marginscontplot and margins interpretation after negative binomial

[Simon Schillebeeckx]

I am hoping to find some clarity as to how to interpret margins, and more specifically the marginscontplot package after negative binomial regression

In essence, my regression is as follows

xtnbreg y X x c.x#c.x z c.x#c.z c.x#c.x#c.z, fe /* X is a vector of controls */

My variable y is left skewed and overdispersed hence the choice of negative binomial. The conditional fixed effects should control somewhat for unobserved individual differences.
I am trying to graphically represent the marginal effect of x on y at various levels of the moderator z.

marginscontplot x z, at1(0(.1)1) at2(%5 25 50 75 95)

The results are consistent with my interpretation but the effect size seems extremely small
- y has mean 5 and standard deviation 10
- the marginal effects plot shows movements from -0.04 to +0.04.
What is the right interpretation for this? If it is percentage change then it would make sense and be economically significant. If these changes are absolute then it means that while the observed interaction is statistically significant, the real economic interpretation is that it barely matters. Or am I wrong?

Upon reading the section on log-transformation in Royston (2013) - the author of the package whom I emailed the same question - I started wondering whether something like this would be required after a negative binomial regression as well?
For as far as I know, xtnbreg uses a log link for its maximum-likelihood solution, which made me think it may be necessary to use the exponentials of the x and z values to get the true effects?

But once again I may be miles off. Any suggestions of the right interpretation or what need be done to get the proper graphs.
In addition, if I winsorize my response variable y, the standard deviation decreases a lot so that I could use
xtpoisson instead of xtnbreg. Would this change the interpretation/work needed to get the right effects?

Thanks

[Simon Schillebeeckx]

I'm adding some concrete results which will hopefully make my question a bit clearer. I got a response from Professor Royston who suggested I'd use the margins command to get some meaningful results at different focal values of the interaction. This is what I will present.

xtset firm_id
xtnbreg fwd claims num_cited_patents degree firm_prod struct unknown log_assets log_breadth log_depth team_size team_div team_sim team_mk ///
num_sbcls backcitation_struct lag exp_k firm_k field_k pers c.pers#c.pers priv c.priv#c.priv pub c.pub#c.pub c.pers#c.firm_k c.pers#c.pers#c.firm_k ///
c.pers#c.field_k c.pers#c.pers#c.field_k c.priv#c.firm_k c.priv#c.priv#c.firm_k c.priv#c.field_k c.priv#c.priv#c.field_k c.pub#c.firm_k c.pub#c.pub#c.firm_k ///
c.pub#c.field_k c.pub#c.pub#c.field_k i.app_year i.grant i.tech_cat , fe

Conditional FE negative binomial regression     Number of obs     =     39,785
Group variable: firm                            Number of groups  =        127

                                                Obs per group:
                                                              min =          2
                                                              avg =      313.3
                                                              max =      8,114

                                                Wald chi2(54)     =    6142.11
Log likelihood  = -125965.06                    Prob > chi2       =     0.0000

