"Not Estimable" results with Margins Command

[Anthony Cozart]

Hi,

I’m looking for help with a STATA margins analysis. My data is a voting and elections database that has one row observation for each election year-state-office code combination, e.g. 2012, California, Presidential Office. Presidential, senatorial, and gubernatorial data goes back to 1980. District level House of Representatives data goes back to 2006.

My regression code is the following, and produces output without any problems:

reg deflator_temp win_margin no_incumbent unopposed senate governor presidential non_senate_year non_gubernatorial_year non_presidential_year i.year##i.state_code, r

However, running the following margins command produces results that are "not estimable:"
margins year#state_code, atmeans

When I run the same regression with decade fixed effects instead of year fixed effects I am able to produce margins predicted values. Any thoughts why this is? Any help would be greatly appreciated.

Anthony

[Clyde Schechter]

Please show the full regression output. If there are some combinations of year and state_code that do not occur in your estimation sample, the corresponding margins will, of course, be non-estimable. But the regression output will show that with a zero coefficient and (empty) in the standard error column.

[Anthony Cozart]

The regression output is provided below (sorry it's not complete, there are 17*50 interacted year*state_codes). There are no combinations of year and state_code that are empty, however, margins remains "non-estimable." Thanks!

. reg deflator_temp c.win_margin unopposed senate president governor non_presidential_y
> ear i.election_cycle##ib1.state_code, r
note: 16.election_cycle omitted because of collinearity

Linear regression Number of obs = 3784
F(824, 2929) = .
Prob > F = .
R-squared = 0.8456
Root MSE = .05428

--------------------------------------------------------------------------------------
| Robust
deflator_temp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------------------+----------------------------------------------------------------
win_margin | -.0555156 .0085691 -6.48 0.000 -.0723176 -.0387136
unopposed | -.0569567 .0079573 -7.16 0.000 -.0725591 -.0413543
senate | .0195503 .0021005 9.31 0.000 .0154317 .0236688
president | .0352048 .0023747 14.82 0.000 .0305485 .0398611
governor | .0199522 .001586 12.58 0.000 .0168424 .0230621
non_presidential_y~r | .0201942 .0302443 0.67 0.504 -.039108 .0794963
|
election_cycle |
2 | -.0764414 .0234632 -3.26 0.001 -.1224475 -.0304354
3 | .0295092 .035298 0.84 0.403 -.0397022 .0987205
4 | -.0451901 .015661 -2.89 0.004 -.0758978 -.0144825
5 | .0004333 .031856 0.01 0.989 -.0620292 .0628958
6 | -.0710912 .0199478 -3.56 0.000 -.1102043 -.0319781
7 | .0959236 .0270375 3.55 0.000 .042909 .1489381
8 | -.0845414 .0142676 -5.93 0.000 -.1125169 -.0565658
9 | .0330271 .0270158 1.22 0.222 -.0199448 .085999
10 | -.0558282 .0149968 -3.72 0.000 -.0852336 -.0264229
11 | .0376432 .0315606 1.19 0.233 -.02424 .0995265
12 | -.0536377 .0144028 -3.72 0.000 -.0818783 -.025397
13 | .1230411 .0271042 4.54 0.000 .0698959 .1761863
14 | -.0597307 .0175485 -3.40 0.001 -.0941394 -.0253219
15 | .1664065 .0318918 5.22 0.000 .103874 .228939
16 | 0 (omitted)
17 | .1581001 .0380935 4.15 0.000 .0834073 .232793
|
state_code |
2 | .1481418 .0288122 5.14 0.000 .0916475 .2046361
3 | .0181749 .026979 0.67 0.501 -.0347249 .0710747
4 | -.0251672 .0927823 -0.27 0.786 -.2070925 .156758
5 | .0954332 .0268609 3.55 0.000 .0427651 .1481013
6 | .1223885 .026956 4.54 0.000 .0695338 .1752432
7 | .1783591 .026895 6.63 0.000 .1256242 .2310941
8 | .101548 .027144 3.74 0.000 .0483248 .1547712
10 | .0416499 .0312265 1.33 0.182 -.0195782 .102878
11 | -.0448297 .0291401 -1.54 0.124 -.1019668 .0123074
12 | .020939 .0278674 0.75 0.452 -.0337026 .0755806
13 | .2416267 .0274532 8.80 0.000 .1877971 .2954562
14 | .1416483 .0268752 5.27 0.000 .0889521 .1943446
15 | .1307786 .027054 4.83 0.000 .0777319 .1838254
16 | .1767611 .0269189 6.57 0.000 .1239793 .2295429
17 | .1207273 .0269433 4.48 0.000 .0678977 .173557
18 | .0091924 .0311258 0.30 0.768 -.0518382 .0702231
19 | -.1495553 .0868697 -1.72 0.085 -.3198872 .0207765
20 | .2085658 .0300834 6.93 0.000 .149579 .2675526
21 | .0355193 .0308758 1.15 0.250 -.0250212 .0960598
22 | .1357834 .0292215 4.65 0.000 .0784866 .1930802
23 | .1430292 .0279947 5.11 0.000 .0881379 .1979206
24 | .2411713 .0277881 8.68 0.000 .1866852 .2956574
25 | .0480209 .0286618 1.68 0.094 -.0081783 .1042201
26 | .1431912 .0271257 5.28 0.000 .0900038 .1963785
27 | .1984741 .0278694 7.12 0.000 .1438284 .2531198
28 | .1363974 .0271425 5.03 0.000 .083177 .1896178
29 | .0008721 .0285834 0.03 0.976 -.0551734 .0569176
30 | .1303641 .027295 4.78 0.000 .0768447 .1838835
31 | .1151984 .0278134 4.14 0.000 .0606626 .1697341
32 | .0545403 .02933 1.86 0.063 -.0029693 .1120499
33 | .0487844 .0272261 1.79 0.073 -.0045998 .1021686
34 | -.0131968 .02749 -0.48 0.631 -.0670985 .0407049
35 | .213603 .0270789 7.89 0.000 .1605074 .2666985
36 | .0972953 .0272367 3.57 0.000 .0438904 .1507003
37 | .0350421 .0448867 0.78 0.435 -.0529705 .1230547
38 | .1646921 .0269428 6.11 0.000 .1118633 .2175209
39 | .0663262 .0269102 2.46 0.014 .0135614 .1190909
40 | .1612359 .0282881 5.70 0.000 .1057693 .2167025
41 | -.0419528 .0279213 -1.50 0.133 -.0967001 .0127946
42 | .2333114 .0270014 8.64 0.000 .1803677 .2862552
43 | -.0016201 .0361242 -0.04 0.964 -.0724514 .0692113
44 | .0073319 .0282184 0.26 0.795 -.0479979 .0626617
45 | .2221861 .027157 8.18 0.000 .1689374 .2754349
46 | .1342967 .0271987 4.94 0.000 .0809661 .1876273
47 | .0042254 .0339798 0.12 0.901 -.0624012 .0708521
48 | .1410684 .0273376 5.16 0.000 .0874655 .1946713
49 | .0762407 .0277358 2.75 0.006 .0218571 .1306243
50 | .2175442 .0269673 8.07 0.000 .1646673 .2704211
51 | .1037342 .027713 3.74 0.000 .0493952 .1580732
|
election_cycle#|
state_code |
2 2 | .0946897 .0345743 2.74 0.006 .0268972 .1624821
2 3 | -.0376782 .0331004 -1.14 0.255 -.1025806 .0272243
2 4 | .1178034 .0947125 1.24 0.214 -.0679064 .3035132

