Dear Statalist,

I am trying to obtain average marginal effects from a population-averaged negative binomial regression.

I ran the following:

Code:
. xtgee cnrparticipants ///
> sqrt_cnrdeaths ///
> pulparticipants_lagged ///
> pulpop_pcent ///
> pulpop_pcent_sq ///
> popchange ///
> popchange_squared ///
> unemployment_ratio ///
> cnrworker ///
> hbclaimants ///
> cnrdegree ///
> cnrparticipants_lagged ///
> electionyear_a ///
> , family(nbinomial 1) exposure(cnrpop) vce(robust) ///
> corr(ind)

Iteration 1: tolerance = 7.528e-07

GEE population-averaged model                   Number of obs     =      1,390
Group variable:               settlementid      Number of groups  =        139
Link:                                  log      Obs per group:
Family:             negative binomial(k=1)                    min =         10
Correlation:                   independent                    avg =       10.0
                                                              max =         10
                                                Wald chi2(12)     =     262.93
Scale parameter:                         1      Prob > chi2       =     0.0000

Pearson chi2(1390):               51831.07      Deviance          =    7213.68
Dispersion (Pearson):             37.28854      Dispersion        =   5.189696

                                     (Std. Err. adjusted for clustering on settlementid)
----------------------------------------------------------------------------------------
                       |             Semirobust
       cnrparticipants |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
        sqrt_cnrdeaths |  -.1507375   .0740523    -2.04   0.042    -.2958774   -.0055976
pulparticipants_lagged |   .0125712    .003579     3.51   0.000     .0055564    .0195859
          pulpop_pcent |   -.076741    .039356    -1.95   0.051    -.1538773    .0003954
       pulpop_pcent_sq |   .0004652   .0004765     0.98   0.329    -.0004687    .0013991
             popchange |  -.1993546   .4461408    -0.45   0.655    -1.073775    .6750654
     popchange_squared |  -.0681788   .1272669    -0.54   0.592    -.3176174    .1812598
    unemployment_ratio |   1.550292   .4837341     3.20   0.001     .6021904    2.498393
             cnrworker |   .0892763   .0353052     2.53   0.011     .0200794    .1584731
           hbclaimants |  -.0436729    .022623    -1.93   0.054    -.0880132    .0006674
             cnrdegree |  -.0225913   .0425565    -0.53   0.596    -.1060004    .0608179
cnrparticipants_lagged |   .0533955   .0115392     4.63   0.000      .030779     .076012
        electionyear_a |  -.1913063   .2326139    -0.82   0.411    -.6472212    .2646085
                 _cons |  -5.327789   1.523732    -3.50   0.000    -8.314249   -2.341329
            ln(cnrpop) |          1  (exposure)
----------------------------------------------------------------------------------------

. 
. margins, dydx(*) post

Average marginal effects                        Number of obs     =      1,390
Model VCE    : Semirobust

Expression   : Exponentiated linear prediction considering offset, predict()
dy/dx w.r.t. : sqrt_cnrdeaths pulparticipants_lagged pulpop_pcent pulpop_pcent_sq popchange popchange_squared unemployment_ratio
               cnrworker hbclaimants cnrdegree cnrparticipants_lagged electionyear_a

----------------------------------------------------------------------------------------
                       |            Delta-method
                       |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
        sqrt_cnrdeaths |  -2501.737   3338.087    -0.75   0.454    -9044.267    4040.793
pulparticipants_lagged |   208.6391   229.0139     0.91   0.362    -240.2199    657.4981
          pulpop_pcent |  -1273.642   1640.604    -0.78   0.438    -4489.167    1941.883
       pulpop_pcent_sq |   7.720792   13.53815     0.57   0.568     -18.8135    34.25509
             popchange |  -3308.617   8823.409    -0.37   0.708    -20602.18    13984.95
     popchange_squared |  -1131.539   2667.132    -0.42   0.671    -6359.022    4095.944
    unemployment_ratio |   25729.64   25755.41     1.00   0.318    -24750.03    76209.31
             cnrworker |   1481.686   1602.212     0.92   0.355    -1658.592    4621.964
           hbclaimants |  -724.8237   910.6557    -0.80   0.426    -2509.676    1060.029
             cnrdegree |   -374.939   832.4995    -0.45   0.652    -2006.608     1256.73
cnrparticipants_lagged |   886.1862   1084.372     0.82   0.414    -1239.145    3011.517
        electionyear_a |  -3175.043   5522.194    -0.57   0.565    -13998.34    7648.259
----------------------------------------------------------------------------------------
As you can see, the p-values of the results obtained from the regression, and from the margins command, are very different. Significant results in the regression are insignificant in the results produced by the margins command.

My question is, does the difference in p-values indicate that I am doing something wrong, and if so, what corrections should I make?

Thank you for any and all help provided.

Best wishes,
Adam