Stata Logit

The logit command runs a logistic regression.

Contents

Stata Logit

Usage

Copied from here:

. use https://stats.idre.ucla.edu/stat/stata/dae/binary, clear

. logit admit gre gpa i.rank

Iteration 0:   log likelihood = -249.98826
Iteration 1:   log likelihood = -229.66446
Iteration 2:   log likelihood = -229.25955
Iteration 3:   log likelihood = -229.25875
Iteration 4:   log likelihood = -229.25875

Logistic regression                               Number of obs   =        400
                                                  LR chi2(5)      =      41.46
                                                  Prob > chi2     =     0.0000
Log likelihood = -229.25875                       Pseudo R2       =     0.0829

------------------------------------------------------------------------------
       admit |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         gre |   .0022644    .001094     2.07   0.038     .0001202    .0044086
         gpa |   .8040377   .3318193     2.42   0.015     .1536838    1.454392
             |
        rank |
          2  |  -.6754429   .3164897    -2.13   0.033    -1.295751   -.0551346
          3  |  -1.340204   .3453064    -3.88   0.000    -2.016992   -.6634158
          4  |  -1.551464   .4178316    -3.71   0.000    -2.370399   -.7325287
             |
       _cons |  -3.989979   1.139951    -3.50   0.000    -6.224242   -1.755717
------------------------------------------------------------------------------

Compare the output of logistic, which always shows the odds ratios, while the or option must be specified on logit to show those.

See here for details on factor variables.

Estimates

The estimates can be accessed through any of the following commands...

predict creates a variable storing the predicted probability for each case
margins displays the marginal predicted probabilities

Tips

One-way causation

If a variable predicts failure or success perfectly, the model cannot be fit with it. Stata's default solution is to omit that variable and any cases with that problematic data pattern.

. use https://www.stata-press.com/data/r18/repair, clear
. logit foreign b3.repair

note: 1.repair != 0 predicts failure perfectly;
      1.repair omitted and 10 obs not used.

Iteration 0: Log likelihood = -26.992087
Iteration 1: Log likelihood = -22.483187
Iteration 2: Log likelihood = -22.230498
Iteration 3: Log likelihood = -22.229139
Iteration 4: Log likelihood = -22.229138

Logistic regression                                      Number of obs =     48
                                                            LR chi2(1) =   9.53
                                                           Prob > chi2 = 0.0020
Log likelihood = -22.229138                                  Pseudo R2 = 0.1765

-------------------------------------------------------------------------------
     foreign | Coefficient  Std. err.       z    P>|z|     [95% conf. interval]
-------------+-----------------------------------------------------------------
      repair |
          1  |          0  (empty)
          2  |  -2.197225   .7698003     -2.85   0.004    -3.706005   -.6884436
             |
       _cons |  -1.85e-17   .4714045     -0.00   1.000    -.9239359    .9239359
-------------------------------------------------------------------------------

Two-way causation

Similarly, if a variable predicts both failure and success perfectly, the model cannot be fit with it. Stata does not have a default solution and will stop execution.

Completely determined

Consider this example:

. use https://www.stata-press.com/data/r18/auto, clear
(1978 Automobile Data)

. drop if foreign == 0 & gear_ratio > 3.1
(6 observations deleted)

. logit foreign mpg weight gear_ratio

Iteration 0:   log likelihood = -42.806086
Iteration 1:   log likelihood = -17.438677
Iteration 2:   log likelihood = -11.209232
Iteration 3:   log likelihood = -8.2749141
Iteration 4:   log likelihood = -7.0018452
Iteration 5:   log likelihood = -6.5795946
Iteration 6:   log likelihood = -6.4944116
Iteration 7:   log likelihood = -6.4875497
Iteration 8:   log likelihood = -6.4874814
Iteration 9:   log likelihood = -6.4874814

Logistic regression                                     Number of obs =     68
                                                        LR chi2(3)    =  72.64
                                                        Prob > chi2   = 0.0000
Log likelihood = -6.4874814                             Pseudo R2     = 0.8484

------------------------------------------------------------------------------
     foreign | Coefficient  Std. err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -.4944907   .2655508    -1.86   0.063    -1.014961    .0259792
      weight |  -.0060919    .003101    -1.96   0.049    -.0121698    -.000014
  gear_ratio |   15.70509   8.166234     1.92   0.054    -.3004359    31.71061
       _cons |  -21.39527   25.41486    -0.84   0.400    -71.20747    28.41694
------------------------------------------------------------------------------
note: 4 failures and 0 successes completely determined.

In this case, the warning means that the continuous variable (i.e., gear_ratio) predicts the outcome very well. This is also hinted at with the extremely large coefficienton that term in the fit model.

If a standard error is omitted, the warning would instead suggest colinearity. This generally only happens with indicator terms created from interactions of categorical variables. The problematic term should be removed.

Stata/Logit