Quick illustration of variable transformations

transform_example.r

# This is a quick script to illustrate how to go about transforming variables
# for statistical analysis and the effects of some basic transformations.
# I'm by no means an expert on transformations, so be sure to read up on
# how to best apply the transformations!

# These two packages are for demonstrating the transformations - 
# not necessary for the transformations themselves.
library(reshape2)
library(ggplot2)


# A sample dataset
dat <- data.frame(id = seq(100),
                  a = rnorm(100, mean = 0, sd = 1),   # Standard normal
                  b = rnorm(100, mean = 20, sd = 5),  # Shifted & more variable
                  c = rlnorm(100)                     # Log-normal
)



# Add the transformed variables - if you really have a lot of varitables
# to transform it might be easier to use apply().
# A few different transformations to try:
#  - scale() calculates z-scores based on the standard deviations; good for standardizing normal-ish 
#  - log() is the standard transformation for positive, right-skewed distributions
dat <- transform(dat,
                 a_scale = scale(a),
                 b_scale = scale(b),
                 c_log = log(c)
)



# Just for plotting purposes, I'm going to melt this data so that each
# value gets one row
dat_melt <- melt(dat, id.var = "id")

# And so I can plot the differences, I'm going to add two variables
# indicating the original variable and the transformation status of
# each record.
dat_melt$variable_original <- substr(dat_melt$variable, 1, 1)

dat_melt$transformed <- ifelse(dat_melt$variable %in% c("a", "b", "c"),
                               yes = "Original",
                               no = "Transformed"
)


ggplot(dat_melt, aes(x = value, fill = variable_original)) +
    geom_density(alpha = 0.2) + # Alpha less than 1 makes objects transparent
    facet_grid(variable_original ~ transformed) +
    theme_bw()