Marginal Effects using AME and MEM

[Alexander Huber]

Dear community,

I have a question concerning the interpretation of the marginal effect within a logistic regression. Is the interpretation of the marginal effect the same using both methods AME (average marginal effects) and marginal effects at the means (MEM)? In other words, when I look for example at the variable D_ProdBus (.1695874) using MEM and (.1651408) using AME: Do both numbers represent the predicted probability a change in the independent variable has on the outcome of my bivariate dependent variable? The only difference the predicted probability is based on is the way it is caluclated, right? For MEM, all other covariates are held at their means whilst for AME they´re held at their actual values. I am just confused by the name "average" marginal effects and marginal effects at the means both pointing out to someting being "averaged"...

I know that there is more calculations and differences to these two methods for calculation marginal effects, however I am for now only interested in the interpretation of the numbers. And if both give me the predicted probability change of y given a change in x, this would be enough of an answer for now :-)

Would be great if someone could help.

Thanks and best regards
Alex Huber


- Logistic regression followed by MEM -
------------------------------------------------------------------------------
margins, dydx (D_Age D_ProdBus Q_Patents Q_NetInc) post atmeans level(90)

Conditional marginal effects Number of obs = 98
Model VCE : OIM

Expression : Pr(Q_VC), predict()
dy/dx w.r.t. : D_Age 1.D_ProdBus 1.Q_Patents 1.Q_NetInc
at : D_Age = 8.173469 (mean)
0.D_ProdBus = .255102 (mean)
1.D_ProdBus = .744898 (mean)
0.Q_Patents = .6326531 (mean)
1.Q_Patents = .3673469 (mean)
0.Q_NetInc = .122449 (mean)
1.Q_NetInc = .877551 (mean)

------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [90% Conf. Interval]
-------------+----------------------------------------------------------------
D_Age | -.0008956 .0101539 -0.09 0.930 -.0175973 .0158061
1.D_ProdBus | .1695874 .1016935 1.67 0.095 .0023165 .3368583
1.Q_Patents | .217947 .1028693 2.12 0.034 .0487421 .3871519
1.Q_NetInc | .1867139 .1075301 1.74 0.082 .0098427 .3635851
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.


- Logistic regression followed by AME -
------------------------------------------------------------------------------
margins, dydx (D_Age D_ProdBus Q_Patents Q_NetInc) post level(90)

Average marginal effects Number of obs = 98
Model VCE : OIM

Expression : Pr(Q_VC), predict()
dy/dx w.r.t. : D_Age 1.D_ProdBus 1.Q_Patents 1.Q_NetInc

------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [90% Conf. Interval]
-------------+----------------------------------------------------------------
D_Age | -.0008379 .0095007 -0.09 0.930 -.0164651 .0147893
1.D_ProdBus | .1651408 .101731 1.62 0.105 -.0021918 .3324734
1.Q_Patents | .211453 .0998145 2.12 0.034 .0472727 .3756332
1.Q_NetInc | .1837894 .1106558 1.66 0.097 .0017768 .365802
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

.
end of do-file

[Melissa Garrido]

Hi Alex,

The marginal effect is the treatment effect (change in y) produced when an individual (or other unit of analysis) goes from “no treatment” to “treatment” (if a dichotomous treatment) or experiences a 1 unit change in the treatment variable (if a continuous value) while all other variables are held constant

A marginal effect at the mean (MEM) is calculated by setting the values of all covariates to their means within the sample.

To get the average marginal effect (AME), the marginal effect is first calculated for each individual with their observed levels of covariates. These values are then averaged across all individuals.

Hope this helps!
Melissa

[Alexander Huber]

Hi Melissa,
thanks for your fast reply. What you are saying ist that, in my case, the dependent variable changes by 1651408 (using MEM) when the indepedent variable D_ProdBus changes from 0 to 1 (its a dichotomous variable). My dependent variable is dichotomous as well. So I wonder how that can change by a value it cannot take?
I was told that in case of a logistic regression with a bivariate dependent variable, the marginal effect states the change in predicted probability (in my case 16,51% more likely) following a change from "no treatment" to "treatment" in the independent variable. In other words, it is 16,51% more likely that the dependent variable changes from 0 to 1 given the specific independent variable (D_ProdBus) changes from no treatment (i.e. 0) to treatment (i.e. 1). If this interpretation is correct, would that apply to both AME and MEM calculations having in mind that both are calculated differently?

Thanks,
Alex

[Richard Williams]

Different types of adjusted predictions and marginal effects are overviewed in

http://www3.nd.edu/~rwilliam/stats/Margins01.pdf