How to deal with Omitted Variables

[hosein bakhtari]

Hi everyone
I am trying to run logistic regression but I have some problems.
here is the :

xtlogit kams2 goingconcern auditortype win_ocf win_roe win_boardindepenence win_auditcost win_fsize win_leverage boardsize i.indcode i.year , re vce(cluster firmcode) nolog

and the result

note: goingconcern != 0 predicts success perfectly;
      goingconcern omitted and 4 obs not used.

note: 10.indcode != 0 predicts success perfectly;
      10.indcode omitted and 6 obs not used.

note: 28.indcode != 0 predicts failure perfectly;
      28.indcode omitted and 6 obs not used.

note: boardsize omitted because of collinearity.
note: 54.indcode omitted because of collinearity.

Calculating robust standard errors ...

Random-effects logistic regression                      Number of obs    = 728
Group variable: firmcode                                Number of groups = 122

Random effects u_i ~ Gaussian                           Obs per group:
                                                                     min =   4
                                                                     avg = 6.0
                                                                     max =   6

Integration method: mvaghermite                         Integration pts. =  12

                                                        Wald chi2(26)    =   .
Log pseudolikelihood = -358.89337                       Prob > chi2      =   .

                                     (Std. err. adjusted for 122 clusters in firmcode)
--------------------------------------------------------------------------------------
                     |               Robust
               kams2 | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
---------------------+----------------------------------------------------------------
        goingconcern |          0  (omitted)
         auditortype |   .8239995   .4402713     1.87   0.061    -.0389165    1.686915
             win_ocf |  -1.848223   .9876459    -1.87   0.061    -3.783974     .087527
             win_roe |  -1.704159   .5625449    -3.03   0.002    -2.806726    -.601591
win_boardindepenence |  -1.528077   .9346605    -1.63   0.102    -3.359978    .3038236
       win_auditcost |  -.0539769   .2998422    -0.18   0.857    -.6416569    .5337031
           win_fsize |   .1582842   .2109013     0.75   0.453    -.2550747    .5716431
        win_leverage |  -1.426802   .9602935    -1.49   0.137    -3.308943    .4553386
           boardsize |          0  (omitted)
                     |
             indcode |
                 10  |          0  (empty)
                 11  |   1.611654   1.161584     1.39   0.165    -.6650091    3.888317
                 13  |   .3956403   1.605448     0.25   0.805     -2.75098     3.54226
                 14  |   2.886265   1.059655     2.72   0.006     .8093791    4.963152
                 23  |  -.2562683   1.803915    -0.14   0.887    -3.791876    3.279339
                 25  |   -.781918   1.912321    -0.41   0.683    -4.529999    2.966163
                 27  |   1.274422   1.132625     1.13   0.261    -.9454823    3.494326
                 28  |          0  (empty)
                 29  |   2.377334   1.440187     1.65   0.099    -.4453807    5.200049
                 31  |    4.52582   1.551252     2.92   0.004     1.485421    7.566218
                 34  |   .8938229   1.132032     0.79   0.430     -1.32492    3.112566
                 38  |   .5772835   1.030465     0.56   0.575    -1.442391    2.596958
                 42  |  -.8353585   1.301148    -0.64   0.521    -3.385561    1.714844
                 43  |   .5225873   1.182988     0.44   0.659    -1.796026    2.841201
                 44  |    1.11104   1.209117     0.92   0.358    -1.258786    3.480866
                 49  |  -.8858398   1.943006    -0.46   0.648    -4.694061    2.922382
                 53  |  -1.164449   1.276902    -0.91   0.362    -3.667131    1.338232
                 54  |          0  (omitted)
                     |
                year |
               1397  |  -.1929489   .2243773    -0.86   0.390    -.6327204    .2468225
               1398  |   -1.00974   .3571861    -2.83   0.005    -1.709812   -.3096684
               1399  |  -1.682763   .4669916    -3.60   0.000     -2.59805   -.7674763
               1400  |  -1.519616    .456696    -3.33   0.001    -2.414724   -.6245087
               1401  |   .6046043   .6346018     0.95   0.341    -.6391924    1.848401
                     |
               _cons |  -.6281887   2.727991    -0.23   0.818    -5.974952    4.718575
---------------------+----------------------------------------------------------------
            /lnsig2u |   1.388739    .253732                      .8914329    1.886044
---------------------+----------------------------------------------------------------
             sigma_u |   2.002446   .2540423                      1.561609     2.56773
                 rho |   .5493119    .062816                      .4257006     .667122
--------------------------------------------------------------------------------------

In this model, the variable” going concern” has been omitted but I need this variable, So how can I fix this?
For information,” going concern” is a dummy variable.
Thank you in advance!