[Stephen Jenkins]

Anthony -- welcome to Statalist. Thanks for posting your output. It would be a great help to legibility if you were to include your Stata code and output between CODE delimiters -- that way it gets nicely formatted and easier to read (and copy/paste). It's easy to do. Use the advanced editor functions which are accessible by hitting the underlined-A on RHS above where you enter text. On the strip that appears you'll see a "#" button. There are also ways to "tag" URLs to ensure they become links. Etc. thanks.

[Clyde Schechter]

So, the first thing I notice from your regression output is that your overall F-statistic is missing. When you are doing regression with robust standard errors, this can arise when you have a dummy variable that only takes the 1-value in a single observation (within the estimation sample). I'm not 100% sure that this is the source of the non-estimable results in -margins-, but I suspect it is. The particular -margins- that are not estimable might give you a hint as to which variable(s) are singleton dummies. Or you can just -tab- them and look directly for that phenomenon.

This would also explain why when you aggregate up to decades instead of years the problem disappears, as those singletons get merged with other years.

Also, I notice that the indicator for election cycle 16 has been dropped due to collinearity, which may mean that it is not instantiated in the estimation sample.

Both of these suggest that you review the distributions of all your indicator variables in the estimation sample.

[Anthony Cozart]

Hi Stephen, Thanks for the information -- I searched how to include output in a better format but couldn't find anything. Here's the output:

 reg deflator_temp c.win_margin unopposed senate president governor non_presidential_year i.election_cycle##ib1.state_code, r

 Output
note: 16.election_cycle omitted because of collinearity

Linear regression                                      Number of obs =    3784
                                                       F(824,  2929) =       .
                                                       Prob > F      =       .
                                                       R-squared     =  0.8456
                                                       Root MSE      =  .05428

--------------------------------------------------------------------------------------
                     |               Robust
       deflator_temp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------------+----------------------------------------------------------------
          win_margin |  -.0555156   .0085691    -6.48   0.000    -.0723176   -.0387136
           unopposed |  -.0569567   .0079573    -7.16   0.000    -.0725591   -.0413543
              senate |   .0195503   .0021005     9.31   0.000     .0154317    .0236688
           president |   .0352048   .0023747    14.82   0.000     .0305485    .0398611
            governor |   .0199522    .001586    12.58   0.000     .0168424    .0230621
non_presidential_y~r |   .0201942   .0302443     0.67   0.504     -.039108    .0794963
                     |
      election_cycle |
                  2  |  -.0764414   .0234632    -3.26   0.001    -.1224475   -.0304354
                  3  |   .0295092    .035298     0.84   0.403    -.0397022    .0987205
                  4  |  -.0451901    .015661    -2.89   0.004    -.0758978   -.0144825
                  5  |   .0004333    .031856     0.01   0.989    -.0620292    .0628958
                  6  |  -.0710912   .0199478    -3.56   0.000    -.1102043   -.0319781
                  7  |   .0959236   .0270375     3.55   0.000      .042909    .1489381
                  8  |  -.0845414   .0142676    -5.93   0.000    -.1125169   -.0565658
                  9  |   .0330271   .0270158     1.22   0.222    -.0199448     .085999
                 10  |  -.0558282   .0149968    -3.72   0.000    -.0852336   -.0264229
                 11  |   .0376432   .0315606     1.19   0.233      -.02424    .0995265
                 12  |  -.0536377   .0144028    -3.72   0.000    -.0818783    -.025397
                 13  |   .1230411   .0271042     4.54   0.000     .0698959    .1761863
                 14  |  -.0597307   .0175485    -3.40   0.001    -.0941394   -.0253219
                 15  |   .1664065   .0318918     5.22   0.000      .103874     .228939
                 16  |          0  (omitted)
                 17  |   .1581001   .0380935     4.15   0.000     .0834073     .232793
  

