Quantcast

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

classic Classic list List threaded Threaded
3 messages Options
Reply | Threaded
Open this post in threaded view
|  
Report Content as Inappropriate

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

Paul GERRANS
Hello Statalisters,
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. 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?
Appreciate any advice, thanks
Paul

________________________________
This e-mail is confidential. If you are not the intended recipient you must not disclose or use the information contained within. If you have received it in error please return it to the sender via reply e-mail and delete any record of it from your system. The information contained within is not the opinion of Edith Cowan University in general and the University accepts no liability for the accuracy of the information provided.

CRICOS IPC 00279B

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
Reply | Threaded
Open this post in threaded view
|  
Report Content as Inappropriate

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

Johannes Geyer
> 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
>
> ________________________________
> This e-mail is confidential. If you are not the intended recipient
> you must not disclose or use the information contained within. If
> you have received it in error please return it to the sender via
> reply e-mail and delete any record of it from your system. The
> information contained within is not the opinion of Edith Cowan
> University in general and the University accepts no liability for
> the accuracy of the information provided.
>
> CRICOS IPC 00279B
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/


*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
Reply | Threaded
Open this post in threaded view
|  
Report Content as Inappropriate

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

Paul GERRANS
Thanks very much Johannes
Paul

-----Original Message-----
From: [hidden email] [mailto:[hidden email]] On Behalf Of Johannes Geyer
Sent: Wednesday, 23 June 2010 4:17 PM
To: [hidden email]
Subject: Antwort: st: Interpreting marginal effects with a transformed independent variable in a logit using margins

> 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
>
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/


*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/

This e-mail is confidential. If you are not the intended recipient you must not disclose or use the information contained within. If you have received it in error please return it to the sender via reply e-mail and delete any record of it from your system. The information contained within is not the opinion of Edith Cowan University in general and the University accepts no liability for the accuracy of the information provided.

CRICOS IPC 00279B

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
Loading...