Factor variable interactions providing a base category that is not specified with the ib notation

[Nico Ochmann]

Dear Statalist,
I would appreciate your help on the following.
I use factor variable notation in the following way and I specify a base category; however, Stata drops the wrong, in this example, year.

regress temp ib2013.year#i.ukb ib1000.country ib2013.year if year<=2020

For whatever reason, I do not obtain the right base category.
When I run it with the full dataset, I get all interactions of year with ukb, but 2020.year#1.ukb is omitted rather than 2013.year#1.ukb.
I am not sure why this is the case and would greatly appreciate your help.
Best,
Nico

* Example generated by -dataex-. For more info, type help dataex
clear
input float(temp year ukb country)
0 2015 0    5
0 2017 0   10
1 2015 0   14
0 2016 0   18
0 2012 0   19
0 2012 0   22
0 2012 0   26
0 2010 0   26
1 2013 0   27
0 2020 0  265
0 2011 0  309
0 2012 0  386
0 2014 1 1000
0 2014 1 1000
0 2009 1 1000
0 2019 1 1000
0 2011 1 1000
0 2011 1 1000
0 2010 1 1000
0 2013 1 1000
1 2011 1 1000
0 2015 1 1000
0 2013 1 1000
0 2018 1 1000
0 2019 1 1000
0 2011 1 1000
0 2015 1 1000
0 2018 1 1000
0 2015 1 1000
0 2016 1 1000
0 2020 1 1000
0 2013 1 1000
0 2017 1 1000
0 2011 1 1000
1 2015 1 1000
0 2012 1 1000
0 2014 1 1000
1 2012 1 1000
0 2009 1 1000
0 2019 1 1000
0 2012 1 1000
0 2013 1 1000
0 2013 1 1000
0 2010 1 1000
0 2016 1 1000
0 2020 1 1000
0 2019 1 1000
0 2011 1 1000
0 2010 1 1000
0 2016 1 1000
0 2014 1 1000
0 2013 1 1000
1 2009 1 1000
0 2020 1 1000
0 2017 1 1000
0 2020 1 1000
0 2015 1 1000
0 2015 1 1000
0 2014 1 1000
0 2012 1 1000
0 2017 1 1000
0 2018 1 1000
0 2012 1 1000
0 2011 1 1000
0 2010 1 1000
0 2015 1 1000
0 2010 1 1000
0 2018 1 1000
0 2012 1 1000
0 2010 1 1000
0 2019 1 1000
0 2014 1 1000
0 2017 1 1000
0 2019 1 1000
0 2019 1 1000
0 2015 1 1000
0 2010 1 1000
0 2012 1 1000
0 2010 1 1000
0 2014 1 1000
0 2019 1 1000
0 2011 1 1000
0 2012 1 1000
0 2010 1 1000
0 2016 1 1000
0 2012 1 1000
0 2017 1 1000
0 2011 1 1000
0 2010 1 1000
0 2021 1 1000
0 2012 1 1000
0 2012 1 1000
0 2011 1 1000
0 2017 1 1000
0 2018 1 1000
0 2010 1 1000
1 2010 1 1000
0 2009 1 1000
0 2015 .    .
0 2012 .    .
end

[Rich Goldstein]

when I estimate your model on your example data, I get numerous notes about terms being omitted due to collinearity - do you get any notes when you estimate on the full data? here is what I mean:

. regress temp ib2013.year#i.ukb ib1000.country ib2013.year if year<=2020
note: 2009.year#0b.ukb identifies no observations in the sample.
note: 2009.year#1.ukb omitted because of collinearity.
note: 2011.year#1.ukb omitted because of collinearity.
note: 2012.year#1.ukb omitted because of collinearity.
note: 2013b.year#1.ukb omitted because of collinearity.
note: 2014.year#0b.ukb identifies no observations in the sample.
note: 2014.year#1.ukb omitted because of collinearity.
note: 2015.year#1.ukb omitted because of collinearity.
note: 2016.year#1.ukb omitted because of collinearity.
note: 2017.year#1.ukb omitted because of collinearity.
note: 2018.year#0b.ukb identifies no observations in the sample.
note: 2018.year#1.ukb omitted because of collinearity.
note: 2019.year#0b.ukb identifies no observations in the sample.
note: 2019.year#1.ukb omitted because of collinearity.
note: 2020.year#1.ukb omitted because of collinearity.

note that I have omitted the rest of the output as it is lengthy and appears to be uninformative

[Jeff Pitblado (StataCorp)]

Here is what I get from my Stata/SE 18. I added option
allbaselevels to get Stata to show the factor and interaction
levels it identifies as base levels.