[George Ford]

Probably being eaten up (perfect correlation) by the i.indcode i.year

[Clyde Schechter]

Actually, the warnings at the top of the regression output explain what happened:

note: goingconcern != 0 predicts success perfectly;
goingconcern omitted and 4 obs not used.

This means that whenever goingconcern is non-zero, kams2 is always 1. This is called perfect prediction, and it is incompatible with maximum likelihood estimation: the maximum likelihood estimate for this coefficient is infinite. Stata (and every statistical package I know of) checks for situations like that, and eliminates such variables from the model. If you were not working with panel data, you could use -firthlogit-, which works by penalized maximum likelihood estimation and can tolerate perfect prediction. But I am not aware of any similar Stata command for panel data.

You should consider two possible situations underlying this problem. If there is a structural reason why, in the entire universe at all times, goingconcern being true implies kams2 is true, then the true odds ratio for goingconcern really is infinite, and it is inappropriate to try to include it in a logistic model. On the other hand, it may just be that kams2 being false is rare, but not non-existent, in the universe at large when goingconcern is true. In that case, you can, if feasible, solve the problem by getting more data, including some cases that have goingconcern true and kams2 false.

If a logistic model is inappropriate altogether (per last paragraph) or getting more data is not feasible, consider switching to a linear probability model (-xtreg-), which does not have this problem.

[hosein bakhtari]

Thanks George Ford
is it correct? or i shloud not use - i.indcode i.year-.
here is

 xtlogit kams2 goingconcern auditortype win_ocf win_roe win_boardindepenence win_auditcost win_fsize win_leverage boardsize, re nol
> og
note: goingconcern != 0 predicts success perfectly;
      goingconcern omitted and 4 obs not used.

note: boardsize omitted because of collinearity.

Random-effects logistic regression                   Number of obs    =    740
Group variable: firmcode                             Number of groups =    124

Random effects u_i ~ Gaussian                        Obs per group:
                                                                  min =      4
                                                                  avg =    6.0
                                                                  max =      6

Integration method: mvaghermite                      Integration pts. =     12

                                                     Wald chi2(7)     =  25.78
Log likelihood = -396.93494                          Prob > chi2      = 0.0006

--------------------------------------------------------------------------------------
               kams2 | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
---------------------+----------------------------------------------------------------
        goingconcern |          0  (omitted)
         auditortype |  -.1828471    .292804    -0.62   0.532    -.7567324    .3910383
             win_ocf |  -1.338407   .9886855    -1.35   0.176    -3.276195    .5993811
             win_roe |  -2.471563   .5744298    -4.30   0.000    -3.597425   -1.345701
win_boardindepenence |  -.8961638   .7710304    -1.16   0.245    -2.407356    .6150281
       win_auditcost |   -.005515   .2336519    -0.02   0.981    -.4634642    .4524343
           win_fsize |   .1335576   .1499397     0.89   0.373    -.1603188    .4274341
        win_leverage |  -.4147616   .7854918    -0.53   0.597    -1.954297    1.124774
           boardsize |          0  (omitted)
               _cons |  -.6893048   2.059058    -0.33   0.738    -4.724984    3.346374
---------------------+----------------------------------------------------------------
            /lnsig2u |   1.485949   .2418019                      1.012027    1.959872
---------------------+----------------------------------------------------------------
             sigma_u |    2.10218   .2541555                      1.658665    2.664286
                 rho |   .5732447   .0591533                      .4554135    .6833099
--------------------------------------------------------------------------------------
LR test of rho=0: chibar2(01) = 155.30                 Prob >= chibar2 = 0.000

I have rerun the model but the results have not changed and "goingconcern" has been omitted.

[Clyde Schechter]

#4 crossed with #3. To O.P.: I think the information in #3 will resolve your problem.

[hosein bakhtari]

ِDear Clyde Schechter and George Ford
.I appreciate your guidance.