Interpretation of Negative Binomial Regression Model with Panel Data

[Ben Koch]

Dear All,

I am using Stata 14 and investigating the impact of Corporate Venture Capital Investment on the Innovation performance of corporates. For my study, I am using unbalanced panel data as my dataset consists of around 70 firms in a time period of 8 years.

My dependent variable is the number of patents, measured as a count variable. Since, it is overdispersed i have decided to run

xtnbreg EcoPatents Revenue RandD ROA CVCDeals i.Industry i.Year, re

My results look as follows

Random-effects negative binomial regression     Number of obs     =        485
Group variable: id                              Number of groups  =         72

Random effects u_i ~ Beta                       Obs per group:
                                                              min =          2
                                                              avg =        6.7
                                                              max =          8

                                                Wald chi2(19)     =     488.06
Log likelihood  = -2051.3666                    Prob > chi2       =     0.0000

----------------------------------------------------------------------------------------------
                  EcoPatents |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------------------+----------------------------------------------------------------
                     Revenue |   .0021823   .0010251     2.13   0.033     .0001731    .0041915
                       RandD |   .0045523   .0017063     2.67   0.008      .001208    .0078967
                         ROA |  -.1024272   .5633483    -0.18   0.856     -1.20657    1.001715
                    CVCDeals |   .0200437   .0084855     2.36   0.018     .0034125     .036675
             InvestmentStage |   .1869527   .0915727     2.04   0.041     .0074736    .3664319
                             |
c.CVCDeals#c.InvestmentStage |  -.0257762   .0134832    -1.91   0.056    -.0522029    .0006505
                             |
                    Industry |
                          2  |  -.7948941   .5029193    -1.58   0.114    -1.780598    .1908096
                          3  |  -.1072463   .5006072    -0.21   0.830    -1.088418    .8739257
                          4  |  -1.631532   .4985119    -3.27   0.001    -2.608597   -.6544667
                          5  |  -.2224191   .7265788    -0.31   0.760    -1.646487    1.201649
                          6  |  -.7628642   .6077591    -1.26   0.209     -1.95405    .4283218
                          7  |  -.2909924   .8854289    -0.33   0.742    -2.026401    1.444416
                             |
                        Year |
                       2011  |  -.0415641   .0717578    -0.58   0.562    -.1822067    .0990785
                       2012  |  -.0477043   .0709135    -0.67   0.501    -.1866922    .0912836
                       2013  |  -.3043772   .0768562    -3.96   0.000    -.4550125   -.1537418
                       2014  |  -.4286997   .0780602    -5.49   0.000    -.5816949   -.2757045
                       2015  |  -.5881658   .0835155    -7.04   0.000    -.7518532   -.4244785
                       2016  |  -1.086586   .0935873   -11.61   0.000    -1.270014   -.9031582
                       2017  |  -2.294929   .1353113   -16.96   0.000    -2.560134   -2.029724
                             |
                       _cons |   2.404181   .4972169     4.84   0.000     1.429654    3.378708
-----------------------------+----------------------------------------------------------------
                       /ln_r |  -.2576163   .1521891                     -.5559014    .0406688
                       /ln_s |   .7930667   .2019342                      .3972831     1.18885
-----------------------------+----------------------------------------------------------------
                           r |   .7728917   .1176257                       .573555    1.041507
                           s |   2.210164   .4463076                      1.487777    3.283305
----------------------------------------------------------------------------------------------
LR test vs. pooled: chibar2(01) = 857.82               Prob >= chibar2 = 0.000

Currently, I am struggling to interpret the coefficients of the negative binomial regression output.
Can anyone help with the interpretation of the coefficients CVCDeals (number of Deals), InvestmentStage (continuous variable between 0 and 1) and the interaction term c.CVCDeals#c.InvestmentStage? In particular, I would like to understand how much % the dependent variable changes with an increase of the independent variable.

Any help is greatly appreciated!

Best,
Ben

[Phil Bromiley]

The margins command is the easiest way to do this.

[Ben Koch]

Dear Phil,

Thank you very much for your reply.

Richard Williams' presentation about the Margins Command,https://www3.nd.edu/~rwilliam/stats/Margins01.pdf, (Thanks to Clyde for bringing up this reference in an other thread), helped me to better understand the output of a margins command. Nevertheless, he has not discussed the application of the margins command in a negative binomial regression. Since, this is my first time working with the margins command I have 2 further questions:

1. Am I using the correct command?
2. How do I interpret the margins command for the xtnbreg. Is it correct to say that "the probability that a firm has one more Ecopatent inceases by 0.00564 as CVCDeals increases by one"?

. margins, dydx(*)

Average marginal effects                        Number of obs     =        485
Model VCE    : OIM

Expression   : Linear prediction, predict()
dy/dx w.r.t. : Revenue RandD ROA CVCDeals InvestmentStage 2.Industry 3.Industry 4.Industry 5.Industry 6.Industry 7.Industry 2011.Year 2012.Year
               2013.Year 2014.Year 2015.Year 2016.Year 2017.Year

---------------------------------------------------------------------------------
                |            Delta-method
                |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
        Revenue |   .0021823   .0010251     2.13   0.033     .0001731    .0041915
          RandD |   .0045523   .0017063     2.67   0.008      .001208    .0078967
            ROA |  -.1024272   .5633483    -0.18   0.856     -1.20657    1.001715
       CVCDeals |   .0056405   .0042194     1.34   0.181    -.0026293    .0139103
InvestmentStage |   .0085389   .0943034     0.09   0.928    -.1762924    .1933702
                |
       Industry |
             2  |  -.7948941   .5029193    -1.58   0.114    -1.780598    .1908096
             3  |  -.1072463   .5006072    -0.21   0.830    -1.088418    .8739257
             4  |  -1.631532   .4985119    -3.27   0.001    -2.608597   -.6544667
             5  |  -.2224191   .7265788    -0.31   0.760    -1.646487    1.201649
             6  |  -.7628642   .6077591    -1.26   0.209     -1.95405    .4283218
             7  |  -.2909924   .8854289    -0.33   0.742    -2.026401    1.444416
                |
           Year |
          2011  |  -.0415641   .0717578    -0.58   0.562    -.1822067    .0990785
          2012  |  -.0477043   .0709135    -0.67   0.501    -.1866922    .0912836
          2013  |  -.3043772   .0768562    -3.96   0.000    -.4550125   -.1537418
          2014  |  -.4286997   .0780602    -5.49   0.000    -.5816949   -.2757045
          2015  |  -.5881658   .0835155    -7.04   0.000    -.7518532   -.4244785
          2016  |  -1.086586   .0935873   -11.61   0.000    -1.270014   -.9031582
          2017  |  -2.294929   .1353113   -16.96   0.000    -2.560134   -2.029724
---------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

Many thanks for your patience and your support

Best,
Ben

[Ben Koch]

Dear Statalist users,

to follow up on my last question, I am still not sure whether I am able to use the simple margin command for a negative binomial regression model. Currently, I am trying to use the IRR coefficients in order to interpret by coefficients. What exactly is the difference between the margins and IRR coefficient?
I would be also very grateful for any answers concerning my previous question..

I appreciate all your support!

Best,
Marko