. regress temp ib2013.year#i.ukb ib1000.country ib2013.year if year<=2020, allbaselevels
note: 2009.year#0b.ukb identifies no observations in the sample.
note: 2009.year#1.ukb omitted because of collinearity.
note: 2011.year#1.ukb omitted because of collinearity.
note: 2012.year#1.ukb omitted because of collinearity.
note: 2013b.year#1.ukb omitted because of collinearity.
note: 2014.year#0b.ukb identifies no observations in the sample.
note: 2014.year#1.ukb omitted because of collinearity.
note: 2015.year#1.ukb omitted because of collinearity.
note: 2016.year#1.ukb omitted because of collinearity.
note: 2017.year#1.ukb omitted because of collinearity.
note: 2018.year#0b.ukb identifies no observations in the sample.
note: 2018.year#1.ukb omitted because of collinearity.
note: 2019.year#0b.ukb identifies no observations in the sample.
note: 2019.year#1.ukb omitted because of collinearity.
note: 2020.year#1.ukb omitted because of collinearity.

      Source |       SS           df       MS      Number of obs   =        97
-------------+----------------------------------   F(23, 73)       =      1.56
       Model |  2.14408779        23  .093221208   Prob > F        =    0.0775
    Residual |  4.35075758        73  .059599419   R-squared       =    0.3301
-------------+----------------------------------   Adj R-squared   =    0.1191
       Total |  6.49484536        96  .067654639   Root MSE        =    .24413

------------------------------------------------------------------------------
        temp | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
    year#ukb |
     2009 0  |          0  (empty)
     2009 1  |          0  (omitted)
     2010 0  |          0  (base)
     2010 1  |  -.0075758   .3599772    -0.02   0.983    -.7250093    .7098578
     2011 0  |          0  (base)
     2011 1  |          0  (omitted)
     2012 0  |          0  (base)
     2012 1  |          0  (omitted)
     2013 0  |          0  (base)
     2013 1  |          0  (omitted)
     2014 0  |          0  (empty)
     2014 1  |          0  (omitted)
     2015 0  |          0  (base)
     2015 1  |          0  (omitted)
     2016 0  |          0  (base)
     2016 1  |          0  (omitted)
     2017 0  |          0  (base)
     2017 1  |          0  (omitted)
     2018 0  |          0  (empty)
     2018 1  |          0  (omitted)
     2019 0  |          0  (empty)
     2019 1  |          0  (omitted)
     2020 0  |          0  (base)
     2020 1  |          0  (omitted)
             |
     country |
          5  |      -.125   .2589389    -0.48   0.631    -.6410645    .3910645
         10  |  -1.30e-17   .2636905    -0.00   1.000    -.5255343    .5255343
         14  |       .875   .2589389     3.38   0.001     .3589355    1.391064
         18  |  -2.46e-17   .2729456    -0.00   1.000    -.5439797    .5439797
         19  |  -.0909091   .2549854    -0.36   0.722    -.5990942    .4172761
         22  |  -.0909091   .2549854    -0.36   0.722    -.5990942    .4172761
         26  |  -.0909091   .2549854    -0.36   0.722    -.5990942    .4172761
         27  |          1   .2636905     3.79   0.000     .4744657    1.525534
        265  |  -2.74e-17   .2729456    -0.00   1.000    -.5439797    .5439797
        309  |        -.1   .2560456    -0.39   0.697    -.6102982    .4102982
        386  |  -.0909091   .2549854    -0.36   0.722    -.5990942    .4172761
       1000  |          0  (base)
             |
        year |
       2009  |        .25   .1575852     1.59   0.117    -.0640668    .5640668
       2010  |   .0909091   .3668109     0.25   0.805    -.6401439    .8219621
       2011  |         .1   .1260681     0.79   0.430    -.1512535    .3512535
       2012  |   .0909091   .1239006     0.73   0.465    -.1560245    .3378427
       2013  |          0  (base)
       2014  |   2.62e-16   .1358214     0.00   1.000    -.2706916    .2706916
       2015  |       .125   .1318452     0.95   0.346    -.1377672    .3877672
       2016  |   2.82e-16   .1575852     0.00   1.000    -.3140668    .3140668
       2017  |   2.70e-16   .1409485     0.00   1.000    -.2809099    .2809099
       2018  |   2.74e-16    .147828     0.00   1.000    -.2946208    .2946208
       2019  |   2.82e-16   .1318452     0.00   1.000    -.2627672    .2627672
       2020  |   2.82e-16   .1575852     0.00   1.000    -.3140668    .3140668
             |
       _cons |  -2.64e-16   .0996656    -0.00   1.000    -.1986333    .1986333
------------------------------------------------------------------------------

There are 4 empty cells in the interaction between year and ukb.