-----------------------------------------------------------------------------------------
                    fwd |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------------+----------------------------------------------------------------
                 claims |   .0049837   .0002365    21.07   0.000     .0045202    .0054472
      num_cited_patents |    .001215   .0001458     8.33   0.000     .0009292    .0015008
                 degree |   .0003122    .000263     1.19   0.235    -.0002033    .0008277
              firm_prod |  -.0000138   .0000177    -0.78   0.434    -.0000485    .0000208
                 struct |  -.2436991   .0630098    -3.87   0.000    -.3671961   -.1202021
                unknown |  -.4579558   .1213173    -3.77   0.000    -.6957334   -.2201782
             log_assets |   .0028118   .0033733     0.83   0.405    -.0037998    .0094234
            log_breadth |   .0069819   .0193117     0.36   0.718    -.0308683     .044832
              log_depth |  -.0495728   .0085805    -5.78   0.000    -.0663903   -.0327552
              team_size |   .0260166   .0030426     8.55   0.000     .0200533    .0319799
               team_div |   .0105567    .018692     0.56   0.572    -.0260789    .0471924
               team_sim |  -.0110808   .0156172    -0.71   0.478    -.0416898    .0195283
                team_mk |  -.0002198   .0047016    -0.05   0.963    -.0094348    .0089952
              num_sbcls |   .0142212   .0013109    10.85   0.000     .0116519    .0167904
    backcitation_struct |  -.0016426   .0047063    -0.35   0.727    -.0108668    .0075815
                    lag |  -.0510641   .0596025    -0.86   0.392    -.1678829    .0657546
                  exp_k |  -.0763197   .0189168    -4.03   0.000     -.113396   -.0392434
                 firm_k |  -.0025858   .0015259    -1.69   0.090    -.0055765    .0004048
                field_k |   .1270678   .0323343     3.93   0.000     .0636936    .1904419
                   pers |   .1300448   .1024925     1.27   0.205    -.0708368    .3309263
                        |
          c.pers#c.pers |  -.1015341    .103132    -0.98   0.325    -.3036692     .100601
                        |
                   priv |   .2974514   .0865601     3.44   0.001     .1277967    .4671062
                        |
          c.priv#c.priv |  -.2740141     .08894    -3.08   0.002    -.4483333   -.0996948
                        |
                    pub |   .1420732   .0597384     2.38   0.017      .024988    .2591583
                        |
            c.pub#c.pub |  -.1112915   .0538098    -2.07   0.039    -.2167567   -.0058263
                        |
        c.pers#c.firm_k |   .0163444   .0091099     1.79   0.073    -.0015108    .0341995
                        |
 c.pers#c.pers#c.firm_k |   -.019108   .0092439    -2.07   0.039    -.0372257   -.0009903
                        |
       c.pers#c.field_k |   .3258023   .2079811     1.57   0.117    -.0818332    .7334378
                        |
c.pers#c.pers#c.field_k |   -.398517   .2111706    -1.89   0.059    -.8124037    .0153697
                        |
        c.priv#c.firm_k |  -.0169148   .0100623    -1.68   0.093    -.0366365    .0028069
                        |
 c.priv#c.priv#c.firm_k |   .0140956   .0095722     1.47   0.141    -.0046655    .0328568
                        |
       c.priv#c.field_k |  -.0666787   .2309481    -0.29   0.773    -.5193286    .3859711
                        |
c.priv#c.priv#c.field_k |    .019387   .2410233     0.08   0.936      -.45301    .4917841
                        |
         c.pub#c.firm_k |   .0208968   .0095201     2.20   0.028     .0022376    .0395559
                        |
   c.pub#c.pub#c.firm_k |  -.0160072   .0088952    -1.80   0.072    -.0334415    .0014272
                        |
        c.pub#c.field_k |   .2959359   .1827368     1.62   0.105    -.0622217    .6540935
                        |
  c.pub#c.pub#c.field_k |  -.3376882   .1766718    -1.91   0.056    -.6839585    .0085821
                        |
               app_year |
                  2001  |  -.0831546   .0609588    -1.36   0.173    -.2026316    .0363223
                  2002  |  -.1053847   .1198914    -0.88   0.379    -.3403675    .1295981
                  2003  |  -.1162318   .1788953    -0.65   0.516    -.4668601    .2343965
                  2004  |  -.2252228   .2384281    -0.94   0.345    -.6925334    .2420877
                        |
                  grant |
                  2001  |  -.2114983   .1172296    -1.80   0.071    -.4412641    .0182674
                  2002  |  -.2588022    .155375    -1.67   0.096    -.5633316    .0457271
                  2003  |  -.2490793   .2044986    -1.22   0.223    -.6498893    .1517306
                  2004  |  -1.325461   .2582886    -5.13   0.000    -1.831697   -.8192248
                  2005  |  -.2629144   .3202001    -0.82   0.412    -.8904951    .3646662
                  2006  |  -.3805254   .3709358    -1.03   0.305    -1.107546    .3464955
                  2007  |  -.4127656   .4286241    -0.96   0.336    -1.252853    .4273222
                  2008  |  -.4082876   .4877517    -0.84   0.403    -1.364263    .5476882
                        |
               tech_cat |
                     2  |   .2759584   .0270858    10.19   0.000     .2228713    .3290456
                     3  |  -.0037093   .1265231    -0.03   0.977      -.25169    .2442714
                     4  |   .2379766   .0272443     8.73   0.000     .1845789    .2913744
                     5  |   .0738643    .032656     2.26   0.024     .0098596    .1378689
                     6  |   .1180079   .0468128     2.52   0.012     .0262564    .2097594
                        |
                  _cons |   .8842308   .1526103     5.79   0.000     .5851202    1.183341
-----------------------------------------------------------------------------------------