​

[Anthony Cozart]

                   |
          state_code |
                  2  |   .1481418   .0288122     5.14   0.000     .0916475    .2046361
                  3  |   .0181749    .026979     0.67   0.501    -.0347249    .0710747
                  4  |  -.0251672   .0927823    -0.27   0.786    -.2070925     .156758
                  5  |   .0954332   .0268609     3.55   0.000     .0427651    .1481013
                  6  |   .1223885    .026956     4.54   0.000     .0695338    .1752432
                  7  |   .1783591    .026895     6.63   0.000     .1256242    .2310941
                  8  |    .101548    .027144     3.74   0.000     .0483248    .1547712
                 10  |   .0416499   .0312265     1.33   0.182    -.0195782     .102878
                 11  |  -.0448297   .0291401    -1.54   0.124    -.1019668    .0123074
                 12  |    .020939   .0278674     0.75   0.452    -.0337026    .0755806
                 13  |   .2416267   .0274532     8.80   0.000     .1877971    .2954562
                 14  |   .1416483   .0268752     5.27   0.000     .0889521    .1943446
                 15  |   .1307786    .027054     4.83   0.000     .0777319    .1838254
                 16  |   .1767611   .0269189     6.57   0.000     .1239793    .2295429
                 17  |   .1207273   .0269433     4.48   0.000     .0678977     .173557
                 18  |   .0091924   .0311258     0.30   0.768    -.0518382    .0702231
                 19  |  -.1495553   .0868697    -1.72   0.085    -.3198872    .0207765
                 20  |   .2085658   .0300834     6.93   0.000      .149579    .2675526
                 21  |   .0355193   .0308758     1.15   0.250    -.0250212    .0960598
                 22  |   .1357834   .0292215     4.65   0.000     .0784866    .1930802
                 23  |   .1430292   .0279947     5.11   0.000     .0881379    .1979206
                 24  |   .2411713   .0277881     8.68   0.000     .1866852    .2956574
                 25  |   .0480209   .0286618     1.68   0.094    -.0081783    .1042201
                 26  |   .1431912   .0271257     5.28   0.000     .0900038    .1963785
                 27  |   .1984741   .0278694     7.12   0.000     .1438284    .2531198
                 28  |   .1363974   .0271425     5.03   0.000      .083177    .1896178
                 29  |   .0008721   .0285834     0.03   0.976    -.0551734    .0569176
                 30  |   .1303641    .027295     4.78   0.000     .0768447    .1838835
                 31  |   .1151984   .0278134     4.14   0.000     .0606626    .1697341
                 32  |   .0545403     .02933     1.86   0.063    -.0029693    .1120499
                 33  |   .0487844   .0272261     1.79   0.073    -.0045998    .1021686
                 34  |  -.0131968     .02749    -0.48   0.631    -.0670985    .0407049
                 35  |    .213603   .0270789     7.89   0.000     .1605074    .2666985
                 36  |   .0972953   .0272367     3.57   0.000     .0438904    .1507003
                 37  |   .0350421   .0448867     0.78   0.435    -.0529705    .1230547
                 38  |   .1646921   .0269428     6.11   0.000     .1118633    .2175209
                 39  |   .0663262   .0269102     2.46   0.014     .0135614    .1190909
                 40  |   .1612359   .0282881     5.70   0.000     .1057693    .2167025
                 41  |  -.0419528   .0279213    -1.50   0.133    -.0967001    .0127946
                 42  |   .2333114   .0270014     8.64   0.000     .1803677    .2862552
                 43  |  -.0016201   .0361242    -0.04   0.964    -.0724514    .0692113
                 44  |   .0073319   .0282184     0.26   0.795    -.0479979    .0626617
                 45  |   .2221861    .027157     8.18   0.000     .1689374    .2754349
                 46  |   .1342967   .0271987     4.94   0.000     .0809661    .1876273
                 47  |   .0042254   .0339798     0.12   0.901    -.0624012    .0708521
                 48  |   .1410684   .0273376     5.16   0.000     .0874655    .1946713
                 49  |   .0762407   .0277358     2.75   0.006     .0218571    .1306243
                 50  |   .2175442   .0269673     8.07   0.000     .1646673    .2704211
                 51  |   .1037342    .027713     3.74   0.000     .0493952    .1580732
                     |
      election_cycle#|
          state_code |
               2  2  |   .0946897   .0345743     2.74   0.006     .0268972    .1624821
               2  3  |  -.0376782   .0331004    -1.14   0.255    -.1025806    .0272243
               2  4  |   .1178034   .0947125     1.24   0.214    -.0679064    .3035132
               2  5  |   .0001964   .0329798     0.01   0.995    -.0644695    .0648623
               2  6  |  -.0622423    .033009    -1.89   0.059    -.1269654    .0024808
               2  7  |  -.0826772   .0331769    -2.49   0.013    -.1477296   -.0176248
               2  8  |  -.0387451   .0334703    -1.16   0.247    -.1043728    .0268826
               2 10  |  -.0846556   .0404029    -2.10   0.036    -.1638766   -.0054346
               2 11  |  -.0664823   .0420196    -1.58   0.114    -.1488733    .0159086
               2 12  |   .0708298   .0339551     2.09   0.037     .0042514    .1374081
               2 13  |  -.1252286   .0338254    -3.70   0.000    -.1915527   -.0589046
               2 14  |  -.0632857   .0333434    -1.90   0.058    -.1286646    .0020933
               2 15  |  -.0451108   .0333605    -1.35   0.176    -.1105233    .0203016
               2 16  |  -.0636097   .0329818    -1.93   0.054    -.1282796    .0010601
               2 17  |  -.0628908   .0333612    -1.89   0.060    -.1283045    .0025229
               2 18  |  -.1125319   .0365025    -3.08   0.002    -.1841049   -.0409588
               2 19  |  -.0474921   .0889254    -0.53   0.593    -.2218547    .1268705
               2 20  |  -.0251833   .0356155    -0.71   0.480    -.0950174    .0446507
               2 21  |  -.0436427   .0363324    -1.20   0.230    -.1148824    .0275969
               2 22  |  -.0351829   .0360393    -0.98   0.329    -.1058477     .035482
               2 23  |  -.0606683   .0343819    -1.76   0.078    -.1280834    .0067468
               2 24  |   .0019419   .0380669     0.05   0.959    -.0726987    .0765825
               2 25  |  -.0526868   .0344601    -1.53   0.126    -.1202552    .0148816
               2 26  |  -.0941645   .0337496    -2.79   0.005    -.1603399    -.027989
