1.931  -.74785
 32 2015 4 2.0484  -.67952
 32 2016 4 2.0645  -.65397
 38 2013 4      .        .
 38 2014 4 2.0291  -.13596
 38 2015 4 1.9806  -.12736
 38 2016 4 1.8509  -.13341
 41 2013 4      .        .
 41 2014 4 1.7563  -.13596
 41 2015 4 1.6905  -.12736
 41 2016 4 1.6615  -.13341
 43 2013 5      .        .
 43 2014 5 2.5922  -.29758
 43 2015 5 2.5728  -.33368
 43 2016 5 2.6214  -.29843
 45 2013 4      .        .
 45 2014 4  2.086  -.58434
 45 2015 4 2.0805  -.66139
 53 2013 4      .        .
 53 2014 4 2.0291  -.13596
 53 2015 4 1.9806  -.12736
 53 2016 4 1.8509  -.13341
 78 2013 4      .        .
 78 2014 4 2.1538  -.13596
 78 2015 4    2.4  -.12736
 78 2016 4 2.3929  -.13341
 80 2013 1      .        .
 80 2014 1 1.2785  -.13596
 93 2013 4      .        .
 93 2014 4 2.0291  -.13596
 93 2015 4 1.9806  -.12736
 93 2016 4 1.8509  -.13341
 96 2013 5      .        .
 96 2014 5 2.2212   -.9864
 96 2015 5 2.1905 -1.01184
 96 2016 5 2.1782  -.91109
 98 2013 4      .        .
 98 2014 4 2.0122  -.13596
 98 2015 4 1.9024  -.12736
 98 2016 4 1.8519  -.13341
102 2013 4      .        .
102 2014 4 1.8889  -.13596
102 2015 4 1.8222  -.12736
102 2016 4 1.6471  -.13341
105 2013 5      .        .
105 2014 4 2.0194  -.13596
105 2015 4 1.9806  -.12736
105 2016 4 1.8509  -.13341
107 2013 4      .        .
107 2014 4 2.1308   -.9864
107 2015 4 2.1471 -1.01184
107 2016 4  2.049  -.91109
119 2013 3      .        .
119 2014 3      2   -.3133
119 2015 3 1.9706  -.30741
119 2016 3      2  -.25386
130 2013 4      .        .
130 2014 4 2.2333  -.13596
130 2015 4    2.2  -.12736
130 2016 4 2.0909  -.13341
131 2013 4      .        .
131 2014 4 2.6019  -.74785
131 2015 4 2.5825  -.67952
131 2016 4 2.6311  -.65397
132 2013 4      .        .
132 2014 4 1.9848  -.13596
132 2015 4 1.9559  -.12736
132 2016 4 1.9851  -.13341
end

------------------ copy up to and including the previous line ------------------

Listed 100 out of 6705 observations
Use the count() option to list more

Thanks so much for your help,
Laura

[Carlo Lazzaro]

Laura:
IMHO, the issues with your -xtoprobit- are the following one:
1) regerssand: the number of observation belonging to -4- outperforms the other ones;
2) predictor -f2_env_1: the most frequent values are -.13596; -.13341;-.12736.

These issues cause convergence nuisances even reducing the regressand to level 4 and 5 only.
That said (and in the light of the Stata slip reported below) I would go pooled -oprobit- with clusteres standard error:

. xtset company_id year

Panel variable: company_id (unbalanced)
 Time variable: year, 2013 to 2016
         Delta: 1 unit

. xtoprobit dependiente260nueva sector_ans260_1 f2_env_1 i.year

Fitting comparison model:

Iteration 0:   log likelihood = -38.285906 
Iteration 1:   log likelihood = -29.623046 
Iteration 2:   log likelihood = -28.768322 
Iteration 3:   log likelihood =  -28.75611 
Iteration 4:   log likelihood = -28.756109 

Refining starting values:

Grid node 0:   log likelihood = -24.219394

Fitting full model:

