tutorial-scaling.md

This is the start of a tutorial explaining why you should scale your variables. Some of it is still missing though.

Scaling formula

Scaling (or Z-score normalization) follows the formula $$ x' = \frac{x- \bar x}{\sigma} $$ Where x − x̄ centers the variables around zero and where dividing by σ constitutes the normalization of the variables.

The scale function performs a Z-score normalization, which can be seen here:

set.seed(1) # set seed to ensure random number generation is the same
x <- runif(7) # generate random numbers

# Manually scaling
(x - mean(x)) / sd(x)

## [1] -1.01951259 -0.68940037 -0.06788275  0.97047346 -1.21713898  0.94007371
## [7]  1.08338753

#scale using scale
scale(x)

##             [,1]
## [1,] -1.01951259
## [2,] -0.68940037
## [3,] -0.06788275
## [4,]  0.97047346
## [5,] -1.21713898
## [6,]  0.94007371
## [7,]  1.08338753
## attr(,"scaled:center")
## [1] 0.5947772
## attr(,"scaled:scale")
## [1] 0.3229666

class(scale(x))

## [1] "matrix"

note that scale is a class matrix, which might cause problems. If you want scale to return a numeric vector (a list of numbers) use scale(x)[[1]]. Furthermore note that the mean (scale:center) and SD (scaled:scale) is also provided by the scale function, which is useful for going back to the original values.

Will come in the future

1. Why scaling improves model fit (and convergence)
2. Why center (and scaling) improves model interpretability
3. Other ways to scale / normalize

FAQ

How do i include formula in my R markdown?

This is done using LaTeX. You first need to install a LaTeX distribution on your system e.g. using the following install command tinytex::install_tinytex() You also need to set your header to output latex. The header for this script is for example:

---
title: "Tutorial_Scaling"
author: "Kenneth C. Enevoldsen"
date: "10/14/2019"
header-includes:
   - \usepackage{bbm}
output:
    html_document: md_document
---

You then include latex using the double dollarsigns, in the following way: $$ x - \bar x$$