interaction effect logistic regression

[Anna Utke]

Dear Stata users,
I am working on a paper that includes a logistic regression (logistics command for OR, vce(cluster Country)). A reviewer suggested to include an interaction effect which I did with the following command:

margins, dydx(VAR!) at(VAR2=(1(1)3))

initiator has 4 categories, but I want to include the fourth because it has only 2 cases. I'm not sure how to describe that in the justification for the reviewer and I'm not sure if I run into any fundamental problems I'm not thinking about att the moment. Any help or a literature suggestions about a similar case is appreciated.

Best Anna

[Carlo Lazzaro]

Anna:
welcome to this forum.
Without further details/example/excerpt about your data (see -help dataex-) it is difficult (for me, at least) to reply positively.
That said, if part of your query deals with choosing the reference category for categorical variables, you can take a look at -help fvvarlist-.

[Anna Utke]

Thank you Carlo! Thank you very much for you quick reply. I hope this is the correct format, I have never used the dataex command before, but other posts here look similar, thus I hope it is correct.
The interaction term is between initiator and CSO but one category in initiator has only 3 observations and thus STATA runs into problems: the output has 1 in OR for this category and "empty" for SE. Thus I used the following command margins, dydx(CSO) at(initiator=(1(1)3)) to show only the first three categories of this variable. My question is, whether I run into problems, when I report these three and mention in the text, that there were too few observations for the fourth category?
Thanks again!
Anna

