Finding the marginal effects of interactions terms

[Nico Ochmann]

Dear Stata Forum,

I would like to determine the marginal effects of the interaction terms

ib1998.year#c.logbite3

and graph them on the vertical axis and year on the horizontal axis.
The regression I am running is the following:

regress self_c ib1998.year##c.logbite3

margins, dydx(c.logbite3) at(year(1993(1)2022))

However, the margins command gives me an error message.
I would appreciate you help.
Here you find a data sample:

* Example generated by -dataex-. For more info, type help dataex
clear
input float(self_c logbite3 year)
         .          . 1991
         .          . 1992
         .          . 1993
         .          . 1994
         .          . 1995
         .          . 1996
         0          . 1997
         0 -2.0409904 1998
         0  -.7741088 1999
         0  -.4291192 2000
         0  -.6162011 2001
        .2  -.6442134 2002
       .25 -.40889165 2003
  .3333333  -.7611812 2004
         0 -1.2132735 2005
         0 -1.0570409 2006
         0  -1.248903 2007
         0 -1.3217868 2008
.037037037 -1.3166054 2009
       .05  -.7443178 2010
  .0952381  -.7682025 2011
         0  -.8468925 2012
       .05    -.70977 2013
.071428575  -.7923768 2014
  .0952381    -.74603 2015
       .05  -.8348222 2016
 .05263158  -.6987573 2017
         0  -.6215868 2018
 .07692308  -.6011775 2019
         0  -.5080077 2020
         0   -.419554 2021
         0  -.4576086 2022
         .          . 1991
         0          . 1992
         0 -1.6483593 1993
         0 -1.7577775 1994
         0  -1.416572 1995
         0 -1.7994494 1996
         0  -1.833351 1997
 .11111111 -1.7447444 1998
      .125  -.6034867 1999
         0 -.50562984 2000
         0  -.4476819 2001
  .3333333 -.54213685 2002
  .3333333  -.9721524 2003
  .3333333  -.8914877 2004
         1 -1.2174888 2005
  .3333333          . 2006
  .3333333 -1.1037213 2007
         1  -.9452747 2008
         0          . 2009
         0  -.5233285 2010
 .15384616  -.3239966 2011
  .0909091  -.4137999 2012
 .08333334  -.3003126 2013
.037037037 -.31665915 2014
 .04761905   -.437026 2015
 .26086956 -.25689384 2016
  .0909091  -.3406061 2017
       .05 -.15568754 2018
       .08  -.4489613 2019
 .05555556  -.1754757 2020
 .08695652 -.27745017 2021
         0 -.27312517 2022
         .          . 1991
  .0952381          . 1992
 .08333334  -1.714637 1993
       .08  -1.860475 1994
  .0909091   -1.81326 1995
 .08333334 -2.0264544 1996
 .04545455  -1.948107 1997
         0 -2.0730786 1998
         0  -.6481928 1999
         0 -.58449304 2000
         0  -.4257042 2001
         0  -.2682134 2002
         0  -.3425188 2003
         0 -.29530093 2004
         0  -.4778255 2005
         0  -.4895479 2006
         0  -.3615529 2007
         0  -.6257899 2008
 .08333334 -.43232635 2009
.014492754 -.56207335 2010
 .05714286  -.3648208 2011
 .09756097  -.5524424 2012
.071428575 -.57270056 2013
 .04878049  -.4556111 2014
 .08333334  -.4946106 2015
  .2051282  -.4723745 2016
 .11538462  -.4804807 2017
 .14285715 -.30491325 2018
 .13333334  -.4541697 2019
 .11111111   -.226769 2020
.071428575   -.307143 2021
         0  -.2073963 2022
         .          . 1991
 .03921569          . 1992
         0 -1.7754605 1993
 .04651163  -1.861579 1994
end

[Nico Ochmann]

I would appreciate your help.
Thanks,
Best,
Nico

[Felix Bittmann]

You need to type

margins, dydx(c.logbite3) at(year=(1993(1)2022))

[Nico Ochmann]

Hi Felix,
Thanks for your reply, but that was just a typo of mine. The same issue remains:

 margins, dydx(c.logbite3) at(year=(1993(1)2023))
invalid at() option;
variable year may not be present in model as factor and continuous predictor

I would appreciate further help.
Thanks,
Nico

[Felix Bittmann]

Then try

 regress self_c i.year##c.logbite3

The reference coding does not affect the margins estimation.

