The `bestNormalize`

R package was designed to help find a
normalizing transformation for a vector. There are many techniques that
have been developed in this aim, however each has been subject to their
own strengths/weaknesses, and it is unclear on how to decide which will
work best until the data is observed. This package will look at a range
of possible transformations and return the best one, i.e. the one that
makes it look the *most* normal.

Note that some authors use the term “normalize” differently than in this package. We define “normalize”: to transform a vector of data in such a way that the transformed values follow a Gaussian distribution (or equivalently, a bell curve). This is in contrast to other such techniques designed to transform values to the 0-1 range, or to the -1 to 1 range.

This package also introduces a new adaptation of a normalization
technique, which we call Ordered Quantile normalization
(`orderNorm()`

, or ORQ). ORQ transforms the data based off of
a rank mapping to the normal distribution. This allows us to
*guarantee* normally distributed transformed data (if ties are
not present). The adaptation uses a shifted logit approximation on the
ranks transformation to perform the transformation on newly observed
data outside of the original domain. On new data within the original
domain, the transformation uses linear interpolation of the fitted
transformation.

To evaluate the efficacy of the normalization technique, the
`bestNormalize()`

function implements repeated
cross-validation to estimate the Pearson’s P statistic divided by its
degrees of freedom. This is called the “Normality statistic”, and if it
is close to 1 (or less), then the transformation can be thought of as
working well. The function is designed to select the transformation that
produces the lowest P / df value, when estimated on out-of-sample data
(estimating this on in-sample data will always choose the orderNorm
technique, and is generally not the main goal of these procedures).

You can install the most recent (devel) version of bestNormalize from GitHub with:

```
# install.packages("devtools")
::install_github("petersonR/bestNormalize") devtools
```

Or, you can download it from CRAN with:

`install.packages("bestNormalize")`

In this example, we generate 1000 draws from a gamma distribution, and normalize them:

`library(bestNormalize)`

```
set.seed(100)
<- rgamma(1000, 1, 1)
x
# Estimate best transformation with repeated cross-validation
<- bestNormalize(x, allow_lambert_s = TRUE)
BN_obj #> Warning: package 'lamW' was built under R version 4.0.5
BN_obj#> Best Normalizing transformation with 1000 Observations
#> Estimated Normality Statistics (Pearson P / df, lower => more normal):
#> - arcsinh(x): 3.6204
#> - Box-Cox: 0.96
#> - Center+scale: 6.7851
#> - Exp(x): 50.8513
#> - Lambert's W (type s): 1.0572
#> - Log_b(x+a): 1.908
#> - orderNorm (ORQ): 1.0516
#> - sqrt(x + a): 1.4556
#> - Yeo-Johnson: 1.7385
#> Estimation method: Out-of-sample via CV with 10 folds and 5 repeats
#>
#> Based off these, bestNormalize chose:
#> Standardized Box Cox Transformation with 1000 nonmissing obs.:
#> Estimated statistics:
#> - lambda = 0.2739638
#> - mean (before standardization) = -0.3870903
#> - sd (before standardization) = 1.045498
# Perform transformation
<- predict(BN_obj)
gx
# Perform reverse transformation
<- predict(BN_obj, newdata = gx, inverse = TRUE)
x2
# Prove the transformation is 1:1
all.equal(x2, x)
#> [1] TRUE
```

As of version 1.3, the package supports leave-one-out
cross-validation as well. ORQ normalization works very well when the
size of the test dataset is low relative to the training data set, so it
will often be selected via leave-one-out cross-validation (which is why
we set `allow_orderNorm = FALSE`

here).

```
<- bestNormalize(x, allow_orderNorm = FALSE, allow_lambert_s = TRUE, loo = TRUE))
(BN_loo #> Best Normalizing transformation with 1000 Observations
#> Estimated Normality Statistics (Pearson P / df, lower => more normal):
#> - arcsinh(x): 14.0712
#> - Box-Cox: 0.8077
#> - Center+scale: 26.5181
#> - Exp(x): 451.435
#> - Lambert's W (type s): 1.269
#> - Log_b(x+a): 4.5374
#> - sqrt(x + a): 3.3655
#> - Yeo-Johnson: 5.7997
#> Estimation method: Out-of-sample via leave-one-out CV
#>
#> Based off these, bestNormalize chose:
#> Standardized Box Cox Transformation with 1000 nonmissing obs.:
#> Estimated statistics:
#> - lambda = 0.2739638
#> - mean (before standardization) = -0.3870903
#> - sd (before standardization) = 1.045498
```

It is also possible to visualize these transformations:

`plot(BN_obj, leg_loc = "bottomright")`

For a more in depth tutorial, please consult the package vignette, or the package website.