Interpretation IRR of interaction term - Negative binomial regression model

[Ben Koch]

Dear Statalist,

I am currently struggling with the interpretation of the interactionterm Investm#Stage in my analysis.

After running

xtnbreg Patents Revenue RandD Focus Assets c.investmentment##c.stage i.Industry i.Year, re irr

I got the following output:

Random-effects negative binomial regression     Number of obs     =        472
Group variable: id                              Number of groups  =         70

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

                                                Wald chi2(20)     =     513.89
Log likelihood  = -1990.4528                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------------
        Patents |        IRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------------+----------------------------------------------------------------
           Revenue |   1.001979   .0010452     1.90   0.058     .9999329     1.00403
             RandD |   1.004393   .0015713     2.80   0.005     1.001318    1.007477
             Focus |   1.077438   .0728899     1.10   0.270     .9436427    1.230204
            Assets |   .9516789   .5482813    -0.09   0.931     .3076778     2.94364
           Investm |   1.020654   .0085935     2.43   0.015      1.00395    1.037637
             stage |   1.169925   .1056852     1.74   0.082     .9800871    1.396533
                   |
  c.Investm#c.stage|   .9740871   .0130466    -1.96   0.050     .9488489    .9999965
                   |
          Industry |
                2  |   .4541281   .2296434    -1.56   0.119     .1685555    1.223528
                3  |   .9333449   .4720072    -0.14   0.892     .3463986    2.514827
                4  |     .18199   .0918296    -3.38   0.001     .0676929    .4892736
                5  |   2.698813   2.121375     1.26   0.207     .5782216    12.59654
                6  |   .4562541   .2767226    -1.29   0.196     .1389775    1.497852
                7  |   .7626905   .6887046    -0.30   0.764     .1299328    4.476904
                   |
              Year |
             2011  |   .9554278   .0670738    -0.65   0.516     .8326089    1.096364
             2012  |   .9710882   .0667718    -0.43   0.670     .8486533    1.111187
             2013  |   .7419934   .0566072    -3.91   0.000     .6389417    .8616657
             2014  |   .6401209   .0495466    -5.76   0.000     .5500186    .7449836
             2015  |   .5455575   .0459118    -7.20   0.000     .4626014    .6433896
             2016  |   .3290881   .0308789   -11.84   0.000     .2738056    .3955323
             2017  |   .0985694   .0133412   -17.12   0.000      .075602    .1285141
                   |
             _cons |   10.42205    5.30899     4.60   0.000     3.840177    28.28492
-------------------+----------------------------------------------------------------
             /ln_r |  -.2604066   .1540182                     -.5622767    .0414635
             /ln_s |   .7328332   .2041451                      .3327161     1.13295
-------------------+----------------------------------------------------------------
                 r |   .7707381   .1187077                      .5699101    1.042335
                 s |   2.080968   .4248195                      1.394751    3.104803
------------------------------------------------------------------------------------
LR test vs. pooled: chibar2(01) = 848.68               Prob >= chibar2 = 0.000

The variable stage is value continous variable between 0 and 1 indicating the average investment stage.(The closer to 1, the later the investment stage and vice versa)

Currently, my interpretation looks as follows: My dependent variable, patents, decreases by ~2.6%, with a one unit increase in the average investmentstage.
Is that correct? In case not, does anyone have a suggestion?

Thank you very much.

Best
Ben

[Clyde Schechter]

Currently, my interpretation looks as follows: My dependent variable, patents, decreases by ~2.6%, with a one unit increase in the average investmentstage.

Is that correct?

No. When you use an interaction term you are stipulating that there is no such thing as the rate of change of Patents per unit difference in Investm. Rather, there are infinitely many different rates of change, depending on the value of stage. The rate of change in Patents associated with a unit change in Investm is 1.02 * 0.974^stage. The interaction IRR itself represents the rate at which the rate associated with Investm depends on stage. It is, in contexts like this, generally not of direct interest in its own right but simply as an ingredient needed to calculate the rate of change in Patents conditional on specific values of Investm and stage.

To get a better sense of what your model says, rerun the -xtnbreg- and follow it with:

margins, at(Investm = (list_of_interesting_values_of_Investm) stage = (list_of_interesting_values_of_stage)), predict(iru0)
marginsplot, xdimension(Investm)

By interesting values of a variable I mean a list of numeric values that span the range of observed or realistically possible values of those variables and are closely enough spaced that graphs plotted at those values will look reasonably smooth. The resulting graph will show you the modeled incidence rate of patents (conditional on the random effects being zero) at all combinations of those variables. In particular you will be able to see how the effect of Investm depends on stage.

[Ben Koch]

Hello Clyde,

I really appreciate your extensive answer!

I have tried to follow your suggestion, however I received the following error code.

. margins, at(Investm = (1 5 10 15 20 25 30) stage = (0 0.2 0.4 0.6 0.8 1)), predict (iru0)
invalid 'predict'
r(198);

Any idea why I got this error code?

Thank you very much!
Best
Ben

[Clyde Schechter]

Remove the comma that precedes -predict-.

[Ben Koch]

Unfortunately, I received the following error code:

. margins, at(Investm = (1 5 10 15 20 25 30) stage = (0 0.2 0.4 0.6 0.8 1)) predict (iru0)
Warning: prediction constant over observations.
missing predicted values encountered within the estimation sample

As 0 has a meaning for my variables, I am not able to define my missing values as 0. Is there any workaround?

Thank you very much !
Best
Ben

[Maarten Buis]

For nbreg you don't need margins. You can easily enough interpret the coefficients directly: http://www.maartenbuis.nl/publicatio...eractions.html

[Ben Koch]

For nbreg you don't need margins. You can easily enough interpret the coefficients directly: http://www.maartenbuis.nl/publicatio...eractions.html

Thank your Maarten ! It that also applicable for xtnbreg?

Any idea how i could visualize the interaction effect?

Best
Ben

[Maarten Buis]

it also applies to xtnbreg. The point is the link function, so it work with or without xt in exactly the same way.

[Rutger spijker]

Hi all,

I am doing research to patenting growth and venture capital. One of the models is a fixed effect panel data xtnbreg analysis. Everything seems fine the only concern is that I do net get the PseudoR2 out of the model if I look at the e(). The -eret list- command did not return the e(r2_p).

Browsing the internet didn't bring me further.

I hope someone can help me with my quesiton, also if it does not make sense to look for pseudo R2

best
Rutger

[Weiwen Ng]

Hi all,

I am doing research to patenting growth and venture capital. One of the models is a fixed effect panel data xtnbreg analysis. Everything seems fine the only concern is that I do net get the PseudoR2 out of the model if I look at the e(). The -eret list- command did not return the e(r2_p).

Browsing the internet didn't bring me further.

I hope someone can help me with my quesiton, also if it does not make sense to look for pseudo R2

best
Rutger

This isn't related to the post. You might want to post it as a new question.