It's also harder to interpret. What the heck does `log(x + sqrt(x^2 + 1))` mean?
It's a great transformation for data viz or machine learning / statistical modeling, but its not really obvious what an IHS-transformed variable represents.
> It's also harder to interpret. What the heck does `log(x + sqrt(x^2 + 1))` mean?
once you see the shape plotted, i dont think it's much harder than understanding the shape of logistic functions, which have similar formulations, and are used all over the place in ai/ml for activation, etc.
It's not hard to see that it's sigmoidal, sure. But both the logistic function and the logarithm itself have a lot of nice mathematical properties that are useful for qualitatively interpretation. I'm not aware of equivalent nice properties for the inverse hyperbolic sine, other than those that arise from it being a logarithm of something, but it's not a logarithm of anything particularly meaningful.
It's a great transformation for data viz or machine learning / statistical modeling, but its not really obvious what an IHS-transformed variable represents.