# Table 3 Transformations applied to the covariates

Name Equation
1) Untransformed X* = X
2) Normalize $${X}^{*} = \left(X-\overline{X}\right)/{X}_{\sigma }$$
3) Reciprocal X* = 1/X
4) Log Base 10 $${X}^{*} = \mathsf{l}\mathsf{o}{\mathsf{g}}_{\mathsf{10}}X$$
5) Natural Log X* = loge X
6) Inverse Hyperbolic Sine (IHS)a X* = loge(X + (X 2 + 1)0.5
7) Square X* = X 2
8) Square Root X* = X 0.5
9) Cube Root X* = X 1/3
10) BoxCox Power Transformation X* = X λ
11) Absolute Normal $${X}^{*} = \left(X-\overline{X}\right)/{X}_{\sigma }$$
1. Where X is a vector of values for a given variable, X * is the resulting transformed vector, $$\overline{X}$$ is the mean of X, X σ is the standard deviation of X , and λ is the optimal univariate lambda for the BoxCox transformation calculated form the profile likelihood function in a precursor step.
2. aIf the minimum value in the original data was zero, IHS was applied to the unadjusted values. If the minimum value was negative IHS was applied to the rescaled values.