Antwort: st: Interpreting marginal effects with a transformed independent variable in a logit using margins

[Johannes Geyer <JGeyer@diw.de>]

> I have a logit regression with wealth as an independent variable, 
> which enters the regression in natural log form.  I then estimate 
> the marginal effect at means after the logit
> <margins, dydx(*) atmeans>
> My question relates to the interpretation of the marginal effect. In
> the output it indicates the mean value of wealth is 8.9814 (in its 
> natural log form) whereas the mean of wealth is $24873 in its 
> original form. I appreciate that by taking the log I have changed 
> the distribution and hence the mean values won?t directly translate.

If you exponentiate the mean of the log-transformed variable you get the 
geometric mean.

> But my question is how best to report the marginal effect?  If the 
> marginal effect is 0.03 for the transformed variable can I talk in 
> terms of the original level terms? Can I say the probability 
> increases by 0.03 if the wealth increases from $7954 to $21622 which
> is a unit change in the transformed variable (8.9814 to 9.9814) .
> Equivalently would it be okay to estimate the marginal effect at 10.
> 1215 (which is the mean level of the untransformed variable) and 
> report the marginal effect as the change in probability for a unit 
> change in the log of wealth, which would be 10.1215 to 11.1215 or 
> $42738 change in untransformed terms?

I guess there is no "best" method to report log-transformed effects in 
your model. But 
I agree that the default that you get is hard to interpret. You could 
calculate the 
marginal effect of a 1 or - if the effect is "too" low - a 10 percent 
increase in 
wealth from the mean. From my experience, people find this a lot easier to 
understand 
than an one-unit log increase that is equivalent to some large number. 

Or what you could also do is to plot the effect over the whole range of 
wealth at some 
specified values of the other x-variables:

twoway (function y = invlogit(Constant + B_1 * mean(X) + B_2 * 
log(wealth))

Hope this helps,

Johannes







> Appreciate any advice, thanks
> Paul
> 
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