The "omitted" results in interaction between two dummy variables

[Vincent Li]

Hi there,

I'm running a logistic regression and put two interaction terms between dummies in the model. The code is like (just put a part of variables in the example):

logit daily_f feduy ocpfm_dum2 ocpfm_dum3  livewothr_c pintim ///
ocpfm_dum2#livewothr_c ocpfm_dum3#livewothr_c  ///
,or

livewothr_c indicates whether other adult relatives live in the household other than parents (yes or no)
ocpfm_dum2 refers to whether the individual is in a specific category of the occupational status (yes or no)
ocpfm_dum3 is similar to ocpfm_dum2
they are three dummy variables.

Then I ran the command. The results about the interaction terms are:

daily_f | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
ocpfm_dum2#livewothr_c |
0 1 | 1.377075 .2156025 2.04 0.041 1.013185 1.871657
1 0 | 1 (omitted)
1 1 | 1 (omitted)
|
livewothr_c#ocpfm_dum3 |
0 1 | 1.967462 .4669052 2.85 0.004 1.235677 3.132622
1 0 | 1 (omitted)
1 1 | 1 (omitted)
|

I'm confused about why 1 0 and 1 1 are omitted.Should I check the data? Or the command is wrong? Or it is normal but I did not understand it?

Thank you so much.

[Carlo Lazzaro]

Vincent:
first, your code can be written in a more efficient way:

logit daily_f feduy pintim ocpfm_dum2##livewothr_c ocpfm_dum3##livewothr_c, or

It remains to be told to interested lister whether Stata reported the reason of omission (es collinearity; perfect prediction) above the -logit- outcome table.
As a (relevant) aside, please use CODE delimiters (just click the # toggle available from the Advanced editor bar) to share what you typed and what Stata gave you back (as per FAQ). Thanks.

[Ken Chui]

If you follow the FAQ (http://www.statalist.org/forums/help) and actually provide a slice of sample data, I may be able to dig into it more. But overall, it's perhaps caused by two problems: fitting manually created dummies (which is not wrong per se, but just prone to confusion) and possible mislabeling.

A 2x2 interaction should estimate four means: 0-0, 0-1, 1-0, and 1-1. The point 0-0 is picked up by intercept so that's given. You fitted ocpfm_dum2, livewothr_c, and ocpfm_dum2#livewothr_c, which are totally three estimates, so the model should have captured all of them. Same goes for the dum3; I wont' repeat that assessment.

Left as numeric, the interaction ocpfm_dum2#livewothr_c should pick up when the combination 1-1. But the output shows only 0-1. My guess is that liveworthr_c was mislabeled (aka 0 was applied a label "1" and 1 was applied a label "0"). Use -browse- to check if the data inside that column is in blue color (or use -describe- to see if it has a labeling scheme.)

Back to manually created dummies. You may stop doing that, use -help fvvarlist- to learn more about how to model interactions without creating dummies. Simply, your model can be modified into:

logit daily_f feduy pintim i.ocpfm_dum2##i.livewothr_c i.ocpfm_dum3##i.livewothr_c, or

or, if ocpfm is a 3-level variable to begin with, use the original 3-level variable (I'm assuming it's called ocpfm):

logit daily_f feduy pintim i.ocpfm##i.livewothr_c, or

and the output will make a lot more sense.

[Vincent Li]

Dear Carlo,

First, thank you for reminding me about the use of delimiters.I'll use them in the appropriate way next time.

Then, yes, Stata did report the reason:

1.ocpfm_dum2#0.livewothr_c omitted because of collinearity
1.ocpfm_dum2#1.livewothr_c omitted because of collinearity

it's because of the collinearity.

and then, I rewrite the code just like what you suggested (thanks a lot):

 logit daily_f feduy pintim ocpfm_dum2##livewothr_c ocpfm_dum3##livewothr_c, or

It works. The results are:

                  daily_f | Odds Ratio    Std. Err.       z         P>|z|     [95% Conf. Interval]
     1.ocpfm_dum2 |   1.481956   .1396938     4.17   0.000     1.231965    1.782676
      1.livewothr_c |   .9404549   .1329639    -0.43   0.664     .7128415    1.240746
                      
ocpfm_dum2#livewothr_c |
                   1 1  |    .726177   .1136943    -2.04   0.041     .5342858    .986986
            1.ocpfm_dum3 |   2.053498    .323048     4.57   0.000     1.508644    2.795129
                      
ocpfm_dum3#livewothr_c |
                  1 1  |   .5082689    .120619    -2.85   0.004     .3192214    .8092732

So....why was there a collinearity before? because I put the interaction terms (in a wrong way) and the original variables in the model at the same time? how to know who has the collinearity with the interaction term when values are 1 0 and 1 1?