[Clyde Schechter]

I don't think O.P. is showing us what actually happened.

margins, dydx(c.logbite3) at(year=(1993(1)2023))
invalid at() option;
variable year may not be present in model as factor and continuous predictor

simply is not what happens. That error message only appears when some variable appears as both a discrete and continuous explanatory variable in the regression, or when it is treated as one of those in the regression and the other in -margins-. None of those things happen in the code that has been shown so far.

With the correction of the omitted = in the -at()- option the code shown by O.P. runs without error messages and produces sensible results, at least in the example data:

. regress self_c ib1998.year##c.logbite3

      Source |       SS           df       MS      Number of obs   =        85
-------------+----------------------------------   F(59, 25)       =      0.34
       Model |  1.05139164        59  .017820197   Prob > F        =    0.9996
    Residual |  1.30651651        25   .05226066   R-squared       =    0.4459
-------------+----------------------------------   Adj R-squared   =   -0.8618
       Total |  2.35790815        84  .028070335   Root MSE        =    .22861

---------------------------------------------------------------------------------
         self_c | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
----------------+----------------------------------------------------------------
           year |
          1993  |   -.730753   4.695339    -0.16   0.878    -10.40098    8.939478
          1994  |  -1.798479   5.254437    -0.34   0.735     -12.6202    9.023238
          1995  |  -1.051059   2.194853    -0.48   0.636    -5.571443    3.469325
          1996  |  -1.386999   3.241528    -0.43   0.672    -8.063052    5.289054
          1997  |  -1.452608     5.6088    -0.26   0.798    -13.00415    10.09893
          1999  |  -.2977607   2.144436    -0.14   0.891     -4.71431    4.118789
          2000  |  -.7264229   2.046143    -0.36   0.726    -4.940533    3.487688
          2001  |  -.7264229   1.915604    -0.38   0.708    -4.671684    3.218838
          2002  |  -.8754679     1.7997    -0.49   0.631     -4.58202    2.831085
          2003  |  -.7507196   1.774401    -0.42   0.676    -4.405167    2.903727
          2004  |  -.8941742   1.785658    -0.50   0.621    -4.571806    2.783457
          2005  |  -1.055966   1.792174    -0.59   0.561    -4.747017    2.635085
          2006  |  -.7264229   1.810862    -0.40   0.692    -4.455963    3.003117
          2007  |  -.7477614   1.780687    -0.42   0.678    -4.415154    2.919631
          2008  |  -.3175785   1.810143    -0.18   0.862    -4.045638    3.410481
          2009  |  -.6204551   1.785318    -0.35   0.731    -4.297386    3.056475
          2010  |  -.8369212   1.942798    -0.43   0.670    -4.838188    3.164346
          2011  |   -.604723   1.782885    -0.34   0.737    -4.276643    3.067196
          2012  |  -.5252647   1.808746    -0.29   0.774    -4.250447    3.199917
          2013  |  -.6180313   1.801076    -0.34   0.734    -4.327416    3.091354
          2014  |  -.7112244   1.787518    -0.40   0.694    -4.392686    2.970237
          2015  |   -.719247   1.838225    -0.39   0.699    -4.505142    3.066648
          2016  |  -.3607673   1.777555    -0.20   0.841     -4.02171    3.300176
