Conditional marginal effects with arcsinh-linear

[Giordana Sabella]

Hello! I have a specification arcsinh-linear with dummy variable as regressor (triple interaction between 3 categorical variable). How can I compute conditional marginal effects: margins HH_type#Grid_type_40, dydx(SPEI6_class) or margins HH_type#Grid_type_40, eydx(SPEI6_class) or margins HH_type#Grid_type_40, eydx(SPEI6_class), expression(.5*(exp(predict(xb)) + exp(-1*predict(xb)))) dydx(SPEI6_class) and how to interpret the coefficients? Thank you very much

[Joao Santos Silva]

Dear Giordana Sabella,

I cannot help you with that, but I suggest you do not use the arcsinh transformation for the motives clearly explained by John Mullahy in the following paper with Ed Norton

"Why Transform Y? The Pitfalls of Transformed Regressions with a Mass at Zero." Oxford Bulletin of Economics and Statistics (2023).

Best wishes,

Joao

[Nick Cox]

A tiny piece of pedantry (if you like) or correctness (otherwise): The terminology or notation arcsinh (or arccosh or arctanh) is common but it is ill-founded, and strictly incorrect. It grows out of a presumption that inverse hyperbolic functions are like inverse trigonometric functions such as arcsine, arccosine or arctangent which all have direct interpretations as returning the arc or angle corresponding to any particular argument. Rather, if inverse hyperbolic functions have geometric interpretations it is as returning areas, not arcs. The alphabetic accident that the words arc and area start the same way may contribute to the minor mischief here.

Sometimes I communicate this arcanum to authors if I see this in their drafts, and sometimes they correct it!