. margins, dydx(priv) at(field_k = (0 0.04 0.25 .5)) atmeans
/* I omit the long list of mean values */
Conditional marginal effects                    Number of obs     =     39,785
Model VCE    : OIM

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
priv         |
         _at |
          1  |   .1579886   .0462934     3.41   0.001     .0672552     .248722
          2  |   .1556596   .0455666     3.42   0.001     .0663507    .2449686
          3  |   .1434324   .0511018     2.81   0.005     .0432748    .2435901
          4  |   .1288763   .0720292     1.79   0.074    -.0122984     .270051
------------------------------------------------------------------------------

margins, dydx(priv) at(field_k = (0 0.04 0.25 .5)) atmeans predict(iru0)

/* I omit the long list of mean values */
------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
priv         |
         _at |
          1  |     .17158   .0520516     3.30   0.001     .0695607    .2735993
          2  |   .1705654     .05168     3.30   0.001     .0692745    .2718563
          3  |   .1647029   .0605659     2.72   0.007     .0459959      .28341
          4  |   .1564732   .0898728     1.74   0.082    -.0196742    .3326206
------------------------------------------------------------------------------

So, I have three primary questions
1) What's the difference between the first and second use of margins? How do I interpret the respective values for dydx?
2) The regression table shows that the interaction terms between priv and field_k are insignificant but the marginal effects seem to be significant (in terms of p-value at least, although this is probably a straw man hypothesis and thus not really important.
3) Given that priv is constrained by 0 and 1 (with most observations in one of both extremes) and that my response fwd is a count between 0 and 65, what is a correct interpretation of these tables?

.

 sum priv, detail

                            priv
-------------------------------------------------------------
      Percentiles      Smallest
 1%            0              0
 5%            0              0
10%            0              0       Obs              42,993
25%            0              0       Sum of Wgt.      42,993

50%            0                      Mean           .2108743
                        Largest       Std. Dev.      .3838067
75%     .0589256              1
90%            1              1       Variance       .1473076
95%            1              1       Skewness       1.383245
99%            1              1       Kurtosis       3.065822

. sum fwd, de

                             fwd
-------------------------------------------------------------
      Percentiles      Smallest
 1%            0              0
 5%            0              0
10%            1              0       Obs              42,993
25%            2              0       Sum of Wgt.      42,993

50%            6                      Mean           9.324053
                        Largest       Std. Dev.      11.03751
75%           12             65
90%           23             65       Variance       121.8266
95%           33             65       Skewness       2.239239
99%           53             65       Kurtosis        8.75067

Finally, using xtpoisson generally results in more significant interaction terms. Taking the log of my responses and using xtreg also creates more significant interaction terms (see output below). So in the festival of significance stars (something unfortunately important in my field), those are preferred, but I want to make sure that my interpretation is correct and meaningful.

xtpoisson fwd claims num_cited_patents degree firm_prod struct unknown log_assets log_breadth log_depth team_size team_div team_sim team_mk ///
num_sbcls backcitation_struct lag exp_k firm_k field_k pers c.pers#c.pers priv c.priv#c.priv pub c.pub#c.pub c.pers#c.firm_k c.pers#c.pers#c.firm_k ///
c.pers#c.field_k c.pers#c.pers#c.field_k c.priv#c.firm_k c.priv#c.priv#c.firm_k c.priv#c.field_k c.priv#c.priv#c.field_k c.pub#c.firm_k c.pub#c.pub#c.firm_k ///
c.pub#c.field_k c.pub#c.pub#c.field_k i.app_year i.grant i.tech_cat , fe

note: 10 groups (10 obs) dropped because of only one obs per group

Iteration 0:   log likelihood = -263803.46  
Iteration 1:   log likelihood = -243962.54  
Iteration 2:   log likelihood = -243465.97  
Iteration 3:   log likelihood = -243463.23  
Iteration 4:   log likelihood = -243463.23  

Conditional fixed-effects Poisson regression    Number of obs     =     39,785
Group variable: firm                            Number of groups  =        127

                                                Obs per group:
                                                              min =          2
                                                              avg =      313.3
                                                              max =      8,114

