Box-Cox vs Yeo-Johnson Both Box-Cox and Yeo-Johnson transform non-normal distribution into a normal distribution. However, Box-Cox requires all samples to be positive, while Yeo-Johnson has no restrictions. 
To me, it seems that Yeo-Johnson is superior to Box-Cox. Is there any reason why I shouldn't always blindly use Yeo-Johnson over Box-cox ? (ex: back-transform, interpretability, computation efficiency...)
 A: Interpretability is a major issue.
The power parameter is different for positive and negative values; and the transformation therefore has a different interpretation for positive and negative values.
When you have both, the transformation over the whole range seems somewhat arbitrary and it is very tricky to explain - especially to a lay audience.
A: I have found transformations like the cube root
$$ \text{sign}(y)\ |y|^{1/3}$$ and the so-called neglog
$$\text{sign}(y)\ \ln(1 + |y|)$$ and the inverse hyperbolic sine
$$\text{asinh}(y)$$
helpful for responses that can be negative, zero, or positive and that are skewed and/or have very long tails.
Their advantages include


*pulling in the tails relative to zero


*working smoothly around 0


*preserving the sign of the response (which usually has substantive or scientific meaning: consider profit/loss or increase/decrease)


*having derivatives that are easy to work with


*having exact or approximate limiting behaviour as usually desired, in particular that for $y \gg 0$ the second is close to $\ln y$.
In these cases there is no question of choosing a different power for positive and negative values, and any analyst should want to see a very strong justification for that.
The practical test of a transformation is often just that it aids visualization. It's not essential that coefficients from regressions are easy to interpret. If the cube root of $y$ changes linearly with predictors, that is what you have found. The coefficients don't need chit-chat; they are the gradients in that space (which you should be using for visualization).
Despite deeply impressive work on estimating a transformation, it is not often that I choose a transformation formally. Logarithms, reciprocals and square roots are often obvious candidates on a variety of grounds. Try out candidates and see if they help.