Thank you so much.

[Vincent Li]

Dear Ken,

Thanks for your suggestions.

First, the reason for the "omitted" is collinearity not the mismatch between the label and the value.

Second, yes, I did create the interaction terms in an inappropriate way.
I tried the code you suggested:

 
 logit daily_f feduy pintim i.ocpfm##i.livewothr_c, or

and the results are :

    1.livewothr_c |   .9404549   .1329639    -0.43   0.664     .7128415    1.240746
                  |
            ocpfm |
               1  |   1.481956   .1396938     4.17   0.000     1.231965    1.782676
               2  |   2.053498    .323048     4.57   0.000     1.508644    2.795129
                  |
livewothr_c#ocpfm |
             1 1  |    .726177   .1136943    -2.04   0.041     .5342858    .9869867
             1 2  |   .5082689    .120619    -2.85   0.004     .3192214    .8092732
                  |
            _cons |    .287379   .2123928    -1.69   0.092     .0675085    1.223352
-----------------------------------------------------------------------------------

The results are same as the results when using dummy variables. And I think recoding the categorical variable into dummy variables is necessary.

Thank you so much.

[Carlo Lazzaro]

Vincent:
it is difficult to reply without taking a look at an excerpt/example of your data, that you can easily share via -dataex-.

[Vincent Li]

Dear Carlo,

Sorry.
Below is an example of the data, but does not include all variables because input statement exceeds linesize limit (does it matter?).
Will it help?
Or would you mind sharing what you would do if it were you?

Thank you very much.