                                                Wald chi2(54)     =   41192.09
Log likelihood  = -243463.23                    Prob > chi2       =     0.0000

-----------------------------------------------------------------------------------------
                    fwd |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------------+----------------------------------------------------------------
                 claims |   .0064992   .0000888    73.21   0.000     .0063252    .0066732
      num_cited_patents |   .0014391   .0000564    25.52   0.000     .0013286    .0015496
                 degree |   .0013402   .0001046    12.81   0.000     .0011351    .0015452
              firm_prod |   -.000159   .0000136   -11.70   0.000    -.0001856   -.0001324
                 struct |   -.427752   .0251334   -17.02   0.000    -.4770125   -.3784914
                unknown |  -.7541217   .0479956   -15.71   0.000    -.8481914    -.660052
             log_assets |  -.0415302   .0051996    -7.99   0.000    -.0517212   -.0313392
            log_breadth |  -.0575411   .0155309    -3.70   0.000     -.087981   -.0271012
              log_depth |  -.0173745   .0075839    -2.29   0.022    -.0322386   -.0025104
              team_size |   .0357097   .0011353    31.45   0.000     .0334844    .0379349
               team_div |   .0115198   .0073342     1.57   0.116    -.0028549    .0258945
               team_sim |  -.0089119   .0060535    -1.47   0.141    -.0207765    .0029526
                team_mk |   .0090114   .0018139     4.97   0.000     .0054562    .0125666
              num_sbcls |   .0207031   .0004979    41.58   0.000     .0197271     .021679
    backcitation_struct |   .0051363   .0017929     2.86   0.004     .0016224    .0086503
                    lag |  -.0012381   .0254197    -0.05   0.961    -.0510598    .0485836
                  exp_k |  -.1199823   .0074442   -16.12   0.000    -.1345727   -.1053918
                 firm_k |  -.0023093   .0006131    -3.77   0.000     -.003511   -.0011076
                field_k |   .1598641   .0121745    13.13   0.000     .1360026    .1837256
                   pers |   .1135655   .0388322     2.92   0.003     .0374557    .1896753
                        |
          c.pers#c.pers |  -.0570222   .0390234    -1.46   0.144    -.1335066    .0194622
                        |
                   priv |   .4397489   .0321638    13.67   0.000      .376709    .5027887
                        |
          c.priv#c.priv |  -.4101538   .0330199   -12.42   0.000    -.4748716   -.3454359
                        |
                    pub |   .1647223   .0232118     7.10   0.000      .119228    .2102165
                        |
            c.pub#c.pub |  -.1475536   .0208895    -7.06   0.000    -.1884962   -.1066111
                        |
        c.pers#c.firm_k |   .0156028   .0034399     4.54   0.000     .0088607    .0223449
                        |
 c.pers#c.pers#c.firm_k |  -.0197544   .0034878    -5.66   0.000    -.0265904   -.0129184
                        |
       c.pers#c.field_k |   .3190476   .0742231     4.30   0.000      .173573    .4645222
                        |
c.pers#c.pers#c.field_k |  -.4519214    .075868    -5.96   0.000    -.6006199   -.3032229
                        |
        c.priv#c.firm_k |  -.0150464   .0038071    -3.95   0.000    -.0225082   -.0075845
                        |
 c.priv#c.priv#c.firm_k |   .0127892   .0035829     3.57   0.000     .0057668    .0198116
                        |
       c.priv#c.field_k |  -.1303623   .0824817    -1.58   0.114    -.2920235    .0312988
                        |
c.priv#c.priv#c.field_k |   .0894445   .0855325     1.05   0.296    -.0781961    .2570851
                        |
         c.pub#c.firm_k |   .0248737   .0036564     6.80   0.000     .0177072    .0320402
                        |
   c.pub#c.pub#c.firm_k |  -.0222853   .0033906    -6.57   0.000    -.0289308   -.0156398
                        |
        c.pub#c.field_k |    .317472   .0669685     4.74   0.000     .1862161    .4487279
                        |
  c.pub#c.pub#c.field_k |  -.2994733   .0643361    -4.65   0.000    -.4255697   -.1733768
                        |
               app_year |
                  2001  |  -.0574705   .0258724    -2.22   0.026    -.1081795   -.0067614
                  2002  |  -.0304748   .0510686    -0.60   0.551    -.1305675    .0696179
                  2003  |  -.0125755   .0762789    -0.16   0.869    -.1620794    .1369285
                  2004  |  -.1222683   .1017238    -1.20   0.229    -.3216433    .0771067
                        |
                  grant |
                  2001  |  -.3024258   .0420415    -7.19   0.000    -.3848256   -.2200259
                  2002  |  -.4418447   .0606158    -7.29   0.000    -.5606494   -.3230401
                  2003  |  -.5307047    .083021    -6.39   0.000    -.6934229   -.3679865
                  2004  |  -1.263861   .1068297   -11.83   0.000    -1.473243   -1.054478
                  2005  |  -.6732148   .1335537    -5.04   0.000    -.9349751   -.4114544
                  2006  |  -.9158552   .1559353    -5.87   0.000    -1.221483   -.6102276
                  2007  |  -1.023631   .1808529    -5.66   0.000    -1.378097   -.6691661
                  2008  |  -1.097159   .2063254    -5.32   0.000    -1.501549   -.6927687
                        |
               tech_cat |
                     2  |   .4100907   .0119486    34.32   0.000     .3866718    .4335096
                     3  |   .1752106   .0491525     3.56   0.000     .0788736    .2715477
                     4  |   .3570815   .0120064    29.74   0.000     .3335494    .3806136
                     5  |   .0974154   .0143193     6.80   0.000       .06935    .1254808
                     6  |   .1494345   .0198745     7.52   0.000     .1104813    .1883878
-----------------------------------------------------------------------------------------

