Coefficient interpretation from a GLM regression family(gamma) link(log)

[Rodrigo Badilla]

Hi all,

I am trying to explain some coefficients from a GLM regression with family(gamma) link(log), I did read that for coefficients I need transform to a exp(b1). But I am more interesting in dy/dx results. I need to transforms this results too?, some example of my results are:

. sysuse auto
(1978 Automobile Data)

.
. glm mpg weight length displacement , family(gamma) link(log)

Iteration 0:   log likelihood =  -298.5288  
Iteration 1:   log likelihood = -298.52698  
Iteration 2:   log likelihood = -298.52698  

Generalized linear models                          No. of obs      =        74
Optimization     : ML                              Residual df     =        70
                                                   Scale parameter =  .0214501
Deviance         =  1.422701405                    (1/df) Deviance =  .0203243
Pearson          =  1.501510196                    (1/df) Pearson  =  .0214501

Variance function: V(u) = u^2                      [Gamma]
Link function    : g(u) = ln(u)                    [Log]

                                                   AIC             =  8.176405
Log likelihood   = -298.5269823                    BIC             = -299.8619

------------------------------------------------------------------------------
             |                 OIM
         mpg |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |  -.0001956   .0000818    -2.39   0.017    -.0003559   -.0000352
      length |  -.0033186    .002328    -1.43   0.154    -.0078814    .0012441
displacement |   5.40e-06   .0004179     0.01   0.990    -.0008136    .0008245
       _cons |    4.24724   .2591944    16.39   0.000     3.739228    4.755251
------------------------------------------------------------------------------

.
. margins, dydx(*)

Average marginal effects                          Number of obs   =         74
Model VCE    : OIM

Expression   : Predicted mean mpg, predict()
dy/dx w.r.t. : weight length displacement

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |  -.0041641   .0017465    -2.38   0.017    -.0075871    -.000741
      length |  -.0706644   .0496204    -1.42   0.154    -.1679186    .0265898
displacement |    .000115   .0088983     0.01   0.990    -.0173252    .0175553
------------------------------------------------------------------------------

Any comments I will grateful
Thanks In advance

[John Mullahy]

Rodrigo: If your interest is in the marginal effects of the x's on E[y|x] then your margins, dydx(*) command should suffice. No need for any transformations/retransformations.

[Rodrigo Badilla]

Thanks John Mullahy for you reply, just 2 questions:

1) marginal effects have the same units that original variables?
2) just for curiosity if I want use regression coefficients I need to transform: exp(b1), the units are the same that original variables?

Thanks in advance

[Dimitriy V. Masterov]

You might find this answer useful. -margins- can do all three, while -eform- option with -glm- or -nlcom- can do the third.

[Rodrigo Badilla]

Thanks Dimitriy your explanation in Cross validated is great!