Iteration 0:   log likelihood = -24.219394 
Iteration 1:   log likelihood = -14.727796 
cannot compute an improvement -- discontinuous region encountered
r(430);


. tab dependiente260nueva

dependiente |
   260nueva |      Freq.     Percent        Cum.
------------+-----------------------------------
          1 |          2        2.00        2.00
          2 |          1        1.00        3.00
          3 |          5        5.00        8.00
          4 |         83       83.00       91.00
          5 |          9        9.00      100.00
------------+-----------------------------------
      Total |        100      100.00

. xtoprobit dependiente260nueva sector_ans260_1 f2_env_1 i.year if dependiente260nueva>=3

Fitting comparison model:

Iteration 0:   log likelihood = -32.988628 
Iteration 1:   log likelihood = -27.502153 
Iteration 2:   log likelihood = -27.015622 
Iteration 3:   log likelihood = -27.011553 
Iteration 4:   log likelihood = -27.011551 

Refining starting values:

Grid node 0:   log likelihood = -21.958659

Fitting full model:

Iteration 0:   log likelihood = -21.958659 
Iteration 1:   log likelihood =  -13.24823 
cannot compute an improvement -- discontinuous region encountered
r(430);


. xtoprobit dependiente260nueva sector_ans260_1 f2_env_1 i.year if dependiente260nueva>=4

Fitting comparison model:

Iteration 0:   log likelihood = -20.475593 
Iteration 1:   log likelihood = -13.674416 
Iteration 2:   log likelihood = -12.288659 
Iteration 3:   log likelihood =  -12.25383 
Iteration 4:   log likelihood = -12.253821 
Iteration 5:   log likelihood = -12.253821 

Refining starting values:

Grid node 0:   log likelihood = -9.1031647

Fitting full model:

Iteration 0:   log likelihood = -9.1031647 
Iteration 1:   log likelihood = -6.1792547 
Iteration 2:   log likelihood = -5.2856598  (not concave)
Iteration 3:   log likelihood = -5.0964147  (not concave)
Iteration 4:   log likelihood = -5.0751825  (not concave)
Iteration 5:   log likelihood =  -5.057029  (not concave)
Iteration 6:   log likelihood = -5.0542374  (not concave)
Iteration 7:   log likelihood = -732.52624  (not concave)
Iteration 8:   log likelihood = -5.1679583  (not concave)
Iteration 9:   log likelihood =   -5.05212  (not concave)
Iteration 10:  log likelihood = -5.0469519  (not concave)
Iteration 11:  log likelihood = -5.0435058  (not concave)
Iteration 12:  log likelihood = -5.0413634  (not concave)
Iteration 13:  log likelihood = -5.0407204  (not concave)
Iteration 14:  log likelihood =   -5.04034  (not concave)
Iteration 15:  log likelihood = -5.0401172  (not concave)
Iteration 16:  log likelihood = -5.0399874  (not concave)
Iteration 17:  log likelihood = -5.0399496  (not concave)
Iteration 18:  log likelihood = -5.0399277  (not concave)
Iteration 19:  log likelihood =  -5.039915  (not concave)
Iteration 20:  log likelihood = -5.0399112  (not concave)
Iteration 21:  log likelihood = -5.0399103  (not concave)
Iteration 22:  log likelihood = -5.0399096  (not concave)
Iteration 23:  log likelihood = -5.0399094  (not concave)
Iteration 24:  log likelihood = -5.0399093  (not concave)
<snip>
Iteration 300: log likelihood = -5.0399093  (not concave)
convergence not achieved

Random-effects ordered probit regression                Number of obs    =  70
Group variable: company_id                              Number of groups =  24

Random effects u_i ~ Gaussian                           Obs per group:
                                                                     min =   2
                                                                     avg = 2.9
                                                                     max =   3

Integration method: mvaghermite                         Integration pts. =  12

                                                        Wald chi2(2)     =   .
Log likelihood = -5.0399093                             Prob > chi2      =   .

