tidybayes: Bayesian analysis + tidy data + geoms

tidybayes is an R package that aims to make it easy to integrate popular Bayesian modeling methods into a tidy data + ggplot workflow. It builds on top of (and re-exports) several functions for visualizing uncertainty from its sister package, ggdist

Tidy data frames (one observation per row) are particularly convenient for use in a variety of R data manipulation and visualization packages. However, when using Bayesian modeling functions like JAGS or Stan in R, we often have to translate this data into a form the model understands, and then after running the model, translate the resulting sample (or predictions) into a more tidy format for use with other R functions. tidybayes aims to simplify these two common (often tedious) operations:

Composing data for use with the model. This often means translating data from a data.frame into a list , making sure factors are encoded as numerical data, adding variables to store the length of indices, etc. This package helps automate these operations using the compose_data() function, which automatically handles data types like numeric, logical, factor, and ordinal, and allows easy extensions for converting other data types into a format the model understands by providing your own implementation of the generic as_data_list().
Extracting tidy draws from the model. This often means extracting indices from parameters with names like "b[1,1]", "b[1,2]" into separate columns of a data frame, like i = c(1,1,..) and j = c(1,2,...). More tediously, sometimes these indices actually correspond to levels of a factor in the original data; e.g. "x[1]" might correspond to a value of x for the first level of some factor. We provide several straightforward ways to convert draws from a variable with indices into useful long-format (“tidy”) data frames, with automatic back-conversion of common data types (factors, logicals) using the spread_draws() and gather_draws() functions, including automatic recovery of factor levels corresponding to variable indices. In most cases this kind of long-format data is much easier to use with other data-manipulation and plotting packages (e.g., dplyr, tidyr, ggplot2) than the format provided by default from the model.

tidybayes also provides some additional functionality for data manipulation and visualization tasks common to many models:

Extracting tidy fits and predictions from models. For models like those provided by rstanarm and brms, tidybayes provides a tidy analog of the fitted and predict functions, called add_fitted_draws() and add_predicted_draws(). These functions are modeled after the modelr::add_predictions() function, and turn a grid of predictions into a long-format data frame of draws from either the fits or predictions from a model. These functions make it straightforward to generate arbitrary fit lines from a model.
Summarizing posterior distributions from models. tidybayes re-exports the ggdist::point_interval() family of functions (median_qi(), mean_qi(), mode_hdi(), etc), which are methods for generating point summaries and intervals that are designed with tidy workflows in mind. They can generate point summaries plus an arbitrary number of probability intervals from tidy data frames of draws, they return tidy data frames, and they respect data frame groups. These functions
Visualizing priors and posteriors. The focus on tidy data makes the output from tidybayes easy to visualize using ggplot. While existing geoms (like ggdist::geom_pointrange() and ggdist::geom_linerange()) can give useful output, the output from tidybayes is designed to work well with several geoms and stats in its sister package, ggdist. These geoms have sensible defaults suitable for visualizing posterior point summaries and intervals (ggdist::geom_pointinterval(), ggdist::stat_pointinterval()), visualizing distributions with point summaries and intervals (the ggdist::stat_sample_slabinterval() family of stats, including eye plots, half-eye plots, CCDF bar plots, gradient plots, dotplots, and histograms), and visualizing fit lines with an arbitrary number of uncertainty bands (ggdist::geom_lineribbon() and ggdist::stat_lineribbon()). Priors can also be visualized in the same way using the ggdist::stat_dist_slabinterval() family of stats. The ggdist::geom_dotsinterval() family also automatically finds good binning parameters for dotplots, and can be used to easily construct quantile dotplots of posteriors (see example in this document). For convenience, tidybayes re-exports the ggdist stats and geoms.

See vignette("slabinterval", package = "ggdist") for more information.
Comparing a variable across levels of a factor, which often means first generating pairs of levels of a factor (according to some desired set of comparisons) and then computing a function over the value of the comparison variable for those pairs of levels. Assuming your data is in the format returned by spread_draws, the compare_levels function allows comparison across levels to be made easily.

