knitr::opts_chunk$set( collapse = TRUE, comment = "#>" )

When the response variable is right skewed, many think regression becomes difficult. Skewed data is generally thought of as problematic. However the glm framework provides two options for dealing with right skewed response variables. For the gamma and inverse gaussian distributions, a right skewed response variable is actually helpful.

The critical step is being able to spot a gamma distribution when you see one. Theatrical skewness is $\frac{2}{\sqrt(shape)}$. If shape is small, the gamma distribution is right skewed. If shape increases, the gamma becomes more symmetrical

library(GlmSimulatoR) library(ggplot2) library(dplyr, warn.conflicts = FALSE) library(stats) set.seed(1) # Very right skewed. Skewness 2 gamma_rv <- rgamma(1000, shape = 1, scale = 1) temp <- tibble(gamma = gamma_rv) ggplot(temp, aes(x = gamma)) + geom_histogram(bins = 30) # Hump moves slightly more towards the middle. Skewness 1.154701 gamma_rv <- rgamma(1000, shape = 3, scale = 1) temp <- tibble(gamma = gamma_rv) ggplot(temp, aes(x = gamma)) + geom_histogram(bins = 30) # Nearly gaussian. Very slightly right skewed. Skewness .2 gamma_rv <- rgamma(1000, shape = 100, scale = 1) temp <- tibble(gamma = gamma_rv) ggplot(temp, aes(x = gamma)) + geom_histogram(bins = 30)

```
rm(gamma_rv, temp)
```

To show the generalized linear model can handle skewness, lets make data and train a model and calculate mean squared error.

# Make data set.seed(1) simdata <- simulate_gamma( N = 10000, link = "inverse", weights = c(1, 2, 3), ancillary = .05 ) # Confirm Y ~ gamma ggplot(simdata, aes(x = Y)) + geom_histogram(bins = 30) glm <- glm(Y ~ X1 + X2 + X3, data = simdata, family = Gamma("inverse")) # Mean Squared Error mean((simdata$Y - predict(glm, newdata = simdata, type = "response"))^2)

**Any scripts or data that you put into this service are public.**

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.