-------------------------------------------------------------------------------------
dependiente260nueva | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
--------------------+----------------------------------------------------------------
    sector_ans260_1 |   22.27126          .        .       .            .           .
           f2_env_1 |  -10.90114          .        .       .            .           .
                    |
               year |
              2015  |   .2613234   2.550509     0.10   0.918    -4.737582    5.260229
              2016  |   .6254498   3.708819     0.17   0.866    -6.643702    7.894601
--------------------+----------------------------------------------------------------
              /cut1 |   64.85193          .                             .           .
--------------------+----------------------------------------------------------------
          /sigma2_u |   45.83049          .                             .           .
-------------------------------------------------------------------------------------

. tab f2_env_1

   f2_env_1 |      Freq.     Percent        Cum.
------------+-----------------------------------
   -1.01184 |          2        2.70        2.70
     -.9864 |          2        2.70        5.41
    -.95268 |          2        2.70        8.11
    -.91109 |          2        2.70       10.81
    -.76785 |          2        2.70       13.51
    -.74878 |          2        2.70       16.22
    -.74785 |          2        2.70       18.92
    -.67952 |          2        2.70       21.62
    -.66139 |          2        2.70       24.32
    -.65397 |          2        2.70       27.03
      -.621 |          1        1.35       28.38
    -.58434 |          2        2.70       31.08
    -.33368 |          2        2.70       33.78
     -.3133 |          2        2.70       36.49
    -.30741 |          2        2.70       39.19
    -.29843 |          2        2.70       41.89
    -.29758 |          2        2.70       44.59
    -.25386 |          2        2.70       47.30
    -.13596 |         14       18.92       66.22
    -.13341 |         12       16.22       82.43
    -.12736 |         13       17.57      100.00
------------+-----------------------------------
      Total |         74      100.00


. oprobit dependiente260nueva sector_ans260_1 f2_env_1 i.year, vce(cluster company_id)

Iteration 0:   log pseudolikelihood = -38.285906 
Iteration 1:   log pseudolikelihood = -29.623046 
Iteration 2:   log pseudolikelihood = -28.768322 
Iteration 3:   log pseudolikelihood =  -28.75611 
Iteration 4:   log pseudolikelihood = -28.756109 

Ordered probit regression                               Number of obs =     74
                                                        Wald chi2(4)  =   8.89
                                                        Prob > chi2   = 0.0639
Log pseudolikelihood = -28.756109                       Pseudo R2     = 0.2489

                                   (Std. err. adjusted for 26 clusters in company_id)
-------------------------------------------------------------------------------------
                    |               Robust
dependiente260nueva | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
--------------------+----------------------------------------------------------------
    sector_ans260_1 |   2.617832   1.144352     2.29   0.022     .3749443     4.86072
           f2_env_1 |  -1.302963   1.061604    -1.23   0.220    -3.383669    .7777425
                    |
               year |
              2015  |   .1755779   .1105152     1.59   0.112    -.0410279    .3921837
              2016  |    .250019   .1238135     2.02   0.043     .0073491     .492689
--------------------+----------------------------------------------------------------
              /cut1 |   3.069412     2.1843                     -1.211737    7.350561
              /cut2 |   3.921286   2.046657                      -.090088     7.93266
              /cut3 |    7.90058   2.466431                      3.066464     12.7347
-------------------------------------------------------------------------------------

.

[Laura Cabeza]

Thanks your sooner answer and your opinion. Thus, if I have understand correctly, it is preferable to estimate a pool ordered probit model with cluster option at firm level. Is this correct?

Considering the problem in our data, I suppose that the above option is better than estimate, for example, a GMM (panel data model controlling by endogeneity) due to the dependant variable values rank from 1 to 5 (exceptional, good, moderate, weak, inadequate)?

Best regards,
Laura

[Carlo Lazzaro]

Laura:
I would go pooled -oprobit- with cluster option at firm level.
I do not think that your data support anything better.