GLM Model With Gaussian Family and Log Link Interpretation

[Ash Summerfield]

Hi,

Am I right to assume that a GLM model with Gaussian family and log link is essentially the same as running an OLS model with a logged dependent variable?
Also, the GLM model I am running uses dummy independent variables. So would it be correct to interpret the following way; a change in x1 from 0 to 1 would produce a [(e^B1)-1] change in y, where B1 is the coefficient on the x1 independent variable?

Thanks,

Ash

[Maarten Buis]

Am I right to assume that a GLM model with Gaussian family and log link is essentially the same as running an OLS model with a logged dependent variable?

Close, but not quite. In a linear regression model with the log transformed variable you model \(\mathrm{E}(\ln(y))\), while with a GLM with the log link function you model \(\ln(\mathrm{E}(y))\). Since the logarithm is a non-linear transformation the two are not equal. For more see: http://blog.stata.com/2011/08/22/ . For even more references see the comments to that post.

Also, the GLM model I am running uses dummy independent variables. So would it be correct to interpret the following way; a change in x1 from 0 to 1 would produce a [(e^B1)-1] change in y, where B1 is the coefficient on the x1 independent variable?

That is correct, you can let Stata display \(e^b\) by adding the eform option

[Ash Summerfield]

Thank you for your reply, Maarten. It was very helpful!