Definition: marginal effect or marginal effect

[josef...@gmail.com]

Our discrete Margins implement marginal marginal effects   (marginal is twice)

I just realized that I never understood that these might mean marginal effects and not marginal effects.

simplest model:

y = f(x, beta) + e

with error e E(e) = 0, and (maybe) E(x e) = 0

margins (1)

marginal effect

what is dy/dx?    (effect of a marginal infinitesimal change in x)

or more precise `d E(y|x) / dx`  or maybe `d E(y|x, e) / dx`

"marginal effect" is the change in the value of a function given an infinitesimal change in a argument of the function evaluated at a point (use partial derivative everywhere)

margins (2)

marginal mean: E(y)  where expectation is over the distribution of x

marginal effect   `E (d E(y|x) / dx)`  or  `d E(E(y|x)) / dx` or `d E(E(y|x, e)) / dx`

where the outer expectation E is with respect to the distribution of x and e

"marginal" refers to the marginal distribution in contrast to the conditional or joint distribution.

to make up some names ( I don't know if they are used)

above in part 2 we have marginal marginal effects,

either 

average infinitesimal_change of a prediction (?) or 

infinitesimal_change of average prediction (?) 

(correction: The latter doesn't make sense in this form, since the average prediction is not a function of x anymore.  We keep x_k for the derivative and integrate/average over x_not_k.)

(I find the Stata manual for Margins still confusing, even though they try.)

http://stackoverflow.com/questions/30948997/evaluate-slope-and-error-for-specific-category-for-statsmodels-ols-fit

Topic: "Modern Econometrics" that imported some terms from statistics that "shadow" existing names and defintions. 

which is which after `from pylab_and_everything import *`?

Josef

[josef...@gmail.com]

On Sat, Jun 20, 2015 at 4:02 PM, <josef...@gmail.com> wrote:

Our discrete Margins implement marginal marginal effects   (marginal is twice)

I just realized that I never understood that these might mean marginal effects and not marginal effects.

simplest model:

y = f(x, beta) + e

with error e E(e) = 0, and (maybe) E(x e) = 0

margins (1)

marginal effect

what is dy/dx?    (effect of a marginal infinitesimal change in x)

or more precise `d E(y|x) / dx`  or maybe `d E(y|x, e) / dx`

"marginal effect" is the change in the value of a function given an infinitesimal change in a argument of the function evaluated at a point (use partial derivative everywhere)

margins (2)

marginal mean: E(y)  where expectation is over the distribution of x

marginal effect   `E (d E(y|x) / dx)`  or  `d E(E(y|x)) / dx` or `d E(E(y|x, e)) / dx`

where the outer expectation E is with respect to the distribution of x and e

"marginal" refers to the marginal distribution in contrast to the conditional or joint distribution.

to make up some names ( I don't know if they are used)

above in part 2 we have marginal marginal effects,

either 

average infinitesimal_change of a prediction (?) or 

infinitesimal_change of average prediction (?) 

(correction: The latter doesn't make sense in this form, since the average prediction is not a function of x anymore.  We keep x_k for the derivative and integrate/average over x_not_k.)

similar to this part: I misinterpreted, a few weeks or months ago, that "average risk ratio" is that "ratio of average risk" and not the "average of the risk ratios". 

Conclusion:

I think now that we should rename `Margins` to `Effects` or `AverageEffects` in analogy to treatment effects, and drop the name that Stata uses.

Averaging could be over a singleton set, so it still includes conditional or partially Effects.

Josef

https://en.wikipedia.org/wiki/True_name