* Example generated by -dataex-. To install: ssc install dataex
clear
input byte SUCFAI float initiator byte RIGLO double FHI byte(AGE ParlSemi) double ENPP byte(YSA specialbody CSO)
1 2 3   5  1 1 3.26  1 0 1
0 1 3   6  2 1 3.26  2 0 .
1 2 3   6  2 1 3.26  2 0 .
1 2 3   6 10 1 1.95 20 0 1
0 1 3   3 11 0 7.17 11 1 .
1 1 3 3.5 14 0 7.67 14 1 1
0 1 3 2.5  1 1 2.41  1 0 1
0 1 3   2  2 1 2.41  2 0 1
0 1 3   2  2 1 2.41  2 0 1
0 1 3   2  2 1 2.41  2 0 1
0 1 3   2  3 1 2.73  3 0 1
0 1 3   2  3 1 2.73  3 0 1
0 1 3   2 10 1 2.92 10 0 1
1 1 3 1.5 12 1 2.92 12 0 1
1 1 3 1.5 14 1  4.8 14 0 .
1 1 3 1.5 15 1  4.8 15 0 .
1 1 3 1.5 16 1  4.8 16 0 1
0 1 3 1.5 16 1  4.8 16 0 1
0 1 3   2 18 1 3.34 18 0 1
0 1 3   2 20 1 3.34 20 0 1
1 2 3   4  7 1 2.07  7 0 .
1 3 3   4  9 1 2.07  9 0 1
1 3 3 2.5 10 1 4.01 10 0 .
1 1 3   2 11 1 4.01 11 0 .
1 1 3 1.5 20 1 3.07 20 0 .
0 3 3 1.5 21 1 2.59 21 0 .
0 1 3 1.5 23 1 2.59 23 0 .
1 4 3 1.5 23 1 2.59 23 0 0
0 1 6 1.5  0 0  4.8  0 0 1
0 1 6 1.5  0 0  4.8  0 0 1
0 1 6 1.5  1 0  4.8  1 0 1
0 1 6 1.5  2 0  4.8  2 0 0
0 1 6 1.5  3 0 4.15  3 0 1
0 1 6 1.5  3 0 4.15  3 0 1
0 1 6 1.5  3 0 4.15  3 0 1
0 1 6 1.5  3 0 4.15  3 0 1
1 3 6 1.5  4 0 4.15  4 0 1
0 1 6 1.5  4 0 4.15  4 0 1
0 1 6 1.5  4 0 4.15  4 0 1
1 1 6 1.5  5 0 3.71  5 0 0
0 1 6 1.5  5 0 3.71  5 0 1
0 1 6 1.5  5 0 3.71  5 0 1
0 1 6 1.5  5 0 3.71  5 0 1
0 1 6 1.5  6 0 3.71  6 0 1
0 3 6 1.5  6 0 3.71  6 0 1
0 3 6 1.5  6 0 3.71  6 0 1
0 3 6 1.5  6 0 3.71  6 0 .
0 1 6 1.5  7 0 3.71  7 0 1
1 3 6 1.5  7 0 3.71  7 0 1
0 3 6 1.5  7 0 3.71  7 0 1
0 3 6 1.5  7 0 3.71  7 0 1
0 1 6 1.5  8 0 3.71  8 0 1
0 1 6 1.5  8 0 3.71  8 0 1
0 1 6 1.5  8 0 3.71  8 0 1
0 1 6 1.5  8 0 3.71  8 0 1
1 3 6 1.5  8 0 3.71  8 0 1
0 3 6 1.5  8 0 3.71  8 0 1
1 3 6 1.5  8 0 3.71  8 0 .
0 3 6 1.5  8 0 3.71  8 0 .
1 1 6 1.5  9 0 3.67  9 0 1
0 1 6 1.5  9 0 3.67  9 0 1
0 1 6 1.5  9 0 3.67  9 0 1
0 1 6 1.5  9 0 3.67  9 0 1
0 1 6 1.5  9 0 3.67  9 0 1
0 1 6 1.5 10 0 3.67 10 0 1
0 1 6 1.5 10 0 3.67 10 0 1
0 3 6 1.5 10 0 3.67 10 0 0
0 3 6 1.5 10 0 3.67 10 0 1
0 3 6 1.5 10 0 3.67 10 0 1
0 1 6   1 12 0 3.67 12 0 1
0 1 6   1 12 0 3.67 12 0 1
0 3 6   1 12 0 3.67 12 0 1
0 1 6   1 13 0  3.1 13 0 1
0 1 6   1 14 0  3.1 14 0 1
0 1 6   1 14 0  3.1 14 0 1
0 1 6   1 14 0  3.1 14 0 1
0 1 6   1 14 0  3.1 14 0 1
0 1 6   1 14 0  3.1 14 0 1
0 1 6   1 14 0  3.1 14 0 1
1 1 6   1 16 0  3.1 16 0 1
0 1 6   1 16 0  3.1 16 0 1
0 1 6   1 16 0  3.1 16 0 1
0 1 6   1 16 0  3.1 16 0 1
0 1 6   1 16 0  3.1 16 0 1
0 1 6   1 16 0  3.1 16 0 1
0 3 6   1 16 0  3.1 16 0 1
0 1 6   1 17 0 4.51 17 0 1
0 1 6   1 17 0 4.51 17 0 1
0 1 6   1 17 0 4.51 17 0 1
0 1 6   1 18 0 4.51 18 0 1
0 1 6   1 18 0 4.51 18 0 1
0 1 6   1 18 0 4.51 18 0 1
0 3 6   1 18 0 4.51 18 0 1
0 1 6   1 19 1 4.51 19 0 1
0 1 6   1 19 1 4.51 19 0 1
0 1 6   1 19 1 4.51 19 0 1
0 1 6   1 19 1 4.51 19 0 1
1 3 6   1 19 1 4.51 19 0 1
0 3 6   1 19 1 4.51 19 0 1
0 3 6   1 19 1 4.51 19 0 1
end

[Marcos Almeida]

I cannot provide an example with ‘my’ Stata now. But you may also think about something like:
margins var1#var2 if var2 !=4

[Carlo Lazzaro]

Anna:
thanks for your data excerpt...but the code of your regression seems missing!

[Anna Utke]

Carlo, sorry! I thought the information about the command logistics was sufficient. Her is the code:
logistic SUCFAI RIGLO FHI ENPP specialbody ParlSemi AGE i.initiator##CSO , vce(cluster Country)
estat gof
lfit, group(10) table
estat class
lroc

[Carlo Lazzaro]

Anna:
sadly:

. logistic SUCFAI RIGLO FHI ENPP specialbody ParlSemi AGE i.initiator##CSO , vce(cluster Country)
variable Country not found
r(111);

[Anna Utke]

I hope it will work now! I'm sorry about the back and forth...