               2 27  |  -.0166118   .0339096    -0.49   0.624    -.0831008    .0498773
               2 28  |  -.0353319   .0335663    -1.05   0.293    -.1011477    .0304839
               2 29  |  -.0006502   .0344955    -0.02   0.985    -.0682881    .0669876
               2 30  |  -.1077937   .0332963    -3.24   0.001    -.1730801   -.0425073
               2 31  |  -.0810932   .0339692    -2.39   0.017    -.1476991   -.0144872
               2 32  |   .0000618   .0350413     0.00   0.999    -.0686463    .0687698
               2 33  |  -.0181821   .0341882    -0.53   0.595    -.0852174    .0488533
               2 34  |  -.0567637   .0334536    -1.70   0.090    -.1223586    .0088312
               2 35  |  -.0274652   .0344217    -0.80   0.425    -.0949584     .040028
               2 36  |  -.0396265   .0332751    -1.19   0.234    -.1048714    .0256184
               2 37  |  -.0317712   .0487586    -0.65   0.515    -.1273758    .0638335
               2 38  |   .0030845   .0330984     0.09   0.926    -.0618139    .0679829
               2 39  |  -.0319238   .0331841    -0.96   0.336    -.0969903    .0331428
               2 40  |  -.0438472   .0344472    -1.27   0.203    -.1113904    .0236961
               2 41  |  -.0352609   .0339065    -1.04   0.298    -.1017439    .0312221
               2 42  |  -.0373079   .0331426    -1.13   0.260    -.1022931    .0276773
               2 43  |  -.0109795   .0411151    -0.27   0.789     -.091597     .069638
               2 44  |  -.0902371   .0344218    -2.62   0.009    -.1577305   -.0227437
               2 45  |  -.0834703   .0409663    -2.04   0.042     -.163796   -.0031446
               2 46  |  -.0601291   .0346485    -1.74   0.083    -.1280669    .0078087
               2 47  |  -.0384986   .0390175    -0.99   0.324    -.1150032    .0380059
               2 48  |  -.0648269    .034826    -1.86   0.063    -.1331129    .0034591
               2 49  |  -.0494034   .0340039    -1.45   0.146    -.1160775    .0172706
               2 50  |  -.1427151    .033933    -4.21   0.000      -.20925   -.0761802
               2 51  |   .0049931   .0337516     0.15   0.882    -.0611863    .0711724
               3  2  |   -.004645   .0371322    -0.13   0.900    -.0774528    .0681628
               3  3  |   -.025456   .0361614    -0.70   0.482    -.0963603    .0454483
               3  4  |   .0247156   .1111357     0.22   0.824    -.1931965    .2426276
               3  5  |  -.0113801   .0354138    -0.32   0.748    -.0808185    .0580582
               3  6  |  -.0228555   .0357361    -0.64   0.523     -.092926     .047215
               3  7  |  -.0178315   .0354875    -0.50   0.615    -.0874145    .0517515
               3  8  |    -.01127   .0357809    -0.31   0.753    -.0814283    .0588884
               3 10  |  -.0943287   .0893224    -1.06   0.291    -.2694697    .0808123
               3 11  |  -.0133359   .0395449    -0.34   0.736    -.0908745    .0642028
               3 12  |  -.0439663   .0392908    -1.12   0.263    -.1210066     .033074
               3 13  |  -.0846799   .0357818    -2.37   0.018    -.1548401   -.0145198
               3 14  |  -.0186645   .0353897    -0.53   0.598    -.0880557    .0507267
               3 15  |  -.0393464   .0356191    -1.10   0.269    -.1091874    .0304947
               3 16  |  -.0208337   .0354022    -0.59   0.556    -.0902493     .048582
               3 17  |  -.0070703   .0355138    -0.20   0.842    -.0767047    .0625642
               3 18  |   .0038517   .0404347     0.10   0.924    -.0754316     .083135
               3 19  |   .0486123   .1317661     0.37   0.712    -.2097513    .3069758
               3 20  |  -.0156688    .038536    -0.41   0.684    -.0912292    .0598915
               3 21  |   .0001909   .0396415     0.00   0.996    -.0775372     .077919
               3 22  |  -.0293621    .037833    -0.78   0.438    -.1035441      .04482
               3 23  |   -.045258   .0370834    -1.22   0.222    -.1179701    .0274541
               3 24  |  -.0296822   .0364942    -0.81   0.416    -.1012391    .0418747
               3 25  |   .0059474    .038002     0.16   0.876    -.0685659    .0804606
               3 26  |  -.0358105   .0355452    -1.01   0.314    -.1055067    .0338857
               3 27  |  -.0104035    .036282    -0.29   0.774    -.0815443    .0607373
               3 28  |  -.0313022   .0367305    -0.85   0.394    -.1033224     .040718
               3 29  |  -.0408808   .0366134    -1.12   0.264    -.1126714    .0309099
               3 30  |  -.0604482   .0356301    -1.70   0.090    -.1303108    .0094145
               3 31  |   .0007095    .036423     0.02   0.984    -.0707078    .0721269
               3 32  |   .0105575   .0374532     0.28   0.778    -.0628798    .0839948
               3 33  |   .0099164   .0362491     0.27   0.784    -.0611598    .0809927
               3 34  |   .0288304   .0360596     0.80   0.424    -.0418744    .0995352
               3 35  |  -.0251236   .0405687    -0.62   0.536    -.1046697    .0544226
               3 36  |   .0061615   .0356203     0.17   0.863    -.0636819    .0760048
               3 37  |   .0167065   .0523354     0.32   0.750    -.0859113    .1193244
               3 38  |   .0045187   .0358561     0.13   0.900     -.065787    .0748245
               3 39  |   .0004781   .0355836     0.01   0.989    -.0692934    .0702495
               3 40  |  -.0537903    .036722    -1.46   0.143    -.1257938    .0182133
               3 41  |  -.0134118   .0364699    -0.37   0.713     -.084921    .0580975
               3 42  |  -.0531906   .0361731    -1.47   0.142    -.1241179    .0177367
               3 43  |  -.0104976   .0511293    -0.21   0.837    -.1107507    .0897555
               3 44  |   .0093977   .0393389     0.24   0.811    -.0677371    .0865325
               3 45  |  -.0647886   .0357183    -1.81   0.070    -.1348241    .0052469
               3 46  |    .006524    .036272     0.18   0.857    -.0645973    .0776452
               3 47  |   .0185638   .0436984     0.42   0.671    -.0671189    .1042466
               3 48  |  -.0085134   .0358544    -0.24   0.812    -.0788157     .061789
               3 49  |   -.023548   .0365172    -0.64   0.519    -.0951499     .048054
               3 50  |  -.0622166   .0356019    -1.75   0.081    -.1320238    .0075907
               3 51  |   .0018311   .0370646     0.05   0.961    -.0708442    .0745063
....