xtreg logfw claims num_cited_patents degree firm_prod struct unknown log_assets log_breadth log_depth team_size team_div team_sim team_mk ///
num_sbcls backcitation_struct lag exp_k firm_k field_k pers c.pers#c.pers priv c.priv#c.priv pub c.pub#c.pub c.pers#c.firm_k c.pers#c.pers#c.firm_k ///
c.pers#c.field_k c.pers#c.pers#c.field_k c.priv#c.firm_k c.priv#c.priv#c.firm_k c.priv#c.field_k c.priv#c.priv#c.field_k c.pub#c.firm_k c.pub#c.pub#c.firm_k ///
c.pub#c.field_k c.pub#c.pub#c.field_k i.app_year i.grant i.tech_cat , fe

Fixed-effects (within) regression               Number of obs     =     39,795
Group variable: firm                            Number of groups  =        137

R-sq:                                           Obs per group:
     within  = 0.1590                                         min =          1
     between = 0.0710                                         avg =      290.5
     overall = 0.1279                                         max =      8,114

                                                F(54,39604)       =     138.70
corr(u_i, Xb)  = -0.4691                        Prob > F          =     0.0000

-----------------------------------------------------------------------------------------
                  logfw |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
------------------------+----------------------------------------------------------------
                 claims |   .0065213   .0003139    20.77   0.000     .0059061    .0071366
      num_cited_patents |   .0016492   .0001867     8.84   0.000     .0012833     .002015
                 degree |   .0004774   .0002846     1.68   0.093    -.0000804    .0010352
              firm_prod |  -.0000995   .0000368    -2.70   0.007    -.0001717   -.0000273
                 struct |  -.2926457   .0689893    -4.24   0.000    -.4278665    -.157425
                unknown |  -.5479183   .1294006    -4.23   0.000    -.8015467     -.29429
             log_assets |  -.0606266   .0159486    -3.80   0.000    -.0918862    -.029367
            log_breadth |   -.048369   .0476169    -1.02   0.310    -.1416992    .0449612
              log_depth |  -.0312398   .0216747    -1.44   0.150    -.0737227    .0112431
              team_size |   .0288244   .0034058     8.46   0.000     .0221489    .0354999
               team_div |   .0263985   .0202527     1.30   0.192    -.0132972    .0660942
               team_sim |  -.0075647   .0168385    -0.45   0.653    -.0405686    .0254392
                team_mk |   .0005535   .0050295     0.11   0.912    -.0093044    .0104113
              num_sbcls |   .0169557   .0014758    11.49   0.000     .0140632    .0198483
    backcitation_struct |  -.0014113   .0051218    -0.28   0.783    -.0114501    .0086275
                    lag |  -.0577932   .0661261    -0.87   0.382    -.1874019    .0718156
                  exp_k |  -.0840686   .0203486    -4.13   0.000    -.1239524   -.0441848
                 firm_k |   -.002316   .0016485    -1.40   0.160    -.0055472    .0009151
                field_k |   .1432211   .0386131     3.71   0.000     .0675386    .2189036
                   pers |   .0585925    .111622     0.52   0.600    -.1601893    .2773744
                        |
          c.pers#c.pers |  -.0291613   .1121665    -0.26   0.795    -.2490103    .1906877
                        |
                   priv |   .3398888   .0935195     3.63   0.000     .1565884    .5231892
                        |
          c.priv#c.priv |  -.3059043   .0959496    -3.19   0.001    -.4939678   -.1178407
                        |
                    pub |   .1275387   .0633334     2.01   0.044     .0034038    .2516736
                        |
