title	output
Bayesian Categorical Data Analysis	github_document

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "man/figures/README-",
  out.width = "100%"
)
options(digits = 2)
set.seed(0)
ggplot2::theme_set(ggplot2::theme_minimal(base_size = 12))

BCDA

This is a set of tools for Bayesian analysis of categorical data, specifically 2×2 contingency tables.

Use:

• beta_binom() for analysis using the Beta-Binomial model
  • print(), tidy(), glance(), and plot() to view the results
  • present_bbfit() if you want a nicely formatted table of summaries to include in a presentation or report
  • update() if you have additional data
• est_multinom() for estimating multinomial cell probabilities

Installation

You can install the development version from GitHub with:

# install.packages("remotes")
remotes::install_github("bearloga/BCDA")

Example

beta_binom() works with a table of the following format:

	Success	Failure
Group 1	n11	n12
Group 2	n21	n22

and uses the Beta-Binomial model to estimate:

	Success	Failure
Group 1	p1	1 - p1
Group 2	p2	1 - p2

which allows inference on the difference (p1 - p2), the risk ratio (RR), and the odds ratio (OR), defined as follows:

• RR = p1 / p2 -- how much more likely success in group 1 is, relative to success in group 2
• OR = (p1/(1-p1)) / (p2/(1-p2)) -- the ratio of the odds -- where p1/(1-p1) is the odds of success in group 1 and p2/(1-p2) is the odds of success in group 2

All examples will use the following fake data:

fake_data <- matrix(c(200, 150, 250, 300), nrow = 2, byrow = TRUE)
colnames(fake_data) <- c('Safe' ,'Dangerous')
rownames(fake_data) <- c('Animals', 'Plants')

knitr::kable(fake_data)

Note that beta_binom() uses the Jeffreys prior by default and that this README was knit with the seed set to 0 at the start for reproducibility.

library(BCDA)

(fit <- beta_binom(fake_data))

The credible intervals above are calculated using quantiles. If we have the coda package installed, we can also obtain the high posterior density intervals:

print(fit, interval_type = "HPD")

plot(fit)

Presentation of the results

The package includes a variety of functions for looking at the results from fitting a beta_binom() model. To aid in functional programming, we implemented the tidy() and glance() verbs:

library(magrittr) # for %>%
fit %>%
  tidy %>%
  knitr::kable()

When knitting R Markdown to HTML, you can use the {gt} package for creating tables:

library(gt)
fit %>%
  tidy %>%
  gt(rowname_col = "term") %>%
  tab_header(md("Results of `beta_binom()`"))

glance() is used to

Construct a single row summary "glance" of a model, fit, or other object

fit %>%
  glance

This is perfectly okay in an interactive data analysis scenario, but not when presenting the results in a report. glance() is actually a special case of the present_bbfit() function which generates all those nicely formatted credible intervals but outputs a Markdown/LaTeX-formatted table by default:

present_bbfit(fit)

The point estimates include credible intervals by default but these can be turned off:

present_bbfit(fit, conf_interval = FALSE, digits = 3)

Since the underlying code uses tidy() to compute the summaries, we can specify a particular credible level and the type of interval we want (e.g. highest posterior density):

present_bbfit(fit, conf_level = 0.89, interval_type = "HPD")

It also supports multiple models, which can be provided as a named or an unnamed list. See the example below.

Updating the posterior

In Bayesian statistics, we can reuse a previously computed posterior as a prior if we have additional data, allowing us to update the parameter estimates as new data becomes available. Suppose we collect 40 observations from 2 groups (20 per group) on the first day of the A/B test, and 10 observations per day for the next 2 weeks. Here we see what happens when we update the posterior with additional data on a daily basis:

Example Code

fit_2 <- update(fit, x = c(100, 200), n = c(400, 600))
present_bbfit(list("Day 1" = fit, "Day 2" = fit_2))

See also

Other packages for Bayesian analysis of A/B tests include: LearnBayes (GPL), conting (GPL), bandit (GPL), testr (MIT).

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Please note that this project is released with a Contributor Code of Conduct. By participating in this project you agree to abide by its terms.