* Example generated by -dataex-. To install: ssc install dataex
clear
input byte SUCFAI float initiator byte RIGLO double FHI byte(AGE ParlSemi) double ENPP byte(YSA specialbody) str3 Country byte(CSO EU)
1 2 3   5  1 1 3.26  1 0 "BEL" 1 0
0 1 3   6  2 1 3.26  2 0 "BEL" . 0
1 2 3   6  2 1 3.26  2 0 "BEL" . 0
1 2 3   6 10 1 1.95 20 0 "BEL" 1 0
0 1 3   3 11 0 7.17 11 1 "BOS" . 0
1 1 3 3.5 14 0 7.67 14 1 "BOS" 1 0
0 1 3 2.5  1 1 2.41  1 0 "BUL" 1 0
0 1 3   2  2 1 2.41  2 0 "BUL" 1 0
0 1 3   2  2 1 2.41  2 0 "BUL" 1 0
0 1 3   2  2 1 2.41  2 0 "BUL" 1 0
0 1 3   2  3 1 2.73  3 0 "BUL" 1 0
0 1 3   2  3 1 2.73  3 0 "BUL" 1 0
0 1 3   2 10 1 2.92 10 0 "BUL" 1 0
1 1 3 1.5 12 1 2.92 12 0 "BUL" 1 0
1 1 3 1.5 14 1  4.8 14 0 "BUL" . 1
1 1 3 1.5 15 1  4.8 15 0 "BUL" . 1
1 1 3 1.5 16 1  4.8 16 0 "BUL" 1 1
0 1 3 1.5 16 1  4.8 16 0 "BUL" 1 1
0 1 3   2 18 1 3.34 18 0 "BUL" 1 0
0 1 3   2 20 1 3.34 20 0 "BUL" 1 0
1 2 3   4  7 1 2.07  7 0 "CRO" . 0
1 3 3   4  9 1 2.07  9 0 "CRO" 1 0
1 3 3 2.5 10 1 4.01 10 0 "CRO" . 0
1 1 3   2 11 1 4.01 11 0 "CRO" . 0
1 1 3 1.5 20 1 3.07 20 0 "CRO" . 1
0 3 3 1.5 21 1 2.59 21 0 "CRO" . 1
0 1 3 1.5 23 1 2.59 23 0 "CRO" . 1
1 4 3 1.5 23 1 2.59 23 0 "CRO" 0 1
0 1 6 1.5  0 0  4.8  0 0 "CZE" 1 0
0 1 6 1.5  0 0  4.8  0 0 "CZE" 1 0
0 1 6 1.5  1 0  4.8  1 0 "CZE" 1 0
0 1 6 1.5  2 0  4.8  2 0 "CZE" 0 0
0 1 6 1.5  3 0 4.15  3 0 "CZE" 1 0
0 1 6 1.5  3 0 4.15  3 0 "CZE" 1 0
0 1 6 1.5  3 0 4.15  3 0 "CZE" 1 0
0 1 6 1.5  3 0 4.15  3 0 "CZE" 1 0
1 3 6 1.5  4 0 4.15  4 0 "CZE" 1 0
0 1 6 1.5  4 0 4.15  4 0 "CZE" 1 0
0 1 6 1.5  4 0 4.15  4 0 "CZE" 1 0
1 1 6 1.5  5 0 3.71  5 0 "CZE" 0 0
0 1 6 1.5  5 0 3.71  5 0 "CZE" 1 0
0 1 6 1.5  5 0 3.71  5 0 "CZE" 1 0
0 1 6 1.5  5 0 3.71  5 0 "CZE" 1 0
0 1 6 1.5  6 0 3.71  6 0 "CZE" 1 1
0 3 6 1.5  6 0 3.71  6 0 "CZE" 1 1
0 3 6 1.5  6 0 3.71  6 0 "CZE" 1 1
0 3 6 1.5  6 0 3.71  6 0 "CZE" . 1
