Interpretation of marginal effects after interaction

[Ellen Sterk]

Dear all,

I am using OLS with an interaction term between A (I001_umk) and B (Förderung_values) and want to interpret the marginal effects of A at different values of B. My output is below. My question is: what does it mean that the marginal effect at the (second and) third level is insignificant?

Thank you in advance!

. regress FS09_01 c.Förderung_values i.I001_umk c.Förderung_values#i.I001_umk Genehmigung Unterstützung Anerkennung ib3.Gruppe, vce(robust)

Linear regression                               Number of obs     =        802
                                                F(8, 793)         =      26.02
                                                Prob > F          =     0.0000
                                                R-squared         =     0.2051
                                                Root MSE          =     27.586

---------------------------------------------------------------------------------------------
                            |               Robust
                    FS09_01 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
----------------------------+----------------------------------------------------------------
           Förderung_values |   .2497609   .0257975     9.68   0.000     .1991215    .3004003
                            |
                   I001_umk |
               Information  |   12.96504   3.472688     3.73   0.000     6.148291    19.78178
                            |
I001_umk#c.Förderung_values |
               Information  |  -.0901888   .0358205    -2.52   0.012    -.1605031   -.0198745
                            |
                Genehmigung |   7.325913   1.942806     3.77   0.000     3.512263    11.13956
              Unterstützung |   8.188154   1.955397     4.19   0.000     4.349788    12.02652
                Anerkennung |   1.646449   1.950454     0.84   0.399    -2.182215    5.475113
                            |
                     Gruppe |
                 Bauträger  |   12.32666    3.07673     4.01   0.000     6.287167    18.36616
            Organisationen  |    6.80456   2.102073     3.24   0.001     2.678274    10.93085
                            |
                      _cons |   32.82964   3.206492    10.24   0.000     26.53542    39.12385
---------------------------------------------------------------------------------------------

. margins, dydx(I001_umk) at(Förderung_values = (50 100 150))

Average marginal effects                                   Number of obs = 802
Model VCE: Robust

Expression: Linear prediction, predict()
dy/dx wrt:  1.I001_umk
1._at: Förderung_values =  50
2._at: Förderung_values = 100
3._at: Förderung_values = 150

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
0.I001_umk   |  (base outcome)
-------------+----------------------------------------------------------------
1.I001_umk   |
         _at |
          1  |   8.455598   2.229939     3.79   0.000     4.078318    12.83288
          2  |   3.946158   2.073945     1.90   0.057    -.1249127    8.017229
          3  |  -.5632816   3.169451    -0.18   0.859    -6.784788    5.658225
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

[Maarten Buis]

For example if Fördering_values equals 50:

The null-hypothesis is than: The effect of I001_umk equals 0 if Fördering_values is 50. We (barely) cannot reject that hypotheis at the 5% level.

[Ellen Sterk]

Maarten Buis
Dear Maarten, thank you for your reply! I understand now. However I assume you meant the case of Fördering_values being 100, since at 50 we can reject the null hypothesis if I understand correctly (?).