Finally, tidybayes aims to fit into common workflows through compatibility with other packages:

Drop-in functions to translate tidy column names used by tidybayes to/from names used by other common packages and functions, including column names used by ggmcmc::ggs (via to_ggmcmc_names and from_ggmcmc_names) and column names used by broom::tidy (via to_broom_names and from_broom_names), which makes comparison with results of other models straightforward.
The unspread_draws and ungather_draws functions invert spread_draws and gather_draws, aiding compatibility with other Bayesian plotting packages (notably bayesplot).
The gather_emmeans_draws function turns the output from emmeans::emmeans (formerly lsmeans) into long-format data frames (when applied to supported model types, like MCMCglmm and rstanarm models).

Supported model types

tidybayes aims to support a variety of models with a uniform interface. Currently supported models include rstan, brms, rstanarm, runjags, rjags, jagsUI, coda::mcmc and coda::mcmc.list, MCMCglmm, and anything with its own as.mcmc.list implementation. If you install the tidybayes.rethinking package, models from the rethinking package are also supported.

Installation

You can install the currently-released version from CRAN with this R command:

install.packages("tidybayes")

Alternatively, you can install the latest development version from GitHub with these R commands:

install.packages("devtools")
devtools::install_github("mjskay/tidybayes")

Examples

This example shows the use of tidybayes with the Stan modeling language; however, tidybayes supports many other model types, such as JAGS, brm, rstanarm, and (theoretically) any model type supported by coda::as.mcmc.list.

library(magrittr)
library(dplyr)
library(ggplot2)
library(rstan)
library(tidybayes)
library(emmeans)
library(broom)
library(brms)
library(modelr)
library(forcats)
library(cowplot)
library(RColorBrewer)
library(gganimate)

theme_set(theme_tidybayes() + panel_border())

Imagine this dataset:

set.seed(5)
n = 10
n_condition = 5
ABC =
  tibble(
    condition = rep(c("A","B","C","D","E"), n),
    response = rnorm(n * 5, c(0,1,2,1,-1), 0.5)
  )

ABC %>%
  ggplot(aes(x = response, y = condition)) +
  geom_point(alpha = 0.5) +
  ylab("condition")

A hierarchical model of this data might fit an overall mean across the conditions (overall_mean), the standard deviation of the condition means (condition_mean_sd), the mean within each condition (condition_mean[condition]) and the standard deviation of the responses given a condition mean (response_sd):

data {
  int<lower=1> n;
  int<lower=1> n_condition;
  int<lower=1, upper=n_condition> condition[n];
  real response[n];
}
parameters {
  real overall_mean;
  vector[n_condition] condition_zoffset;
  real<lower=0> response_sd;
  real<lower=0> condition_mean_sd;
}
transformed parameters {
  vector[n_condition] condition_mean;
  condition_mean = overall_mean + condition_zoffset * condition_mean_sd;
}
model {
  response_sd ~ cauchy(0, 1);         // => half-cauchy(0, 1)
  condition_mean_sd ~ cauchy(0, 1);   // => half-cauchy(0, 1)
  overall_mean ~ normal(0, 5);
  condition_zoffset ~ normal(0, 1);   // => condition_mean ~ normal(overall_mean, condition_mean_sd)
  for (i in 1:n) {
    response[i] ~ normal(condition_mean[condition[i]], response_sd);
  }
}

Composing data for input to model: `compose_data`

We have compiled and loaded this model into the variable ABC_stan. Rather than munge the data into a format Stan likes ourselves, we will use the tidybayes::compose_data() function, which takes our ABC data frame and automatically generates a list of the following elements:

n: number of observations in the data frame
n_condition: number of levels of the condition factor
condition: a vector of integers indicating the condition of each observation
response: a vector of observations

So we can skip right to modeling:

m = sampling(ABC_stan, data = compose_data(ABC), control = list(adapt_delta=0.99))

Getting tidy draws from the model: `spread_draws`

We decorate the fitted model using tidybayes::recover_types(), which will ensure that numeric indices (like condition) are back-translated back into factors when we extract data:

m %<>% recover_types(ABC)