0 1 6 1.5  7 0 3.71  7 0 "CZE" 1 1
1 3 6 1.5  7 0 3.71  7 0 "CZE" 1 1
0 3 6 1.5  7 0 3.71  7 0 "CZE" 1 1
0 3 6 1.5  7 0 3.71  7 0 "CZE" 1 1
0 1 6 1.5  8 0 3.71  8 0 "CZE" 1 1
0 1 6 1.5  8 0 3.71  8 0 "CZE" 1 1
0 1 6 1.5  8 0 3.71  8 0 "CZE" 1 1
0 1 6 1.5  8 0 3.71  8 0 "CZE" 1 1
1 3 6 1.5  8 0 3.71  8 0 "CZE" 1 1
0 3 6 1.5  8 0 3.71  8 0 "CZE" 1 1
1 3 6 1.5  8 0 3.71  8 0 "CZE" . 1
0 3 6 1.5  8 0 3.71  8 0 "CZE" . 1
1 1 6 1.5  9 0 3.67  9 0 "CZE" 1 1
0 1 6 1.5  9 0 3.67  9 0 "CZE" 1 1
0 1 6 1.5  9 0 3.67  9 0 "CZE" 1 1
0 1 6 1.5  9 0 3.67  9 0 "CZE" 1 1
0 1 6 1.5  9 0 3.67  9 0 "CZE" 1 1
0 1 6 1.5 10 0 3.67 10 0 "CZE" 1 1
0 1 6 1.5 10 0 3.67 10 0 "CZE" 1 1
0 3 6 1.5 10 0 3.67 10 0 "CZE" 0 1
0 3 6 1.5 10 0 3.67 10 0 "CZE" 1 1
0 3 6 1.5 10 0 3.67 10 0 "CZE" 1 1
0 1 6   1 12 0 3.67 12 0 "CZE" 1 0
0 1 6   1 12 0 3.67 12 0 "CZE" 1 0
0 3 6   1 12 0 3.67 12 0 "CZE" 1 0
0 1 6   1 13 0  3.1 13 0 "CZE" 1 0
0 1 6   1 14 0  3.1 14 0 "CZE" 1 0
0 1 6   1 14 0  3.1 14 0 "CZE" 1 0
0 1 6   1 14 0  3.1 14 0 "CZE" 1 0
0 1 6   1 14 0  3.1 14 0 "CZE" 1 0
0 1 6   1 14 0  3.1 14 0 "CZE" 1 0
0 1 6   1 14 0  3.1 14 0 "CZE" 1 0
1 1 6   1 16 0  3.1 16 0 "CZE" 1 0
0 1 6   1 16 0  3.1 16 0 "CZE" 1 0
0 1 6   1 16 0  3.1 16 0 "CZE" 1 0
0 1 6   1 16 0  3.1 16 0 "CZE" 1 0
0 1 6   1 16 0  3.1 16 0 "CZE" 1 0
0 1 6   1 16 0  3.1 16 0 "CZE" 1 0
0 3 6   1 16 0  3.1 16 0 "CZE" 1 0
0 1 6   1 17 0 4.51 17 0 "CZE" 1 0
0 1 6   1 17 0 4.51 17 0 "CZE" 1 0
0 1 6   1 17 0 4.51 17 0 "CZE" 1 0
0 1 6   1 18 0 4.51 18 0 "CZE" 1 0
0 1 6   1 18 0 4.51 18 0 "CZE" 1 0
0 1 6   1 18 0 4.51 18 0 "CZE" 1 0
0 3 6   1 18 0 4.51 18 0 "CZE" 1 0
0 1 6   1 19 1 4.51 19 0 "CZE" 1 0
0 1 6   1 19 1 4.51 19 0 "CZE" 1 0
0 1 6   1 19 1 4.51 19 0 "CZE" 1 0
0 1 6   1 19 1 4.51 19 0 "CZE" 1 0
1 3 6   1 19 1 4.51 19 0 "CZE" 1 0
0 3 6   1 19 1 4.51 19 0 "CZE" 1 0
0 3 6   1 19 1 4.51 19 0 "CZE" 1 0
end