            c.pub#c.pub |  -.0932148   .0572437    -1.63   0.103    -.2054137    .0189841
                        |
        c.pers#c.firm_k |   .0223736   .0100127     2.23   0.025     .0027484    .0419987
                        |
 c.pers#c.pers#c.firm_k |  -.0260538    .010101    -2.58   0.010     -.045852   -.0062556
                        |
       c.pers#c.field_k |   .5361738   .2520818     2.13   0.033     .0420875     1.03026
                        |
c.pers#c.pers#c.field_k |  -.6169355   .2546551    -2.42   0.015    -1.116066   -.1178053
                        |
        c.priv#c.firm_k |  -.0231817   .0108295    -2.14   0.032    -.0444078   -.0019555
                        |
 c.priv#c.priv#c.firm_k |   .0187584   .0102102     1.84   0.066    -.0012539    .0387706
                        |
       c.priv#c.field_k |  -.2149574   .2640878    -0.81   0.416    -.7325759     .302661
                        |
c.priv#c.priv#c.field_k |   .1794383   .2732271     0.66   0.511    -.3560934      .71497
                        |
         c.pub#c.firm_k |   .0267493   .0100862     2.65   0.008     .0069802    .0465184
                        |
   c.pub#c.pub#c.firm_k |  -.0206803   .0093395    -2.21   0.027    -.0389859   -.0023747
                        |
        c.pub#c.field_k |   .3852353   .2157266     1.79   0.074     -.037594    .8080646
                        |
  c.pub#c.pub#c.field_k |  -.4600764    .206776    -2.22   0.026    -.8653624   -.0547904
                        |
               app_year |
                  2001  |  -.0956938    .067649    -1.41   0.157    -.2282874    .0368998
                  2002  |  -.1190142   .1329149    -0.90   0.371    -.3795306    .1415023
                  2003  |  -.1287228   .1983711    -0.65   0.516    -.5175348    .2600892
                  2004  |  -.2589192    .264522    -0.98   0.328    -.7773888    .2595503
                        |
                  grant |
                  2001  |  -.2118187   .1523646    -1.39   0.164    -.5104569    .0868195
                  2002  |  -.2694298   .1895196    -1.42   0.155    -.6408927    .1020331
                  2003  |  -.2642305   .2401359    -1.10   0.271    -.7349027    .2064416
                  2004  |  -1.268453   .2968365    -4.27   0.000     -1.85026   -.6866463
                  2005  |  -.3003078   .3623263    -0.83   0.407    -1.010476    .4098604
                  2006  |  -.4392996   .4188481    -1.05   0.294    -1.260252    .3816526
                  2007  |  -.4830357   .4818457    -1.00   0.316    -1.427465    .4613934
                  2008  |  -.5007083   .5465553    -0.92   0.360     -1.57197    .5705531
                        |
               tech_cat |
                     2  |   .3068639   .0284208    10.80   0.000     .2511586    .3625693
                     3  |   .0392971    .130785     0.30   0.764    -.2170447    .2956388
                     4  |   .2562774   .0285959     8.96   0.000     .2002287    .3123261
                     5  |   .0754664    .033832     2.23   0.026     .0091549    .1417779
                     6  |   .1231078   .0493236     2.50   0.013     .0264324    .2197831
                        |
                  _cons |   3.382757   .2329697    14.52   0.000     2.926131    3.839384
------------------------+----------------------------------------------------------------
                sigma_u |  .49854173
                sigma_e |  .91322516
                    rho |  .22959662   (fraction of variance due to u_i)
-----------------------------------------------------------------------------------------
F test that all u_i=0: F(136, 39604) = 6.71                  Prob > F = 0.0000

Really appreciate any feedback that may be given.