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(daily_f feduy) byte(pedufam_dum2 pedufam_dum3 ocpfm_dum2 ocpfm_dum3 livewp_dum2 livewp_dum3 livewp_dum4) float(livewothr_c pintim)
1  9 1 0 1 0 0 0 0 0 1
1 12 1 0 1 0 0 0 0 0 1
0 16 1 0 1 0 0 0 0 1 0
0 16 0 0 . . 0 0 0 0 1
1 16 0 0 0 0 0 0 0 0 1
0 15 0 1 0 1 0 0 0 1 1
1 12 0 1 0 0 0 0 0 0 1
1 16 1 0 . . 0 0 0 0 1
1  8 1 0 0 0 0 0 0 0 1
0 16 1 0 1 0 0 0 0 0 1
0 15 0 0 1 0 0 0 0 0 1
0  8 0 1 . . 0 1 0 0 0
1  9 1 0 1 0 0 0 0 0 1
1 12 0 1 . . 0 0 0 0 1
1  9 0 1 1 0 0 0 0 1 1
1  8 0 1 1 0 0 0 0 1 1
1 15 1 0 0 0 0 0 0 0 1
0 16 1 0 1 0 0 1 0 0 0
1  9 1 0 1 0 0 0 0 1 1
1 16 1 0 0 1 0 0 0 0 1
1  9 0 0 1 0 0 0 0 0 1
0  9 0 0 . . 0 0 0 1 1
1 16 0 0 . . 0 0 0 0 1
1  8 1 0 1 0 0 0 0 0 1
0 15 1 0 1 0 0 0 1 0 0
0  9 1 0 1 0 0 1 0 1 0
1 19 0 0 1 0 0 0 0 1 1
1  8 0 1 1 0 0 0 0 0 1
0 12 0 0 1 0 0 0 0 1 1
1  8 0 1 1 0 0 0 0 1 1
0 15 0 0 1 0 0 0 0 0 1
1 12 0 0 1 0 0 0 0 0 1
1 15 1 0 1 0 0 0 0 0 1
1 16 0 0 0 1 0 0 0 1 1
1  8 1 0 0 1 0 0 0 1 1
1 16 0 0 1 0 0 0 0 0 1
1  9 0 1 0 1 0 0 0 0 1
1  8 1 0 1 0 0 0 0 0 1
1 15 1 0 0 1 0 0 0 0 1
1 15 0 0 1 0 0 0 0 0 1
0 16 1 0 1 0 0 1 0 1 0
1 15 1 0 0 1 0 0 0 0 0
0 15 0 0 0 1 0 1 0 0 1
0 16 0 0 0 0 0 0 0 0 1
0 19 0 0 1 0 0 0 0 0 1
0 19 0 0 . . 0 1 0 1 0
1 19 1 0 1 0 0 0 0 0 1
0 15 0 0 0 1 0 0 0 0 1
1  8 1 0 1 0 0 0 0 0 1
0 15 1 0 0 0 0 0 0 0 1
1 16 1 0 1 0 0 0 0 0 1
0 15 0 0 0 0 0 0 0 1 1
1 16 1 0 1 0 0 0 0 0 1
1  8 0 1 1 0 0 0 0 0 1
1  8 0 1 0 1 0 0 0 0 1
0  9 0 1 . . 0 1 0 1 1
0  8 0 1 . . 0 1 0 1 0
1 16 1 0 1 0 0 0 0 0 1
0 16 0 1 1 0 0 1 0 0 1
0  8 0 1 1 0 0 0 0 1 1
0 15 0 0 1 0 0 0 0 0 1
1 16 1 0 0 0 0 0 0 0 1
0 19 0 0 1 0 0 0 0 0 0
1 16 1 0 1 0 0 0 0 0 1
0  6 1 0 1 0 0 0 0 0 1
1 19 0 0 0 0 0 0 0 0 1
0 15 0 1 0 0 0 0 0 0 1
0 16 1 0 1 0 0 0 0 0 1
1 15 0 0 0 1 0 0 0 1 1
1 15 0 1 0 1 0 0 0 0 1
1 16 1 0 1 0 0 0 0 0 1
0 16 0 0 1 0 0 0 0 1 1
0  9 1 0 0 0 0 0 0 1 1
1 16 0 0 0 0 0 0 0 0 1
1 11 0 1 0 1 0 0 0 0 1
1 15 1 0 0 0 0 0 0 1 1
1  9 1 0 1 0 0 0 0 0 1
1 16 0 0 0 0 0 1 0 0 1
1 15 0 1 0 1 0 0 0 1 1
0 16 1 0 1 0 0 0 0 0 1
1 19 0 0 1 0 0 0 0 0 1
0 19 1 0 0 0 0 0 0 0 1
0 15 0 0 0 0 0 0 0 0 1
1 15 1 0 0 1 0 0 0 0 1
1 16 0 1 1 0 0 0 0 0 1
1  9 1 0 1 0 0 0 0 0 1
1 16 1 0 . . 0 0 0 0 1
1 15 1 0 1 0 0 0 0 1 1
0 15 1 0 0 1 0 0 0 1 1
0 16 0 0 1 0 0 0 0 0 1
1 19 1 0 . . 0 0 0 0 1
0 16 1 0 1 0 0 0 0 0 1
1  9 0 0 1 0 0 0 0 0 1
1  9 1 0 1 0 0 0 0 0 1
0  6 1 0 0 0 0 0 0 0 1
0  9 1 0 1 0 0 0 0 0 1
1 12 0 0 . . 0 0 0 0 1
0  9 1 0 1 0 0 0 0 0 1
1  9 0 0 1 0 0 0 0 0 1
1  9 1 0 1 0 0 0 0 0 1
end

[Carlo Lazzaro]

Vincent:
yes, it depends on the way you code the interactions as in your first code, for example:

1.ocpfm_dum2#0.livewothr_c=ocpfm_dum2

As you can also see comparing the two models:

. logit daily_f feduy pintim ocpfm_dum2##livewothr_c ocpfm_dum3##livewothr_c, or

Iteration 0:   log likelihood = -58.704243 
Iteration 1:   log likelihood = -52.100632 
Iteration 2:   log likelihood = -52.058353 
Iteration 3:   log likelihood = -52.058231 
Iteration 4:   log likelihood = -52.058231 

