Interpretation cube root

[Barbara Heerkens]

Hi all,

Working on my regressions, a kind person on this forum hinted me the use of cube roots for my model.
I used a cube root for my dependent variable and it really improved my output.
However, I am a bit stuck with the interpretation now...
I have seen on the internet that it can differ a lot per result how you should interpret your coefficients with the use of cube root.
Is there anyone who can tell me how I should these coefficients:

Cube root(Y) = -0.127 X1 + 0.226 X2

Thank you so much!

[Nick Cox]

I can't see that there's an interpretation that differs from the algebra made verbal. There is no neat formulation such as the logarithm offers.

Your coefficients are rates of change of the cube root of the response with respect to each predictor. If you want to translate that into the effects of the changes in the response, then the corresponding rates of change will themselves vary with each predictor.

Best to make this graphical rather than verbal, but much depends on what you want.

Some times when cube root works well logarithm will work well too. If you didn't use a logarithmic scale for the response because there are zeros or negative values in the response, then consider use of a logarithmic link rather than a logarithmic transform.

[Barbara Heerkens]

Thank you Nick!
I used cube root, since Y stands for leverage and there are multiple firms with a value of 0, resulting in missing values for ln(Y).
So I guess I am stuck with the cube root...
Thanks for the tip on making in graphical. I am a real beginner in terms of graphical options in Stata en overflown by the options.
What graph would you recommend when I simply want to show the relationship between Y (leverage) and X (an interaction term).
I tried a twoway graph scatter and line, but it looks horrible, as this.

[Nick Cox]

I've already addressed the problem of zeros. Otherwise see marginsplot

[Barbara Heerkens]

Oh you meant that I should use the logarithmic link, sorry I misread it!!
Thanks for your help!
Again, internet is driving me crazy. So can you maybe help me with how I turn my original regression with the cube root into a regression with a link log?
I am doing a panel data regression, with random effects and it looks like this:

xtreg cuberoot_leverage post##connected ln_size top30 ln_profitability ln_mtb_ratio i.sector i.year, re (cluster id)

Thank you so much.

[Nick Cox]

That doesn't bear much resemblance to the report in #1. I don't know how you'd combine log link and random effects. There may be a simple answer but (sorry) your question is now outside my expertise.

[Barbara Heerkens]

Too bad..
Thank you for your answer Nick!

[Barbara Heerkens]

May I ask one last question regarding cube roots?
Is it possible to apply a cube root to transform the dependent variable, when the independent variable of interest is an interaction term consisting of two dummy variables.
The interaction term will always be 1 or 0. So the increase in X will always be 1 or 0.
Thank you!