{"id":2902,"date":"2023-02-05T22:20:58","date_gmt":"2023-02-05T22:20:58","guid":{"rendered":"http:\/\/optimumsportsperformance.com\/blog\/?p=2902"},"modified":"2023-02-07T15:38:10","modified_gmt":"2023-02-07T15:38:10","slug":"bayesian-priors-for-categorical-variables-using-rstanarm","status":"publish","type":"post","link":"https:\/\/optimumsportsperformance.com\/blog\/bayesian-priors-for-categorical-variables-using-rstanarm\/","title":{"rendered":"Bayesian Priors for Categorical Variables using rstanarm"},"content":{"rendered":"

Continuing with more Bayesian data analysis using the {rstanarm<\/strong>} package, today walk through the ways of setting priors on categorical variables.<\/p>\n

NOTE: <\/strong>Priors are a pretty controversial piece in Bayesian statistics and one of the arguments people make against Bayesian data analysis. Thus, I’ll also show what happens when you are overly bullish with your priors\/<\/p>\n

The full code is accessible on my GITHUB page<\/a><\/span><\/strong>.<\/p>\n

Load Packages & Data<\/strong><\/span><\/p>\n

We are going to use the\u00a0mtcars<\/strong> data set from R. The cylinder variable (cyl) is read in as a numeric but it only have three levels (4, 6, 8), therefore, we will convert it to a categorical variable and treat it as such for the analysis.<\/p>\n

We are going to build a model that estimates miles per gallon (mpg) from the number of cylinders a\u00a0 car has. So, we will start by looking at the mean and standard deviation of mpg for each level of cyl.<\/p>\n

\r\n## Bayesian priors for categorical variables using rstanarm\r\n\r\nlibrary(rstanarm)\r\nlibrary(tidyverse)\r\nlibrary(patchwork)\r\n\r\n### Data -----------------------------------------------------------------\r\nd <- mtcars %>%\r\n  select(mpg, cyl, disp) %>%\r\n  mutate(cyl = as.factor(cyl),\r\n         cyl6 = ifelse(cyl == "6", 1, 0),\r\n         cyl8 = ifelse(cyl == "8", 1, 0))\r\n\r\nd %>% \r\n  head()\r\n\r\nd %>%\r\n  group_by(cyl) %>%\r\n  summarize(avg = mean(mpg),\r\n            SD = sd(mpg))\r\n<\/pre>\n
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Fit the model using Ordinary Least Squares regression<\/strong><\/span><\/p>\n
Before constructing our Bayesian model, we fit the model as a basic regression model to see what the output looks like.<\/p>\n
\r\n## Linear regression ------------------------------------------------------\r\nfit_lm <- lm(mpg ~ cyl, data = d)\r\nsummary(fit_lm)\r\n<\/pre>\n
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