Logistic regression                             Number of obs     =         88
                                                LR chi2(7)        =      13.29
                                                Prob > chi2       =     0.0653
Log likelihood = -52.058231                     Pseudo R2         =     0.1132

----------------------------------------------------------------------------------------
               daily_f | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
                 feduy |   .9045513   .0614372    -1.48   0.140     .7918073    1.033349
                pintim |   11.01572   12.93973     2.04   0.041     1.101896    110.1249
          1.ocpfm_dum2 |   1.261524   .8224156     0.36   0.722     .3515429    4.527023
         1.livewothr_c |   .3123884   .4247131    -0.86   0.392     .0217485     4.48705
                       |
ocpfm_dum2#livewothr_c |
                  1 1  |   2.383191   3.679699     0.56   0.574     .1155807     49.1397
                       |
          1.ocpfm_dum3 |   3.892826   4.073845     1.30   0.194       .50059    30.27247
                       |
ocpfm_dum3#livewothr_c |
                  1 1  |   1.166291   2.154166     0.08   0.934     .0312334     43.5507
                       |
                 _cons |   .5286825   .9092787    -0.37   0.711     .0181642    15.38767
----------------------------------------------------------------------------------------
Note: _cons estimates baseline odds.

. logit daily_f feduy pintim livewothr_c ocpfm_dum2 ocpfm_dum3 ocpfm_dum2#livewothr_c ocpfm_dum3#livewothr_c, or

note: 1.ocpfm_dum2#0.livewothr_c omitted because of collinearity
note: 1.ocpfm_dum2#1.livewothr_c omitted because of collinearity
note: 1.ocpfm_dum3#0.livewothr_c omitted because of collinearity
note: 1.ocpfm_dum3#1.livewothr_c omitted because of collinearity
Iteration 0:   log likelihood = -58.704243 
Iteration 1:   log likelihood = -52.100632 
Iteration 2:   log likelihood = -52.058353 
Iteration 3:   log likelihood = -52.058231 
Iteration 4:   log likelihood = -52.058231 

Logistic regression                             Number of obs     =         88
                                                LR chi2(7)        =      13.29
                                                Prob > chi2       =     0.0653
Log likelihood = -52.058231                     Pseudo R2         =     0.1132

----------------------------------------------------------------------------------------
               daily_f | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
                 feduy |   .9045513   .0614372    -1.48   0.140     .7918073    1.033349
                pintim |   11.01572   12.93973     2.04   0.041     1.101896    110.1249
           livewothr_c |    .868282   1.713673    -0.07   0.943     .0181425    41.55504
            ocpfm_dum2 |   1.261524   .8224156     0.36   0.722     .3515429    4.527023
            ocpfm_dum3 |   3.892826   4.073845     1.30   0.194       .50059    30.27247
                       |
ocpfm_dum2#livewothr_c |
                  0 1  |   .4196055   .6478799    -0.56   0.574     .0203501    8.651965
                  1 0  |          1  (omitted)
                  1 1  |          1  (omitted)
                       |
ocpfm_dum3#livewothr_c |
                  0 1  |   .8574187   1.583671    -0.08   0.934     .0229617    32.01703
                  1 0  |          1  (omitted)
                  1 1  |          1  (omitted)
                       |
                 _cons |   .5286825   .9092787    -0.37   0.711     .0181642    15.38767
----------------------------------------------------------------------------------------
Note: _cons estimates baseline odds.

.

[Vincent Li]

Thank you Carlo,

But one more question, what's the difference between the two codes:

 
 logit daily_f feduy ocpfm_dum2 ocpfm_dum3  livewothr_c pintim ocpfm_dum2#livewothr_c ocpfm_dum3#livewothr_c,or

 
 logit daily_f feduy pintim ocpfm_dum2##livewothr_c ocpfm_dum3##livewothr_c, or

In the first one, I include the original variables and interaction terms (using #) into the model. # will just put the interaction term into the model, right?
In the second one, ## will put the original variable and interaction term into the model at the same time.

they look the same but lead to different results.

