Marginal Effects - interpretation with log var

[Meriel Cochrane]

Hello Everyone,

Hoping you may be able to help.

I am running a logit model with multiple independent variables and one binary dependent variable (0,1). I would like to interpret my var accoring to marginal effects at means.

One of my ind var (income) has been transformed into a log and used throughout my previous analysis OLS (this is for coursework purposes - asked to log)

Can I continue using my log income var or should I revert to the raw income var? If I can continue using my log income var, how do I interpret the coefficient in terms of marginal effects at means?

Please see picture attached!

Thanks for your help

Stata commands.docx

[Clyde Schechter]

If you were explicitly asked to log-transform the income variable, then it would make sense to give the marginal effects in terms of the log-transformed income variable. The key to remember is that adding 1 to a logarithm is equivalent to multiplying the untransformed income variable by the base of the logarithm (which you don't tell us in your post: is it 10 or e?)

So you could explain the marginal effect attributed to the log-transformed income variable as the rate of change in outcome probability per a 10-fold (or, if you used natural logarithm for the transformation, e-fold) difference in income (untransformed) when all predictors are at their mean values . But that seems fairly complicated and I would think any non-technical audience would find that strange and confusing. So I think it is better to say that it is the rate of change in outcome probability per unit increase in log income, all predictors at their mean values.

Please read the Forum FAQ, especially #12, for advice on the most effective way to show code, output and data here. Images are discouraged. Yours in #1 is not readable at all. Even when they are readable, they do not support copy/paste of information, and as a way of showing data they also fail to convey important attributes of the data set. Attachment of Microsoft Office documents is also discouraged because they can contain active malware; so many who respond here are reluctant to take the risk of downloading them. It also makes your information inaccessible to those responders who simply do not use Microsoft Office products.

[AnnaK Jacobs]

Dear Clyde,

from your post I understand that there are essentially two options:

1. interpret the coefficient "unitless"

rate of change in outcome probability per unit increase in log income, all predictors at their mean values.

2. Choose a base for the logarithm that gives interpretation some more sense, e.g. base 2 ("doubling of income")

am I correct?

Then, how can I change the base of the logarithm in Stata? From what I know I can divide ln(income) by log(2). However, I was wondering whether I need to transform it before applying logit/probit and margins or can I just divide the estimated marginal effects by log(2)?

Thank you very much!