---
title: "Customization within bestNormalize"
author: "Ryan A Peterson"
date: "`r Sys.Date()`"
output: 
  rmarkdown::html_vignette:
    toc: true
vignette: >
  %\VignetteIndexEntry{Customization within bestNormalize}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, fig.height = 5, fig.width = 7)
library(bestNormalize)
```

# Custom functions with bestNormalize

This vignette will go over the steps required to implement a custom user-defined function within the `bestNormalize` framework. 

There are 3 steps. 

1) Create transformation function

2) Create predict method for transformation function (that can be applied to new data)

3) Pass through new function and predict method to bestNormalize

## Example: cube-root

## S3 methods 

Here, we start by defining a new function that we'll call `cuberoot_x`, which will take an argument `a` (as does the `sqrt_x` function) which will try to add a constant if it sees any negative numbers in `x`. It will also take the argument `standardize` which will center and scale the transformed data so that it's centered at 0 with SD = 1. 

```{r}
## Define user-function
cuberoot_x <- function(x, a = NULL, standardize = TRUE, ...) {
  stopifnot(is.numeric(x))
  
  min_a <- max(0, -(min(x, na.rm = TRUE)))
  if(!length(a)) 
    a <- min_a
  if(a < min_a) {
    warning("Setting a <  max(0, -(min(x))) can lead to transformation issues",
            "Standardize set to FALSE")
    standardize <- FALSE
  }
  
  
  x.t <- (x + a)^(1/3)
  mu <- mean(x.t, na.rm = TRUE)
  sigma <- sd(x.t, na.rm = TRUE)
  if (standardize) x.t <- (x.t - mu) / sigma
  
  # Get in-sample normality statistic results
  ptest <- nortest::pearson.test(x.t)
  
  val <- list(
    x.t = x.t,
    x = x,
    mean = mu,
    sd = sigma,
    a = a,
    n = length(x.t) - sum(is.na(x)),
    norm_stat = unname(ptest$statistic / ptest$df),
    standardize = standardize
  )
  
  # Assign class
  class(val) <- c('cuberoot_x', class(val))
  val
}

```

Note that we assigned a class to the object this returns of the same name; this is necessary for successful implementation within `bestNormalize`. We'll also need an associated `predict` method that is used to apply the transformation to newly observed data. 
`
```{r}

predict.cuberoot_x <- function(object, newdata = NULL, inverse = FALSE, ...) {
  
  # If no data supplied and not inverse
  if (is.null(newdata) & !inverse)
    newdata <- object$x
  
  # If no data supplied and inverse
  if (is.null(newdata) & inverse)
    newdata <- object$x.t
  
  # Actually performing transformations
  
  # Perform inverse transformation as estimated
  if (inverse) {
    
    # Reverse-standardize
    if (object$standardize) 
      newdata <- newdata * object$sd + object$mean
    
    # Reverse-cube-root (cube)
    newdata <-  newdata^3 - object$a
    
    
    # Otherwise, perform transformation as estimated
  } else if (!inverse) {
    # Take cube root
    newdata <- (newdata + object$a)^(1/3)
    
    # Standardize to mean 0, sd 1
    if (object$standardize) 
      newdata <- (newdata - object$mean) / object$sd
  }
  
  # Return transformed data
  unname(newdata)
}

```

## Optional: print method

This will be printed when bestNormalize selects your custom method or when you print an object returned by your new custom function. 

```{r}
print.cuberoot_x <- function(x, ...) {
  cat(ifelse(x$standardize, "Standardized", "Non-Standardized"),
      'cuberoot(x + a) Transformation with', x$n, 'nonmissing obs.:\n', 
      'Relevant statistics:\n',
      '- a =', x$a, '\n',
      '- mean (before standardization) =', x$mean, '\n',
      '- sd (before standardization) =', x$sd, '\n')
}

```

Note: if you can find a similar transformation in the source code, it's easy to model your code after it. For instance, for `cuberoot_x` and `predict.cuberoot_x`, I used `sqrt_x.R` as a template file. 

## Implementing with bestNormalize

```{r}
# Store custom functions into list
custom_transform <- list(
  cuberoot_x = cuberoot_x,
  predict.cuberoot_x = predict.cuberoot_x,
  print.cuberoot_x = print.cuberoot_x
)

set.seed(123129)
x <- rgamma(100, 1, 1)
(b <- bestNormalize(x = x, new_transforms = custom_transform, standardize = FALSE))
```

Evidently, the cube-rooting was the best normalizing transformation! 

## Sanity check

Is this code actually performing the cube-rooting? 

```{r}
all.equal(x^(1/3), b$chosen_transform$x.t)
all.equal(x^(1/3), predict(b))
```

It does indeed. 

# Using custom normalization statistics

The bestNormalize package can estimate any univariate statistic using its CV framework. A user-defined function can be passed in through the `norm_stat_fn` argument, and this function will then be applied in lieu of the Pearson test statistic divided by its degree of freedom. 

The user-defined function must take an argument `x`, which indicates the data on which a user wants to evaluate the statistic.

Here is an example using Lilliefors (Kolmogorov-Smirnov) normality test statistic: 

```{r}
bestNormalize(x, norm_stat_fn = function(x) nortest::lillie.test(x)$stat)
```

Here is an example using Lilliefors (Kolmogorov-Smirnov) normality test's p-value: 

```{r}
(dont_do_this <- bestNormalize(x, norm_stat_fn = function(x) nortest::lillie.test(x)$p))
```

Note: `bestNormalize` will attempt to minimize this statistic by default, which is definitely not what you want to do when calculating the p-value. This is seen in the example above, as the WORST normalization transformation is chosen. 

In this case, a user is advised to either manually select the best one: 

```{r}
best_transform <- names(which.max(dont_do_this$norm_stats))
(do_this <- dont_do_this$other_transforms[[best_transform]])
```

Or, the user can reverse their defined statistic (in this case by subtracting it from 1): 

```{r}
(do_this <- bestNormalize(x, norm_stat_fn = function(x) 1-nortest::lillie.test(x)$p))
```

