cannot compute an improvement -- discontinuous region encountered

[Daeun Kwan]

Hi, I'm doing ordered logistic regression with panel data set, and ran across with the error message that reads "cannot compute an improvement -- discontinuous region encountered"
Following the advice on the previous questions in Statlist, I did my regression model with one, two, (and so on) predictors, and figured out what variable is a trouble maker.
But then, now what? How should I change my model specification?
The age at the first delivery "age_birth" is one of the important independent variables to explain the independent variable of number of the children.

xtologit children_number age_birth

Fitting comparison model:

Iteration 0:   log likelihood = -8247.2149  
Iteration 1:   log likelihood = -8123.6735  
Iteration 2:   log likelihood = -8123.1374  
Iteration 3:   log likelihood = -8123.1374  

Refining starting values:

Grid node 0:   log likelihood = -5293.4722

Fitting full model:

Iteration 0:   log likelihood = -5293.4722  
Iteration 1:   log likelihood = -3482.5691  
Iteration 2:   log likelihood = -3119.9269  
Iteration 3:   log likelihood = -2363.2178  
Iteration 4:   log likelihood = -2190.7194  
Iteration 5:   log likelihood = -2089.1869  
Iteration 6:   log likelihood = -2041.1365  
Iteration 7:   log likelihood = -2017.9951  (not concave)
cannot compute an improvement -- discontinuous region encountered
r(430);

[Andrew Musau]

There are plenty of things that you can do before giving up. One thing that worked wonders for me back then when fitting such models was to use adaptive quadrature before running Newton-Raphson. This option is available in gllamm from SSC, which can also fit a panel ordered logit model.

ssc install gllamm, replace

webuse tvsfpors
xtset school
xtologit thk prethk cc##tv

*WITH GLLAMM
gen cctv= c.cc#c.tv
gllamm thk prethk cc tv cctv, i(school) link(ologit) adapt

Res.:

. xtologit thk prethk cc##tv

Fitting comparison model:

Iteration 0:   log likelihood =  -2212.775  
Iteration 1:   log likelihood =  -2125.509  
Iteration 2:   log likelihood = -2125.1034  
Iteration 3:   log likelihood = -2125.1032  

Refining starting values:

Grid node 0:   log likelihood = -2136.2426

Fitting full model:

Iteration 0:   log likelihood = -2136.2426  (not concave)
Iteration 1:   log likelihood = -2120.2577  
Iteration 2:   log likelihood = -2119.7574  
Iteration 3:   log likelihood = -2119.7428  
Iteration 4:   log likelihood = -2119.7428  

Random-effects ordered logistic regression      Number of obs     =      1,600
Group variable: school                          Number of groups  =         28

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =         18
                                                              avg =       57.1
                                                              max =        137

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(4)      =     128.06
Log likelihood  = -2119.7428                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
         thk |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      prethk |   .4032892     .03886    10.38   0.000      .327125    .4794534
        1.cc |   .9237904    .204074     4.53   0.000     .5238127    1.323768
        1.tv |   .2749937   .1977424     1.39   0.164    -.1125744    .6625618
             |
       cc#tv |
        1 1  |  -.4659256   .2845963    -1.64   0.102    -1.023724    .0918728
-------------+----------------------------------------------------------------
       /cut1 |  -.0884493   .1641062                     -.4100916     .233193
       /cut2 |   1.153364    .165616                      .8287625    1.477965
       /cut3 |    2.33195   .1734199                      1.992053    2.671846
-------------+----------------------------------------------------------------
   /sigma2_u |   .0735112   .0383106                      .0264695    .2041551
------------------------------------------------------------------------------
LR test vs. ologit model: chibar2(01) = 10.72         Prob >= chibar2 = 0.0005

.
.
.
. *WITH GLLAMM

.
. gen cctv= c.cc#c.tv

.
. gllamm thk prethk cc tv cctv, i(school) link(ologit) adapt

Running adaptive quadrature
Iteration 0:    log likelihood = -2123.8577
Iteration 1:    log likelihood = -2120.0494
Iteration 2:    log likelihood = -2119.7702
Iteration 3:    log likelihood = -2119.7605
Iteration 4:    log likelihood = -2119.7506
Iteration 5:    log likelihood = -2119.7444
Iteration 6:    log likelihood = -2119.7442


Adaptive quadrature has converged, running Newton-Raphson
Iteration 0:   log likelihood = -2119.7442  
Iteration 1:   log likelihood = -2119.7442  (backed up)
Iteration 2:   log likelihood = -2119.7428  
Iteration 3:   log likelihood = -2119.7428  
 
number of level 1 units = 1600
number of level 2 units = 28
 
Condition Number = 16.579687
 
gllamm model
 
log likelihood = -2119.7428
 
------------------------------------------------------------------------------
         thk |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
thk          |
      prethk |   .4032892     .03886    10.38   0.000      .327125    .4794533
          cc |   .9237908   .2040746     4.53   0.000     .5238119     1.32377
          tv |   .2749939   .1977431     1.39   0.164    -.1125754    .6625633
        cctv |  -.4659264   .2845972    -1.64   0.102    -1.023727    .0918739
-------------+----------------------------------------------------------------
_cut11       |
       _cons |  -.0884495   .1641067    -0.54   0.590    -.4100927    .2331937
-------------+----------------------------------------------------------------
_cut12       |
       _cons |   1.153364   .1656165     6.96   0.000     .8287615    1.477966
-------------+----------------------------------------------------------------
_cut13       |
       _cons |    2.33195   .1734203    13.45   0.000     1.992052    2.671847
------------------------------------------------------------------------------
 
 
Variances and covariances of random effects
------------------------------------------------------------------------------

 
***level 2 (school)
 
    var(1): .07351208 (.03831112)
------------------------------------------------------------------------------

You can also fit the same model with a subset of observations (say three-quarters) and if successful, use these estimates as starting values for the estimation with the full sample. There are plenty of examples in the forum showing how you can specify starting values in a maximum likelihood estimation.

[Daeun Kwan]

Wow, it really works wonders for me! Thank you so much!