[Carlo Lazzaro]

Vincent:
the difference in some of the coefficients reported by the two codes is due to the different terms included in the interactions.
take a look at the following elaboration on the orevious codes:

ogit daily_f feduy pintim ocpfm_dum2##livewothr_c ocpfm_dum3##livewothr_c, or
predict pr1, p
logit daily_f feduy pintim livewothr_c ocpfm_dum2 ocpfm_dum3 ocpfm_dum2#livewothr_c ocpfm_dum3#livewothr_c, or
predict pr2, p
list pr1 pr2 in 1/10
. list pr1 pr2 in 1/10

     +---------------------+
     |      pr1        pr2 |
     |---------------------|
  1. | .7486511   .7486511 |
  2. | .6879349   .6879349 |
  3. | .0906954   .0906954 |
  4. |        .          . |
  5. | .5391439   .5391439 |
     |---------------------|
  6. | .6471807   .6471807 |
  7. | .6360271   .6360271 |
  8. |        .          . |
  9. |  .723007    .723007 |
 10. | .5960943   .5960943 |
     +---------------------+

.

[Vincent Li]

Thanks Carlo,

Sorry, I still have a question and thanks for your patience.

The collinearity must be between a and b, but who is a and who is b?
ocpfm_dum2#livewothr_c is collinear with ocpfm_dum2 when the values are 1 0 and 1 1?

 . logit daily_f feduy pintim livewothr_c ocpfm_dum2 ocpfm_dum3 ocpfm_dum2#livewothr_c ocpfm_dum3#livewothr_c, or  
note: 1.ocpfm_dum2#0.livewothr_c omitted because of collinearity
note: 1.ocpfm_dum2#1.livewothr_c omitted because of collinearity
note: 1.ocpfm_dum3#0.livewothr_c omitted because of collinearity
note: 1.ocpfm_dum3#1.livewothr_c omitted because of collinearity
Iteration 0:   log likelihood = -58.704243  
Iteration 1:   log likelihood = -52.100632  
Iteration 2:   log likelihood = -52.058353  
Iteration 3:   log likelihood = -52.058231  
Iteration 4:   log likelihood = -52.058231  
Logistic regression                            
Number of obs     =         88                                                
LR chi2(7)        =      13.29                                                
Prob > chi2       =     0.0653
Log likelihood = -52.058231                    
Pseudo R2         =     0.1132  
----------------------------------------------------------------------------------------                
daily_f | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------------+----------------------------------------------------------------                  
feduy |   .9045513   .0614372    -1.48   0.140     .7918073    1.033349                
pintim |   11.01572   12.93973     2.04   0.041     1.101896    110.1249            
livewothr_c |    .868282   1.713673    -0.07   0.943     .0181425    41.55504            
ocpfm_dum2 |   1.261524   .8224156     0.36   0.722     .3515429    4.527023            
ocpfm_dum3 |   3.892826   4.073845     1.30   0.194       .50059    30.27247                        

ocpfm_dum2#livewothr_c |                  
               0 1  |   .4196055   .6478799    -0.56   0.574     .0203501    8.651965                  
               1 0  |          1  (omitted)                  
               1 1  |          1  (omitted)                       
ocpfm_dum3#livewothr_c |                  
               0 1  |   .8574187   1.583671    -0.08   0.934     .0229617    32.01703                  
               1 0  |          1  (omitted)                  
               1 1  |          1  (omitted)                      
            _cons |   .5286825   .9092787    -0.37   0.711     .0181642    15.38767
----------------------------------------------------------------------------------------
Note: _cons estimates baseline odds.

[Carlo Lazzaro]

Vincent:

note: 1.ocpfm_dum2#0.livewothr_c omitted because of collinearity *omitted because=ocpfm_dum2*
note: 1.ocpfm_dum2#1.livewothr_c omitted because of collinearity *omitted because=ocpfm_dum3*
note: 1.ocpfm_dum3#0.livewothr_c omitted because of collinearity *omitted to avoid the so called dummy trap (
https://en.wikipedia.org/wiki/Dummy_variable_(statistics)
)*
note: 1.ocpfm_dum3#1.livewothr_c omitted because of collinearity *omitted to avoid the so called dummy trap (
https://en.wikipedia.org/wiki/Dummy_variable_(statistics)
)*

See also -margins- and -marginsplot- entries in Stata .pdf manual.

[Vincent Li]

Carlo,

Thank you so much.