. tab year ukb

           |          ukb
      year |         0          1 |     Total
-----------+----------------------+----------
      2009 |         0          4 |         4 
      2010 |         1         12 |        13 
      2011 |         1         10 |        11 
      2012 |         4         11 |        15 
      2013 |         1          6 |         7 
      2014 |         0          7 |         7 
      2015 |         2          8 |        10 
      2016 |         1          4 |         5 
      2017 |         1          6 |         7 
      2018 |         0          5 |         5 
      2019 |         0          8 |         8 
      2020 |         1          4 |         5 
      2021 |         0          1 |         1 
-----------+----------------------+----------
     Total |        12         86 |        98

Given that the main effects of ukb (i.e. i.ukb) are not
present in this model, it is not surprising that 2013.year#1.ukb
is not flagged as a base.

Yet, given the pattern of levels in this dataset, this interaction level
is still omitted because of collinearity (at least in my Stata/SE
session).

When a predictor is omitted because of collinearity, it is also not
surprising that the same data run on a different computer or with
Stata/MP on the same computer might omit a different predictor.
Collinear variables are, by their nature, indistinguishable for
identifying the model; and thus, it is up to the order of operations and
accumulation of tiny errors in finite precision computers that
determines which variable gets omitted.

[Nico Ochmann]

Dear Rich and Jeff,
Thanks for your reply, I very much appreciate your help. The sample I gave was not very informative, my apologies. Below I copied and pasted what I get with the full dataset.
Now Jeff writes that I need to have i.ukb in the regression for 2013.year#1.ukb to be flagged as base.
I appreciate that point now, but I wonder if there is a way around this since I need to use the country dummies instead of (i.ukb) in the regression.
Or shall I just abandon the factor notation in this case and define the dummy variables from scratch.
I would appreciate your input.
Thanks so much,
Nico

year#ukb    
2009 1    -.0234836    .0096554    -2.43    0.015    -.042408    -.0045593
2010 1    -.0124545    .0084261    -1.48    0.139    -.0289695    .0040604
2011 1    -.0077198    .0085642    -0.90    0.367    -.0245053    .0090657
2012 1    -.0021349    .008822    -0.24    0.809    -.0194257    .0151559
2013 1    .0018051    .008885    0.20    0.839    -.0156093    .0192195
2014 1    .0064946    .0090016    0.72    0.471    -.0111484    .0241376
2015 1    -.0056152    .0086047    -0.65    0.514    -.0224801    .0112498
2016 1    .0036982    .008692    0.43    0.670    -.013338    .0207344
2017 1    .0009898    .0089316    0.11    0.912    -.016516    .0184955
2018 1    -.0056581    .0092139    -0.61    0.539    -.0237171    .0124009
2019 1    .0031394    .0093968    0.33    0.738    -.0152781    .0215568
2020 1    0    (omitted)
    
year    
2009    .0278519    .0080459    3.46    0.001    .0120823    .0436216
2010    .0181434    .0068035    2.67    0.008    .0048086    .0314781
2011    .0115418    .0069579    1.66    0.097    -.0020954    .025179
2012    .0027301    .0072467    0.38    0.706    -.0114732    .0169335
2013    0    (base)
2014    -.0009319    .007442    -0.13    0.900    -.015518    .0136542
2015    .0092916    .0069567    1.34    0.182    -.0043434    .0229265
2016    .0114922    .0070546    1.63    0.103    -.0023346    .0253191
2017    .0179823    .007314    2.46    0.014    .0036471    .0323175
2018    .0183142    .0076382    2.40    0.016    .0033436    .0332848
2019    .0159713    .0078403    2.04    0.042    .0006045    .031338
2020    .0193868    .008296    2.34    0.019    .0031269    .0356466