          2017  |  -.5779592   1.811707    -0.32   0.752    -4.309239    3.153321
          2018  |    -.60406   1.771019    -0.34   0.736    -4.251541    3.043421
          2019  |  -.5347362   1.989021    -0.27   0.790    -4.631202     3.56173
          2020  |  -.5969107   1.775244    -0.34   0.739    -4.253094    3.059273
          2021  |  -.4666381   1.896701    -0.25   0.808    -4.372967    3.439691
          2022  |  -.7264229   1.796744    -0.40   0.689    -4.426886    2.974041
                |
       logbite3 |   .3529994   .8930221     0.40   0.696    -1.486214    2.192213
                |
year#c.logbite3 |
          1993  |   -.371745   2.695096    -0.14   0.891    -5.922398    5.178908
          1994  |  -.9629962   2.854872    -0.34   0.739    -6.842715    4.916723
          1995  |  -.5821697   1.209008    -0.48   0.634    -3.072168    1.907829
          1996  |  -.7200985   1.681011    -0.43   0.672    -4.182205    2.742008
          1997  |  -.7490968    2.95541    -0.25   0.802    -6.835878    5.337684
          1999  |   .2201042    2.03365     0.11   0.915    -3.968277    4.408486
          2000  |  -.3529994   2.264237    -0.16   0.877    -5.016283    4.310285
          2001  |  -.3529994   1.789748    -0.20   0.845    -4.039054    3.333055
          2002  |  -1.027063   1.220113    -0.84   0.408    -3.539933    1.485808
          2003  |   -.733736   1.007877    -0.73   0.473    -2.809497    1.342025
          2004  |   -.953584   1.031243    -0.92   0.364    -3.077469    1.170301
          2005  |  -1.036709   .9703552    -1.07   0.296    -3.035193    .9617747
          2006  |  -.3529994   1.059264    -0.33   0.742    -2.534594    1.828596
          2007  |  -.4993969   .9554215    -0.52   0.606    -2.467124    1.468331
          2008  |  -.2746915   1.006368    -0.27   0.787    -2.347345    1.797962
          2009  |  -.3006445   .9649643    -0.31   0.758    -2.288026    1.686737
          2010  |  -.5694192   1.635231    -0.35   0.731    -3.937241    2.798403
          2011  |  -.3125933   1.109479    -0.28   0.780    -2.597609    1.972422
          2012  |  -.1241117   1.153986    -0.11   0.915    -2.500791    2.252567
          2013  |  -.2769228   1.182801    -0.23   0.817    -2.712947    2.159102
          2014  |  -.4243578   1.110934    -0.38   0.706     -2.71237    1.863655
          2015  |  -.4749919   1.328613    -0.36   0.724    -3.211321    2.261337
          2016  |   .0184426   1.050629     0.02   0.986    -2.145369    2.182254
          2017  |   -.230312    1.26472    -0.18   0.857    -2.835052    2.374428
          2018  |  -.1920001   1.122113    -0.17   0.866    -2.503035    2.119035
          2019  |  -.1636741   2.072787    -0.08   0.938    -4.432659     4.10531
          2020  |  -.1092542   1.269949    -0.09   0.932    -2.724764    2.506256
          2021  |   .2654052   2.334138     0.11   0.910    -4.541842    5.072653
          2022  |  -.3529994   1.533098    -0.23   0.820    -3.510475    2.804476
                |
          _cons |   .7264229   1.749004     0.42   0.681    -2.875718    4.328564
---------------------------------------------------------------------------------

.
. margins, dydx(c.logbite3) at(year=(1993(1)2022))

Average marginal effects                                    Number of obs = 85
Model VCE: OLS