               _cons |   .4288561   .0269104    15.94   0.000     .3760909    .4816213
--------------------------------------------------------------------------------------

[Stephen Jenkins]

Thanks for this. I think Clyde is providing you with lots of useful comments to follow up for now. (Clearly, he has better eyes than me too!)

[Anthony Cozart]

Clyde,

Thanks for your insightful comments. I know I have "singleton dummies" that are election and state_code combinations (i.e. state_code==10, year==2006). I need to get more row observations to address this.

Your point about the collinearity brings up a broader issue I'm facing, that is even when altering the sample window, I have one year drop. For example, dropping data for 2010 and 2010, the indicator variable for the year before the final year in the sample drops. The code below provides an example. Any idea why this is the case?

keep if year<=2008
(500 observations deleted)

. reg deflator_temp c.win_margin unopposed senate president governor non_presidential_y
> ear i.election_cycle##ib1.state_code, r
note: 14.election_cycle omitted because of collinearity

Linear regression                                      Number of obs =    2758
                                                       F(726,  2003) =       .
                                                       Prob > F      =       .
                                                       R-squared     =  0.8910
                                                       Root MSE      =  .04625

--------------------------------------------------------------------------------------
                     |               Robust
       deflator_temp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------------+----------------------------------------------------------------
          win_margin |  -.0678246   .0096701    -7.01   0.000     -.086789   -.0488601
           unopposed |  -.0570672   .0091262    -6.25   0.000     -.074965   -.0391695
              senate |   .0275919   .0025205    10.95   0.000     .0226489    .0325349
           president |   .0426071   .0025987    16.40   0.000     .0375106    .0477036
            governor |   .0263274   .0017781    14.81   0.000     .0228403    .0298145
non_presidential_y~r |  -.0285831    .028788    -0.99   0.321    -.0850408    .0278745
                     |
      election_cycle |
                  2  |  -.0245272   .0222417    -1.10   0.270    -.0681464    .0190921
                  3  |   .0314312   .0333937     0.94   0.347    -.0340587    .0969211
                  4  |   .0042712   .0152558     0.28   0.780    -.0256478    .0341901
                  5  |   .0029477   .0295561     0.10   0.921    -.0550163    .0609117
                  6  |  -.0210511   .0187926    -1.12   0.263    -.0579061    .0158039
                  7  |   .0972587   .0256099     3.80   0.000      .047034    .1474835
                  8  |  -.0340818   .0138266    -2.46   0.014    -.0611979   -.0069658
                  9  |   .0333146   .0257187     1.30   0.195    -.0171236    .0837529
                 10  |  -.0052583   .0143776    -0.37   0.715     -.033455    .0229383
                 11  |   .0398936   .0291428     1.37   0.171    -.0172597    .0970469
                 12  |  -.0039894   .0140002    -0.28   0.776    -.0314458    .0234671
                 13  |   .1253206   .0253932     4.94   0.000     .0755208    .1751205
                 14  |          0  (omitted)
                 15  |   .1750798   .0314348     5.57   0.000     .1134314    .2367282
                     |
          state_code |
                  2  |   .1512377   .0290475     5.21   0.000     .0942712    .2082041
                  3  |    .019258   .0256495     0.75   0.453    -.0310444    .0695604
                  4  |  -.0246665      .0931    -0.26   0.791    -.2072494    .1579164
                  5  |   .0965853   .0252613     3.82   0.000     .0470441    .1461265
                  6  |    .123185   .0256221     4.81   0.000     .0729361    .1734338
                  7  |   .1789968   .0253881     7.05   0.000      .129207    .2287865
                  8  |   .1045869   .0257877     4.06   0.000     .0540134    .1551603
                 10  |   .0421952   .0291213     1.45   0.148    -.0149161    .0993064
                 11  |  -.0443076   .0268667    -1.65   0.099    -.0969972    .0083821
                 12  |   .0247217   .0273177     0.90   0.366    -.0288523    .0782957
                 13  |   .2432748   .0256332     9.49   0.000     .1930042    .2935454
