knitr::opts_chunk$set( collapse = TRUE, comment = "#>" )  # Introduction When the response variable is right skewed, many think regression becomes difficult. Skewed data is generally thought of as problematic. However the glm framework provides two options for dealing with right skewed response variables. For the gamma and inverse gaussian distributions, a right skewed response variable is actually helpful. # Different shapes of a gamma distribution The critical step is being able to spot a gamma distribution when you see one. Theatrical skewness is$\frac{2}{\sqrt(shape)}$. If shape is small, the gamma distribution is right skewed. If shape increases, the gamma becomes more symmetrical library(GlmSimulatoR) library(ggplot2) library(dplyr, warn.conflicts = FALSE) library(stats) set.seed(1) # Very right skewed. Skewness 2 gamma_rv <- rgamma(1000, shape = 1, scale = 1) temp <- tibble(gamma = gamma_rv) ggplot(temp, aes(x = gamma)) + geom_histogram(bins = 30) # Hump moves slightly more towards the middle. Skewness 1.154701 gamma_rv <- rgamma(1000, shape = 3, scale = 1) temp <- tibble(gamma = gamma_rv) ggplot(temp, aes(x = gamma)) + geom_histogram(bins = 30) # Nearly gaussian. Very slightly right skewed. Skewness .2 gamma_rv <- rgamma(1000, shape = 100, scale = 1) temp <- tibble(gamma = gamma_rv) ggplot(temp, aes(x = gamma)) + geom_histogram(bins = 30)  rm(gamma_rv, temp)  # Building models with very skewed data To show the generalized linear model can handle skewness, lets make data and train a model and calculate mean squared error. # Make data set.seed(1) simdata <- simulate_gamma( N = 10000, link = "inverse", weights = c(1, 2, 3), ancillary = .05 ) # Confirm Y ~ gamma ggplot(simdata, aes(x = Y)) + geom_histogram(bins = 30) glm <- glm(Y ~ X1 + X2 + X3, data = simdata, family = Gamma("inverse")) # Mean Squared Error mean((simdata$Y - predict(glm, newdata = simdata, type = "response"))^2)


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GlmSimulatoR documentation built on May 29, 2024, 10:27 a.m.