Expression: Linear prediction, predict()
dy/dx wrt:  logbite3
1._at:  year = 1993
2._at:  year = 1994
3._at:  year = 1995
4._at:  year = 1996
5._at:  year = 1997
6._at:  year = 1998
7._at:  year = 1999
8._at:  year = 2000
9._at:  year = 2001
10._at: year = 2002
11._at: year = 2003
12._at: year = 2004
13._at: year = 2005
14._at: year = 2006
15._at: year = 2007
16._at: year = 2008
17._at: year = 2009
18._at: year = 2010
19._at: year = 2011
20._at: year = 2012
21._at: year = 2013
22._at: year = 2014
23._at: year = 2015
24._at: year = 2016
25._at: year = 2017
26._at: year = 2018
27._at: year = 2019
28._at: year = 2020
29._at: year = 2021
30._at: year = 2022

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
logbite3     |
         _at |
          1  |  -.0187457   2.542843    -0.01   0.994    -5.255829    5.218338
          2  |  -.6099968   2.711606    -0.22   0.824    -6.194653     4.97466
          3  |  -.2291703   .8149921    -0.28   0.781    -1.907678    1.449337
          4  |  -.3670991   1.424187    -0.26   0.799    -3.300267    2.566069
          5  |  -.3960974   2.817261    -0.14   0.889    -6.198355     5.40616
          6  |   .3529994   .8930221     0.40   0.696    -1.486214    2.192213
          7  |   .5731036   1.827087     0.31   0.756    -3.189852    4.336059
          8  |   3.86e-14   2.080693     0.00   1.000    -4.285267    4.285267
          9  |   2.44e-15   1.551035     0.00   1.000    -3.194416    3.194416
         10  |  -.6740635   .8313773    -0.81   0.425    -2.386317     1.03819
         11  |  -.3807366   .4672547    -0.81   0.423    -1.343066    .5815924
         12  |  -.6005846    .515727    -1.16   0.255    -1.662744     .461575
         13  |  -.6837098   .3796059    -1.80   0.084    -1.465523    .0981032
         14  |  -1.22e-15   .5696944    -0.00   1.000    -1.173307    1.173307
         15  |  -.1463975     .33962    -0.43   0.670    -.8458581     .553063
         16  |   .0783079   .4639912     0.17   0.867    -.8772999    1.033916
         17  |   .0523549   .3656058     0.14   0.887    -.7006244    .8053341
         18  |  -.2164198   1.369852    -0.16   0.876    -3.037682    2.604842
         19  |   .0404061   .6583737     0.06   0.952     -1.31554    1.396352
         20  |   .2288877   .7308868     0.31   0.757    -1.276402    1.734177
         21  |   .0760766   .7755837     0.10   0.923    -1.521268    1.673421
         22  |  -.0713584   .6608229    -0.11   0.915    -1.432349    1.289632
         23  |  -.1219926   .9837294    -0.12   0.902    -2.148021    1.904036
         24  |    .371442   .5534742     0.67   0.508    -.7684593    1.511343
         25  |   .1226874   .8955603     0.14   0.892    -1.721754    1.967128
         26  |   .1609993    .679448     0.24   0.815     -1.23835    1.560349
         27  |   .1893252    1.87055     0.10   0.920    -3.663144    4.041795
         28  |   .2437452   .9029302     0.27   0.789    -1.615874    2.103365
         29  |   .6184046   2.156551     0.29   0.777    -3.823095    5.059905
         30  |   2.50e-15   1.246155     0.00   1.000    -2.566504    2.566504
------------------------------------------------------------------------------

O.P. has already acknowledged that the code shown in his posts has been typed into the Forum editor. So it is probably not exactly what was really run. In order to get effective help, it is critical to post the actual code and actual outputs (including error messages). To avoid introducing changes that obscure the situation, this should always be done using the computer's copy/paste operations, not by retyping.

If O.P. really did obtain that error message with the code shown, then something is wrong with his Stata installation. First step for dealing with that would be -update all, force-.

[Nico Ochmann]

My apologies to both of you, Clyde is correct, I have made a silly mistake and have not shown all relevant bits.
This will not happen again, thanks for your help.
Best,
Nico