                 14  |   .1422056   .0252311     5.64   0.000     .0927237    .1916876
                 15  |   .1314209   .0256497     5.12   0.000     .0811181    .1817237
                 16  |   .1772896   .0254458     6.97   0.000     .1273867    .2271926
                 17  |   .1226291   .0253383     4.84   0.000     .0729369    .1723212
                 18  |   .0102487   .0289944     0.35   0.724    -.0466137    .0671111
                 19  |  -.1447193   .0854632    -1.69   0.091    -.3123254    .0228868
                 20  |   .2113056   .0310137     6.81   0.000     .1504831    .2721281
                 21  |   .0367508   .0296842     1.24   0.216    -.0214643     .094966
                 22  |   .1370656   .0266582     5.14   0.000     .0847849    .1893463
                 23  |   .1445584   .0257763     5.61   0.000     .0940073    .1951096
                 24  |    .242557   .0255962     9.48   0.000      .192359    .2927549
                 25  |    .049405   .0262033     1.89   0.060    -.0019836    .1007935
                 26  |   .1430884   .0257922     5.55   0.000     .0925061    .1936708
                 27  |   .2002185   .0259367     7.72   0.000     .1493528    .2510842
                 28  |   .1408696   .0258532     5.45   0.000     .0901677    .1915715
                 29  |   .0045753   .0283496     0.16   0.872    -.0510226    .0601731
                 30  |     .13136   .0257507     5.10   0.000      .080859    .1818609
                 31  |   .1171421   .0257143     4.56   0.000     .0667124    .1675717
                 32  |   .0568541   .0271058     2.10   0.036     .0036956    .1100126
                 33  |   .0486137   .0252935     1.92   0.055    -.0009906    .0982179
                 34  |  -.0129733   .0261753    -0.50   0.620    -.0643069    .0383603
                 35  |   .2160601   .0255343     8.46   0.000     .1659835    .2661367
                 36  |   .0990731   .0254215     3.90   0.000     .0492179    .1489284
                 37  |   .0361997    .043486     0.83   0.405    -.0490828    .1214823
                 38  |   .1652861   .0253106     6.53   0.000     .1156483    .2149239
                 39  |   .0663855   .0255237     2.60   0.009     .0163297    .1164413
                 40  |    .164046   .0269052     6.10   0.000      .111281     .216811
                 41  |  -.0405581   .0266485    -1.52   0.128    -.0928198    .0117037
                 42  |    .235104   .0253762     9.26   0.000     .1853374    .2848706
                 43  |  -.0004655   .0333629    -0.01   0.989    -.0658951    .0649641
                 44  |   .0093454   .0260425     0.36   0.720    -.0417278    .0604186
                 45  |   .2252719   .0257236     8.76   0.000     .1748242    .2757197
                 46  |   .1363469   .0261915     5.21   0.000     .0849815    .1877124
                 47  |   .0063245   .0315058     0.20   0.841    -.0554631    .0681121
                 48  |    .141479   .0255363     5.54   0.000     .0913986    .1915595
                 49  |   .0771455   .0260416     2.96   0.003     .0260741     .128217
                 50  |   .2174806   .0252818     8.60   0.000     .1678994    .2670619
                 51  |    .109264   .0271673     4.02   0.000     .0559848    .1625432
                     |
      election_cycle#|
          state_code |
               2  2  |   .0932292   .0339544     2.75   0.006     .0266395    .1598188
               2  3  |  -.0398712   .0313648    -1.27   0.204    -.1013822    .0216398
               2  4  |   .1164415   .0947367     1.23   0.219    -.0693513    .3022344
               2  5  |  -.0037577   .0310188    -0.12   0.904    -.0645901    .0570748
               2  6  |  -.0624186    .031099    -2.01   0.045    -.1234084   -.0014289

[Clyde Schechter]

So it sounds like you have some sparse data in the estimation sample, with empty or singleton cells in your cross-tab of election cycle with state. In situations like that it is very easy for an indicator variable to end up collinear with an interaction term (and, hence, one of those gets dropped). I think your options are either to find more data, or to aggregate up to larger time periods or groups of similar states (whatever that means), or restrict your analysis to time periods or a subset of the states where the data are rich. Another possibility is that your estimation sample is sparse because of missing values for the other variables in your model. Removing some of those from the model might improve the situation, if that doesn't do violence to the underlying theory.

