Interpreting Multinomial Logit Regression/Margins

[Wani Huang]

Hi,

I have a datatset cointaining observations from the video game industry. I want to research how software (video game) developers decide in which genre they want to enter with their game. I'm testing following hypotheses with a multinomial logit:

H1: The choice of genre is dependent on the number of existing top-performing games measured by revenue in a genre.
H1a: Game developers try to imitate top performers’ success by entering into the same genre.
H1b: Game developers try to avoid competition with high-selling games by entering into a different genre from top-performing games,

with top performers being those within the top 20% per year according to revenue.

It currently looks like this:

Multinomial logistic regression                 Number of obs     =     10,475
                                                LR chi2(126)      =   11648.82
                                                Prob > chi2       =     0.0000
Log likelihood = -19497.003                     Pseudo R2         =     0.2300

------------------------------------------------------------------------------------------
              sgenre_id3 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------------------+----------------------------------------------------------------
ACTION                   |  (base outcome)
-------------------------+----------------------------------------------------------------
ADVENTURE                |
            release_date |   .0498489   .0017833    27.95   0.000     .0463537     .053344
                      ps |  -1.103009   .1437939    -7.67   0.000    -1.384839   -.8211778
   top_performer_rev_sum |  -.5747549    .062992    -9.12   0.000    -.6982169   -.4512928
                 atari_p |  -21.28778   28010.81    -0.00   0.999    -54921.47    54878.89
                  sega_p |  -.5510671   .2650814    -2.08   0.038    -1.070617    -.031517
                 micro_p |  -1.060421   .2115886    -5.01   0.000    -1.475127   -.6457145
                   nin_p |  -1.158782   .1617027    -7.17   0.000    -1.475713   -.8418504
                  number |  -.1286186   .0030603   -42.03   0.000    -.1346167   -.1226206
              rev_growth |   .5691262   .0739391     7.70   0.000     .4242083    .7140441
                   _cons |  -14.28717   .8208489   -17.41   0.000      -15.896   -12.67833
-------------------------+----------------------------------------------------------------
ARCADE                   |
            release_date |   .0320185    .003533     9.06   0.000     .0250939    .0389431
                      ps |  -.1778298   .3584196    -0.50   0.620    -.8803193    .5246596
   top_performer_rev_sum |   .2259194   .1234846     1.83   0.067    -.0161059    .4679447
                 atari_p |  -20.38943   53251.92    -0.00   1.000    -104392.2    104351.5
                  sega_p |   .9951693    .446489     2.23   0.026     .1200668    1.870272
                 micro_p |   .5521793    .599354     0.92   0.357     -.622533    1.726892
                   nin_p |   .6415877   .3419701     1.88   0.061    -.0286614    1.311837
                  number |  -.3190956    .013858   -23.03   0.000    -.3462568   -.2919344
              rev_growth |   .5903945   .0972139     6.07   0.000     .3998587    .7809303
                   _cons |  -1.782089   1.836259    -0.97   0.332     -5.38109    1.816913
-------------------------+----------------------------------------------------------------
CHILDREN_S_ENTERTAINMENT |
            release_date |   .0150721   .0080371     1.88   0.061    -.0006803    .0308245
                      ps |   .3108431   .6603469     0.47   0.638    -.9834131    1.605099
   top_performer_rev_sum |   .6036564   .2705252     2.23   0.026     .0734367    1.133876
                 atari_p |  -15.40619   98410.94    -0.00   1.000    -192897.3    192866.5
                  sega_p |  -17.28768   7750.106    -0.00   0.998    -15207.22    15172.64
                 micro_p |  -14.86823   2537.979    -0.01   0.995    -4989.215    4959.478
                   nin_p |   1.369725   .6131861     2.23   0.025     .1679019    2.571547
                  number |   -.572284   .0578387    -9.89   0.000    -.6856458   -.4589223
              rev_growth |   .4400669   .1514842     2.91   0.004     .1431633    .7369706
                   _cons |   8.801733   4.555853     1.93   0.053    -.1275744    17.73104
-------------------------+----------------------------------------------------------------
FAMILY_ENTERTAINMENT     |
            release_date |   .0455727   .0017084    26.68   0.000     .0422244    .0489211
                      ps |  -.4294972   .1278267    -3.36   0.001    -.6800329   -.1789615
   top_performer_rev_sum |   -.126878   .0307522    -4.13   0.000    -.1871513   -.0666048
                 atari_p |   .1598698   1.498964     0.11   0.915    -2.778046    3.097786
                  sega_p |  -.3383123   .2835629    -1.19   0.233    -.8940853    .2174608
                 micro_p |  -.9795381   .1886858    -5.19   0.000    -1.349356   -.6097206
                   nin_p |  -.1098563   .1326103    -0.83   0.407    -.3697677    .1500551
                  number |  -.0674744    .002224   -30.34   0.000    -.0718334   -.0631154
              rev_growth |   .9722408   .0661211    14.70   0.000     .8426459    1.101836
                   _cons |  -17.21225   .7930431   -21.70   0.000    -18.76658   -15.65791
-------------------------+----------------------------------------------------------------

