stata - marginal effects options, margins versus irr -

i estimating poisson regression , want estimate economic significance of coefficients (marginal effects).

i have 3 methods have been suggested me:

1. margins, dydx(_all)
2. margins, dydx(_all) atmeans
3. poisson, irr

i wondering method best use.

marginal effect @ mean (#2) bad idea since mean may correspond unrepresentative, nonsensical value, particularly if x contains categorical variables. care additive effect half female , 10 percent pregnant? not. me more commonly used when computations expensive. can use at() option pick more suitable values if want go route.

average marginal effect (#1) gives average additive effect on expected count.

the irr option (#3) gives multiplicative effect on mean.

here's simple example doctors data:

. use http://www.stata-press.com/data/r13/dollhill3, clear (doll , hill (1966))  . bys smokes: sum deaths   ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ -> smokes = 0      variable |       obs        mean    std. dev.       min        max -------------+--------------------------------------------------------       deaths |         5        20.2    12.61745          2         31  ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ -> smokes = 1      variable |       obs        mean    std. dev.       min        max -------------+--------------------------------------------------------       deaths |         5         126    70.52659         32        206 

as can see, average number of deaths groups of smokers 126. non-smokers, it's 20.2.

irr:

. poisson deaths i.smokes, irr  iteration 0:   log likelihood =  -136.6749   iteration 1:   log likelihood = -136.56351   iteration 2:   log likelihood = -136.56346   iteration 3:   log likelihood = -136.56346    poisson regression                                number of obs   =         10                                                   lr chi2(1)      =     426.21                                                   prob > chi2     =     0.0000 log likelihood = -136.56346                       pseudo r2       =     0.6094  ------------------------------------------------------------------------------       deaths |        irr   std. err.      z    p>|z|     [95% conf. interval] -------------+----------------------------------------------------------------     1.smokes |   6.237624     .66857    17.08   0.000     5.055737    7.695802        _cons |       20.2   2.009975    30.21   0.000     16.62087    24.54986 ------------------------------------------------------------------------------ 

the number of deaths smokers 6.237624*20.2=126.

now calculated additive effect:

. margins, dydx(smokes)  conditional marginal effects                      number of obs   =         10 model vce    : oim  expression   : predicted number of events, predict() dy/dx w.r.t. : 1.smokes  ------------------------------------------------------------------------------              |            delta-method              |      dy/dx   std. err.      z    p>|z|     [95% conf. interval] -------------+----------------------------------------------------------------     1.smokes |      105.8   5.407402    19.57   0.000     95.20169    116.3983 ------------------------------------------------------------------------------ note: dy/dx factor levels discrete change base level. 

this says smokers should have 105.8 more deaths non-smokers. 20.2+105.8=126.

in simple model, margins, dydx(smokes) atmeans give same answer. can see why?