[Anthony Cozart]

Clyde,

Thanks again. Could you elaborate why it might be easy for an indicator variable to end up collinear with an interaction term in data with empty or singleton cells?

Anthony

[Clyde Schechter]

Well, perhaps an example where you can play with it yourself and see what's going on. This example involves sparse data, with some zeroes, and one cell with only two observations:

 . sysuse auto, clear
(1978 Automobile Data)
  . tab rep78 foreign
      Repair |
    Record |       Car type
      1978 |  Domestic    Foreign |     Total
-----------+----------------------+----------
         1 |         2          0 |         2
         2 |         8          0 |         8
         3 |        27          3 |        30
         4 |         9          9 |        18
         5 |         2          9 |        11
-----------+----------------------+----------
     Total |        48         21 |        69
  
. regress price i.rep78##i.foreign
note: 1b.rep78#1.foreign identifies no observations in the sample
note: 2.rep78#1.foreign identifies no observations in the sample
note: 5.rep78#1.foreign omitted because of collinearity
        Source |       SS       df       MS              Number of obs =      69
-------------+------------------------------           F(  7,    61) =    0.39
       Model |    24684607     7  3526372.43           Prob > F      =  0.9049
    Residual |   552112352    61  9051022.16           R-squared     =  0.0428
-------------+------------------------------           Adj R-squared = -0.0670
       Total |   576796959    68  8482308.22           Root MSE      =  3008.5
  -------------------------------------------------------------------------------
        price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
        rep78 |
           2  |   1403.125   2378.422     0.59   0.557    -3352.823    6159.073
           3  |   2042.574   2204.707     0.93   0.358    -2366.011    6451.159
           4  |   1317.056   2351.846     0.56   0.578    -3385.751    6019.863
           5  |       -360   3008.492    -0.12   0.905    -6375.851    5655.851
              |
      foreign |
     Foreign  |   2088.167   2351.846     0.89   0.378     -2614.64    6790.974
              |
rep78#foreign |
   1#Foreign  |          0  (empty)
   2#Foreign  |          0  (empty)
   3#Foreign  |  -3866.574   2980.505    -1.30   0.199    -9826.462    2093.314
   4#Foreign  |  -1708.278   2746.365    -0.62   0.536    -7199.973    3783.418
   5#Foreign  |          0  (omitted)
              |
        _cons |     4564.5   2127.325     2.15   0.036      310.651    8818.349
-------------------------------------------------------------------------------

So, the dropping of the levels 1 and 2 interactions between rep78 and foreign is no surprise: there are no such observations. But notice that 5.rep78#1.foreign ends up being omitted because of collinearity. To see why, let's regress 5.rep78#1.foreign on the other predictors. We can't actually specify our dependent variable as 5.rep78#1.foreign, so first we'll have to make it a "real" variable:

  . gen dropped = 5.rep78#1.foreign
(5 missing values generated)
  . regress dropped i.rep78 i.foreign i(2/4).rep78#i.foreign
note: 2b.rep78#1.foreign identifies no observations in the sample
        Source |       SS       df       MS              Number of obs =      69
-------------+------------------------------           F(  5,    63) =       .
       Model |  7.82608696     5  1.56521739           Prob > F      =       .
    Residual |           0    63           0           R-squared     =  1.0000
-------------+------------------------------           Adj R-squared =  1.0000
       Total |  7.82608696    68  .115089514           Root MSE      =       0
  -------------------------------------------------------------------------------
      dropped |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
        rep78 |
           3  |  -6.43e-17          .        .       .            .           .
           4  |  -2.85e-16          .        .       .            .           .
              |
      foreign |
     Foreign  |          1          .        .       .            .           .
              |
rep78#foreign |
   2#Foreign  |          0  (empty)
   3#Foreign  |         -1          .        .       .            .           .
   4#Foreign  |         -1          .        .       .            .           .
              |
        _cons |   2.78e-17          .        .       .            .           .
-------------------------------------------------------------------------------

This regression tells us that 5.rep78#1.foreign is equal to 1.foreign - (3.rep78#1.foreign + 4.rep78#1.foreign)*, which is an algebraic way of saying that you are in repair category 5 and foreign if and only if you are foreign, but in neither repair category 3 nor repair category 4. This is a coincidental relationship in the data that arises from the absence of repair categories 1 and 2 among the foreign observations and the small number of domestic observations in repair category 5. A richer data set could, of course, contain the same relationship, but it is far less likely to happen (and, if it does, it is likely to be something systematic that should be taken account of in study design). These coincidental relationships can crop up easily when there are lots of small cells.

Hope this helps.

* the other coefficients are just zeroes with a small amount of numerical error.