If I'm interpreting the results correctly, top performers do have a significant effect on choice of genre; however, when I want to look at marginal effects, this significance seems to disappear:

. margins, dydx(top_performer_rev_sum )

Average marginal effects                        Number of obs     =     10,475
Model VCE    : OIM

dy/dx w.r.t. : top_performer_rev_sum
1._predict   : Pr(sgenre_id3==ACTION), predict(pr outcome(1))
2._predict   : Pr(sgenre_id3==ADVENTURE), predict(pr outcome(2))
3._predict   : Pr(sgenre_id3==ARCADE), predict(pr outcome(3))
4._predict   : Pr(sgenre_id3==CHILDREN_S_ENTERTAINMENT), predict(pr outcome(4))
5._predict   : Pr(sgenre_id3==FAMILY_ENTERTAINMENT), predict(pr outcome(5))
6._predict   : Pr(sgenre_id3==FIGHTING), predict(pr outcome(6))
7._predict   : Pr(sgenre_id3==FLIGHT), predict(pr outcome(7))
8._predict   : Pr(sgenre_id3==OTHER_GAMES_COMPILATIONS), predict(pr outcome(9))
9._predict   : Pr(sgenre_id3==RACING), predict(pr outcome(10))
10._predict  : Pr(sgenre_id3==ROLE_PLAYING), predict(pr outcome(11))
11._predict  : Pr(sgenre_id3==SHOOTER), predict(pr outcome(12))
12._predict  : Pr(sgenre_id3==SIMULATION), predict(pr outcome(13))
13._predict  : Pr(sgenre_id3==SPORT_GAMES), predict(pr outcome(15))
14._predict  : Pr(sgenre_id3==STRATEGY), predict(pr outcome(16))
15._predict  : Pr(sgenre_id3==17), predict(pr outcome(17))

---------------------------------------------------------------------------------------
                      |            Delta-method
                      |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------------+----------------------------------------------------------------
top_performer_rev_sum |
             _predict |
                   1  |  -.0023884    .001716    -1.39   0.164    -.0057516    .0009749
                   2  |  -.0233723   .2554385    -0.09   0.927    -.5240227     .477278
                   3  |   .0099778    .286822     0.03   0.972     -.552183    .5721386
                   4  |   .0033038   .0760032     0.04   0.965    -.1456598    .1522674
                   5  |  -.0058774   .0144927    -0.41   0.685    -.0342827    .0225278
                   6  |   .0181605   .4047448     0.04   0.964    -.7751247    .8114457
                   7  |   .0006966   .0409284     0.02   0.986    -.0795215    .0809147
                   8  |  -.0387957   1.294957    -0.03   0.976    -2.576866    2.499274
                   9  |  -.0003055   .0085375    -0.04   0.971    -.0170387    .0164277
                  10  |  -.0028814   .0237131    -0.12   0.903    -.0493581    .0435953
                  11  |  -.0065901   .0042347    -1.56   0.120    -.0148899    .0017097
                  12  |   .0328852   .0057612     5.71   0.000     .0215934    .0441769
                  13  |   .0030331   .0182149     0.17   0.868    -.0326675    .0387338
                  14  |   .0015708   .1059767     0.01   0.988    -.2061398    .2092814
                  15  |   .0105829   .0502787     0.21   0.833    -.0879614    .1091273
---------------------------------------------------------------------------------------

Am I doing something wrong or how do I interpret this?

[Weiwen Ng]

Your main results show the log odds of selecting, for example, adventure games versus outcome games. Being a top performer is associated with lower odds of selecting adventure games over action games, controlling for everything else. When you go to margins, the test is now that the marginal effect of being a top performer on the probability of selecting that category is zero. You might find this interesting, or you might not.

I am unfamiliar with hypothesis testing in multinomial logit models because I don't frequently use them, and I also don't have 15 separate categories when I do. It strikes me that if you want to test if being a top performer has any association with the type of games they developers design, then you could do a joint test that all the separate marginal effects are equal to zero. I'd be interested to hear if other readers think that's a good idea.

By the way, this is something you could use -marginsplot- to show graphically. The graph would be very crowded with 15 outcomes. You could split up the margins command to test, say, 5 outcomes at one go, e.g.

margins, dydx(top_performer_rev_sum) predict(pr outcome(1)) predict(pr outcome(2)) predict(pr outcome(3)) predict(pr outcome(4)) predict(pr outcome(5))