How to remove skewness from the population?

Question

Just want to know the ways to remove skewness from the skewed population. I am working on logistic regression (in the insurance domain) for finding out the repurchase propensity of existing users. Income data is right skewed. Will it cause any problem for runing logistic regression? If yes then how to remove it (deletion or any other transformation)?

Answer 1

A flexible framework for this is provided by the Box-Cox transformation, i.e., a power transformation $y \mapsto C(y,\lambda) y^\lambda$ where the parameter $\lambda$ of transformation $\lambda$ is driven by the data (essentially, towards reducing the skewness); $C(y,\lambda)$ is a scaling parameter to make comparison of the goodness of fit provided by the different powers meaningful.

Answer 2

There's no way to remove skewness from the raw data set without chopping off the tail (i.e. deleting all of the observations that make it "skewed"). In regression it is common to transform the data set so to eliminate skewness in the residuals. If the data is non-negative then the $\log$ or $\sqrt{\cdot}$ transform are the default choices.

Using data from the exponential distribution (a skewed distribution) as an example, each of these choices do reduce the skewness, but don't take care of it entirely (see R code):

 x = rexp(1000,rate=4)
 plot(density(x))
 plot(density(log(x)))
 plot(density(sqrt(x)))

In the case of the log-normal (another skewed distibution), the log transform makes it perfectly symmetric (and normally distributed), since that is how the log-normal is defined. You might try playing around with some other transformations if eliminating skew is important for your application.