[Simon Schillebeeckx]

Following up on suggestions made on another question of mine (here), I am adding some information about the research question.
The data consists of patent data for 137 firms (10 of which only have a single patent and thus drop out of NB and Poisson models). The response variable is the number of times a specific patent is cited in the 10 years after its application (commonly referred to as forward citations). I'm controlling for a few time dimensions (application and grant year) and technical category of the patents and use firm fixed effects (there are big differences between firms in terms of number and impact of patents per year).

The focal variables of interest are three measures of "recombination of previously used knowledge elements" (called pers, priv, and pub) and the interaction terms of interest capture measures of social ties in the organization (firm_k) and social ties outside the organization (field_k).

The goal is to figure out whether there is support for the overarching hypothesis that the recombination of knowledge elements has a curvilinear relationship with the number of forward citations and that this impact is moderated (in various ways) by social ties between inventors.

Hope this helps in understanding the purpose of the research

[Joao Santos Silva]

Dear Simon,

As I said in a different thread, the NB estimator with fixed effects is not a real FE estimator in the usual sense. Please make sure you understand what it does.

The FE Poisson regression does what you have in mind and apparently gives sensible results, so I would stick to it. Notice that (unconditional) overdispersion is irrelevant for the choice between these estimators.

Finally, do not Winsorize your data!

Best wishes,

Joao

[Simon Schillebeeckx]

Thanks Joao for the feedback. If I may ask a few follow-up questions:

- Can you clarify why unconditional overdispersion is irrelevant for the choice between estimators? I was taught that when standard deviation of response is larger than the mean, negative binomial models would be preferred.
- You argued in this post that running margins command to get the marginal effects after an xtpoisson with fixed effects is pretty much meaningless. Given that I am expected to present marginal effects interaction plots of these effects, would it be an acceptable shortcut to use margins after the xtreg regression and present those, or is margins after ANY regression with fixed effects basically meaningless?

[Joao Santos Silva]

Dear Simon,

About your questions:

- I am afraid that is just wrong: what matters is the relation between the conditional mean and the conditional variance. Even if you have (conditional) overdispersion, Poisson regression will give you consistent estimates of the parameters of interest under very general conditions. The cost of overdispersion is that you may lose some efficiency and you cannot use the model to compute the probabilities of specific counts, but in any case you cannot do that if you have fixed effects. In your particular case, the NB and Poisson models with fixed effects are very different and in general the FE NB model does not really control for fixed effects; see this paper. So, if you want to control for fixed effect, you have no choice but to use the Poisson model and therefore whether or not you have overdispersion is irrelevant.

- Marginal effects are meaningless in non-linear models with fixed effects (unless you have large T), so they are fine after xtreg but I would not do that. In the FE Poisson regression the coefficients are elasticities or semi-elasticities, that's what I would report,

Best wishes,

Joao

[Chengyuan Wang]

Dear Joao,
I have another problem with marginal effect. My data is also count data. Also, I use FE Poisson regression.
Now, I want to further analyze the effect of explanatory variables on dependent variable, by using quantile regression for count data (The stata command, qcount).
Should I also report the regression coefficients, rather than marginal effects of qcount results?
Thanks a lot.

With my best regard,
Chengyuan Wang

[Joao Santos Silva]

Dear Chengyuan Wang,

I would say that for the quantile regression the marginal effects are more interesting, but they cannot be compared to anything estimated using Poisson regression with FE.

Best wishes,

Joao

[Chengyuan Wang]

Dear Chengyuan Wang,

I would say that for the quantile regression the marginal effects are more interesting, but they cannot be compared to anything estimated using Poisson regression with FE.

Best wishes,

Joao

Dear Joao,

Thanks a lot for your feedback. I have another further question, that whether I could compare the average marginal effect of Poisson regression with FE, to the marginal effects of quantile Poisson regression, or not.

Best regards,

Chengyuan Wang

[Joao Santos Silva]

Chengyuan Wang

Unfortunately, you cannot.

Best wishes,

Joao

[Chengyuan Wang]

Joao Santos Silva
Thanks a lot for your patience!

Best regards,

Chengyuan Wang