[Anthony Cozart]

Going back to a point you made early in our exchange yesterday, I'm surprised that the the indicator for election cycle 16 is dropped because of collinearity. What I've done to explore the issue is to look at just one state, and the election cycles 2010 and 2012 (cycles 16, 17). The same problem arises. There are 55 observations for both years, so it's not a problem of an election cycle not being instantiated. "Non_senate_year" is dropped because there's no variation. "Non_gubernatorial_year" is dropped because of collinearity as a result of sparse data. Do you have any idea why 17.election_year is dropped?


Thanks again for your help, I really appreciate it.

.
keep if state_code==5
(3570 observations deleted)

keep if year>=2010
(144 observations deleted)


reg deflator_temp c.win_margin unopposed senate president governor non_presidential_year non_senate_year non_gubernatorial_year i.election_cycle, r
note: non_senate_year omitted because of collinearity
note: non_gubernatorial_year omitted because of collinearity
note: 17.election_cycle omitted because of collinearity

Linear regression                                      Number of obs =     110
                                                       F(  4,   103) =       .
                                                       Prob > F      =       .
                                                       R-squared     =  0.2918
                                                       Root MSE      =  .10958

--------------------------------------------------------------------------------------
                     |               Robust
       deflator_temp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------------+----------------------------------------------------------------
          win_margin |   .0808634   .0596059     1.36   0.178    -.0373508    .1990777
           unopposed |  -.1483611   .0419767    -3.53   0.001    -.2316119   -.0651103
              senate |   .0091408   .0224109     0.41   0.684     -.035306    .0535875
           president |    .006913   .0188749     0.37   0.715    -.0305209    .0443469
            governor |   .0342378   .0177401     1.93   0.056    -.0009454     .069421
non_presidential_y~r |  -.1306358   .0214957    -6.08   0.000    -.1732674   -.0880041
     non_senate_year |          0  (omitted)
non_gubernatorial_~r |          0  (omitted)
   17.election_cycle |          0  (omitted)
               _cons |   .5264039   .0267064    19.71   0.000     .4734381    .5793698
--------------------------------------------------------------------------------------

. gen dropped=non_gubernatorial_year

. reg dropped c.win_margin unopposed senate president governor non_presidential_year non_senate_year i.election_cycle
note: non_senate_year omitted because of collinearity
note: 17.election_cycle omitted because of collinearity

      Source |       SS       df       MS              Number of obs =     110
-------------+------------------------------           F(  6,   103) =       .
       Model |        27.5     6  4.58333333           Prob > F      =       .
    Residual |           0   103           0           R-squared     =  1.0000
-------------+------------------------------           Adj R-squared =  1.0000
       Total |        27.5   109  .252293578           Root MSE      =       0

--------------------------------------------------------------------------------------
             dropped |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------------+----------------------------------------------------------------
          win_margin |   2.46e-17          .        .       .            .           .
           unopposed |   8.91e-17          .        .       .            .           .
              senate |   4.31e-18          .        .       .            .           .
           president |  -5.58e-17          .        .       .            .           .
            governor |          0  (omitted)
non_presidential_y~r |         -1          .        .       .            .           .
     non_senate_year |          0  (omitted)
   17.election_cycle |          0  (omitted)
               _cons |          1          .        .       .            .           .
--------------------------------------------------------------------------------------

[Anthony Cozart]

Clearly it's a problem with my data structure. The problem of a election_cycle dropping does not arise if I keep only two non-consecutive election cycles, for example 2006 and 2010, shown below:

. keep if state_code==5
(3570 observations deleted)

. keep if year==2006| year==2010
(144 observations deleted)

. reg deflator_temp c.win_margin unopposed senate president governor non_presidential_year i.election_cycle, r
note: president omitted because of collinearity
note: non_presidential_year omitted because of collinearity

Linear regression                                      Number of obs =     110
                                                       F(  5,   104) =   34.69
                                                       Prob > F      =  0.0000
                                                       R-squared     =  0.2558
                                                       Root MSE      =  .07648

--------------------------------------------------------------------------------------
                     |               Robust
       deflator_temp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------------+----------------------------------------------------------------
          win_margin |  -.0337432   .0533033    -0.63   0.528    -.1394456    .0719592
           unopposed |  -.0887607   .0338874    -2.62   0.010    -.1559606   -.0215607
              senate |   .0124272   .0137183     0.91   0.367    -.0147766    .0396311
           president |          0  (omitted)
            governor |   .0169325   .0145102     1.17   0.246    -.0118417    .0457068
non_presidential_y~r |          0  (omitted)
   16.election_cycle |   .0476196   .0146911     3.24   0.002     .0184865    .0767527
               _cons |   .3855862   .0211857    18.20   0.000     .3435742    .4275982
--------------------------------------------------------------------------------------

* There's no variation in president and non_presidential_year variables.

[Clyde Schechter]

When a variable is dropped due to collinearity, and you don't know why, you can just regress that variable against all the other predictor variables in the offending regression. When the variable is a level of a factor variable, you have to first create a "real" variable that is equal to it, because factor variable notation is not permitted in the dependent variable. So I would do the following immediately after the offending regression:

gen ec_17 = 17.election_cycle
regress ec_17 c.win_margin unopposed senate president governor non_presidential_year non_senate_year if e(sample)

The output of that will have many zero coefficients (or extremely close to zero). The variables whose coefficients are non-zero are the ones which are involved in a collinearity relationship with 17.election_cycle, and they also give you the actual linear relationship among them. You may find out that in state 5 in the years after 2010, the 17th election cycle was the only one in which there was an unopposed election involving a governor, or something like that. Those kinds of coincidental relationships crop up frequently in sparse data with many variables.