How to interpret coefficients of xtpoisson?

[Lars Pete]

Dear all,

How to interpret the coefficient for atet_T1#c.intensity? I'd appreciate any feedback.

. xtpoisson yvar atet_T1##c.intensity i.rural `controls' i.year, fe vce(robust) 
note: 51 groups (505 obs) dropped because of all zero outcomes

Iteration 0:  Log pseudolikelihood = -68040.321  
Iteration 1:  Log pseudolikelihood = -61778.706  
Iteration 2:  Log pseudolikelihood = -61776.723  
Iteration 3:  Log pseudolikelihood = -61776.723  

Conditional fixed-effects Poisson regression         Number of obs    = 23,358
Group variable: countyfips                           Number of groups =  2,338

                                                     Obs per group:
                                                                  min =      5
                                                                  avg =   10.0
                                                                  max =     10

                                                     Wald chi2(12)    = 999.45
Log pseudolikelihood = -61776.723                    Prob > chi2      = 0.0000

                                    (Std. err. adjusted for clustering on countyfips)
-------------------------------------------------------------------------------------
                    |               Robust
               yvar | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
--------------------+----------------------------------------------------------------
          1.atet_T1 |  -.0123125   .0059774    -2.06   0.039    -.0240281   -.0005969
          intensity |    .007263   .0058077     1.25   0.211    -.0041199     .018646
                    |
atet_T1#c.intensity |
                 1  |   .0029754   .0017724     1.68   0.093    -.0004985    .0064493
                    |
            1.rural |          0  (omitted)
                    |
               year |
              2011  |   .0116554   .0018309     6.37   0.000     .0080669    .0152438
              2012  |   .0273192   .0027106    10.08   0.000     .0220065     .032632
              2013  |   .0441604   .0030787    14.34   0.000     .0381262    .0501945
              2014  |   .0619121   .0031232    19.82   0.000     .0557908    .0680335
              2015  |   .0759157    .003672    20.67   0.000     .0687187    .0831127
              2016  |   .0917255    .004615    19.88   0.000     .0826802    .1007707
              2017  |   .1047201   .0053361    19.62   0.000     .0942614    .1151787
              2018  |   .1054591   .0058782    17.94   0.000      .093938    .1169802
              2019  |   .1256125   .0062935    19.96   0.000     .1132774    .1379476
-------------------------------------------------------------------------------------

[Carlo Lazzaro]

Lars:
assuming that your model specifcation is correct, I would say that you can get rid of interaction, as it seems to be led by -intensity- that, in turn, does not reach statistical significance either.

[Erik Ruzek]

I would use margins to help with the interpretation of this interaction. First is the linear prediction of the two values of atet_TQ at representative values of intensity (should get two slopes in the plot)

xtpoisson yvar i.atet_T1##c.intensity i.rural `controls' i.year, fe vce(robust) 
margins atet_T1, at(intensity=(0(1)10)) // replace the numbers in parentheses with relevant values of intensity
marginsplot

Or if you wanted the marginal effect of atet_T1 (predicted difference in yvar between those having 1 vs. 0) at representative values of intensity, you can do:

margins , dydx(atet_T1) at(intensity=(0(1)10))
marginsplot

[Lars Pete]

Thanks Carlo. My question was regarding this interpretation of the coefficient since in other yvars I am getting significant results.

[Lars Pete]

Thanks Erik Ruzek .
Margins is certainly useful in postestimation, and I am getting significant results in other models, but I am not sure whether I should show margins results or actual xtpoisson results in the paper.

In case I do the latter, how do I explain the coefficient .0029754? It is not simply 0.02 % increase in Y as X increases holding other thins constant, but there is more to that since this is poisson. For xtpoisson, the Stata documentation mentions IRR and equal-correlation population-averaged model. I am not specifying either of the two here. Is the interpretation here: IRR = e^0.002?

[Erik Ruzek]

Many, although not all, exponentiate the poisson model coefficients to get IRRs (the expected additional counts/number of yvar for a 1-unit increase in the predictor). Use the option irr in your xtpoission call to get them in the regression output. If you do that, then you could interpret the interaction as the amount by which intensity modifies the IRR of atet_TI. The very small coefficient suggest that it has almost no effect on the IRR of atet_T1. IMO, with generalized linear models, unless your audience is steeped in them very deeply (or you have null results), it is almost always advised to show marginsplots in addition to the regression table output.

[Joao Santos Silva]

Dear Lars Pete and Erik Ruzek,

Following up on #3 and #5, I would strongly advise against using margins after xtpoisson with FE as its results are meaningless; see here.

Best wishes,

Joao

[Lars Pete]

Thanks for the suggestions Erik Ruzek .
Thanks for the comments Joao Santos Silva. I just read these slides santos_uksug16.pdf (repec.org). They're precise, crisp and very helpful along with this thread xtpoisson with fixed effects - Statalist.