[Carlo Lazzaro]

Anna:
thanks for providing full details.
In my opinion, interaction is not meaningful/feasible/advisable due to amissing value problem, too:

. logistic SUCFAI RIGLO FHI ENPP specialbody ParlSemi AGE i.initiator##CSO , vce(cluster Country)
note: specialbody != 0 predicts success perfectly
      specialbody dropped and 1 obs not used

note: 2.initiator != 0 predicts success perfectly
      2.initiator dropped and 2 obs not used

note: 4.initiator != 0 predicts success perfectly
      4.initiator dropped and 1 obs not used

note: 3.initiator#0.CSO != 0 predicts failure perfectly
      3.initiator#0.CSO dropped and 1 obs not used

note: 2.initiator#0.CSO identifies no observations in the sample
note: 2.initiator#1.CSO omitted because of collinearity
note: 3.initiator#1.CSO omitted because of collinearity
note: 4.initiator#1.CSO identifies no observations in the sample

Logistic regression                             Number of obs     =         81
                                                Wald chi2(1)      =          .
                                                Prob > chi2       =          .
Log pseudolikelihood = -24.317264               Pseudo R2         =     0.1968

                                 (Std. Err. adjusted for 3 clusters in Country)
-------------------------------------------------------------------------------
              |               Robust
       SUCFAI | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
        RIGLO |   .5243795   .3586928    -0.94   0.345     .1372132     2.00399
          FHI |   1.516468   1.595678     0.40   0.692     .1928282    11.92603
         ENPP |   1.044307   .5836235     0.08   0.938       .34924    3.122715
  specialbody |          1  (omitted)
     ParlSemi |   .7114512   .6360658    -0.38   0.703     .1233494    4.103489
          AGE |   1.062549   .0257962     2.50   0.012     1.013173     1.11433
              |
    initiator |
           2  |          1  (empty)
           3  |   9.505921   4.803241     4.46   0.000     3.530946    25.59159
           4  |          1  (empty)
              |
        1.CSO |   .0274471     .00703   -14.04   0.000     .0166142    .0453435
              |
initiator#CSO |
         2 0  |          1  (empty)
         2 1  |          1  (empty)
         3 0  |          1  (empty)
         3 1  |          1  (omitted)
         4 0  |          1  (empty)
         4 1  |          1  (empty)
              |
        _cons |   17.31974   57.88003     0.85   0.393     .0247714    12109.66
-------------------------------------------------------------------------------
Note: _cons estimates baseline odds.

. estat gof

Logistic model for SUCFAI, goodness-of-fit test

       number of observations =        81
 number of covariate patterns =        37
             Pearson chi2(29) =        24.27
                  Prob > chi2 =         0.7153

CSO has missing values (I do not know whether you investigated/were asked to investigate them):

. codebook CSO

------------------------------------------------------------------------------------------------------------------------
CSO                                                                                                          (unlabeled)
------------------------------------------------------------------------------------------------------------------------

                  type:  numeric (byte)

                 range:  [0,1]                        units:  1
         unique values:  2                        missing .:  14/100

            tabulation:  Freq.  Value
                             4  0
                            82  1
                            14  .

In sum, before considering interaction, I think you should pay attention to the missing values issue.

[Anna Utke]

Dear Carlo,
thank you for taking the time! Just to clarify: Do you mean the interaction is not meaningful because for one category of the variable initiator I have missing values?
I will deal with the missing values for CSO, I have to wait for the input of my co-author.
Best wishes
Anna

[Carlo Lazzaro]

Anna:
not quite.
I would simply pay attention to missing values first (by diagnosing their mechanism and pattern and decide how to dela with them accordingly) and then consider interaction (and/or model specification at large).