Now we can extract variables of interest using spread_draws, which automatically parses indices, converts them back into their original format, and turns them into data frame columns. This function accepts a symbolic specification of Stan variables using the same syntax you would to index columns in Stan. For example, we can extract the condition means and the residual standard deviation:

m %>%
  spread_draws(condition_mean[condition], response_sd) %>%
  head(15)  # just show the first few rows

## # A tibble: 15 x 6
## # Groups:   condition [1]
##    condition condition_mean .chain .iteration .draw response_sd
##    <chr>              <dbl>  <int>      <int> <int>       <dbl>
##  1 A                0.00544      1          1     1       0.576
##  2 A               -0.0836       1          2     2       0.576
##  3 A                0.0324       1          3     3       0.551
##  4 A                0.113        1          4     4       0.576
##  5 A                0.157        1          5     5       0.583
##  6 A                0.218        1          6     6       0.621
##  7 A                0.276        1          7     7       0.641
##  8 A                0.0130       1          8     8       0.637
##  9 A                0.152        1          9     9       0.609
## 10 A                0.192        1         10    10       0.521
## 11 A                0.154        1         11    11       0.558
## 12 A                0.298        1         12    12       0.552
## 13 A                0.349        1         13    13       0.531
## 14 A                0.471        1         14    14       0.566
## 15 A                0.313        1         15    15       0.568

The condition numbers are automatically turned back into text (“A”, “B”, “C”, …) and split into their own column. A long-format data frame is returned with a row for every draw (\times) every combination of indices across all variables given to spread_draws; for example, because response_sd here is not indexed by condition, within the same draw it has the same value for each row corresponding to a different condition (some other formats supported by tidybayes are discussed in vignette("tidybayes"); in particular, the format returned by gather_draws).

Plotting posteriors as eye plots: `stat_eye()`

Automatic splitting of indices into columns makes it easy to plot the condition means here. We will employ the ggdist::stat_eye() geom, which combines a violin plot of the posterior density, median, 66% and 95% quantile interval to give an “eye plot” of the posterior. The point and interval types are customizable using the point_interval() family of functions. A “half-eye” plot (non-mirrored density) is also available as ggdist::stat_halfeye(). All tidybayes geometries automatically detect their appropriate orientation, though this can be overridden with the orientation parameter if the detection fails.

m %>%
  spread_draws(condition_mean[condition]) %>%
  ggplot(aes(x = condition_mean, y = condition)) +
  stat_eye()

Or one can employ the similar “half-eye” plot:

m %>%
  spread_draws(condition_mean[condition]) %>%
  ggplot(aes(x = condition_mean, y = condition)) +
  stat_halfeye()

A variety of other stats and geoms for visualizing priors and posteriors are available; see vignette("slabinterval", package = "ggdist") for an overview of them.

Plotting posteriors as quantile dotplots

Intervals are nice if the alpha level happens to line up with whatever decision you are trying to make, but getting a shape of the posterior is better (hence eye plots, above). On the other hand, making inferences from density plots is imprecise (estimating the area of one shape as a proportion of another is a hard perceptual task). Reasoning about probability in frequency formats is easier, motivating quantile dotplots (Kay et al. 2016, Fernandes et al. 2018), which also allow precise estimation of arbitrary intervals (down to the dot resolution of the plot, 100 in the example below).

Within the slabinterval family of geoms in tidybayes is the dots and dotsinterval family, which automatically determine appropriate bin sizes for dotplots and can calculate quantiles from samples to construct quantile dotplots. ggdist::stat_dots() is the variant designed for use on samples:

m %>%
  spread_draws(condition_mean[condition]) %>%
  ggplot(aes(x = condition_mean, y = condition)) +
  stat_dots(quantiles = 100)

The idea is to get away from thinking about the posterior as indicating one canonical point or interval, but instead to represent it as (say) 100 approximately equally likely points.

Point and interval summaries

The functions ggdist::median_qi(), ggdist::mean_qi(), ggdist::mode_hdi(), etc (the point_interval functions) give tidy output of point summaries and intervals:

m %>%
  spread_draws(condition_mean[condition]) %>%
  median_qi(condition_mean)

## # A tibble: 5 x 7
##   condition condition_mean .lower .upper .width .point .interval
##   <chr>              <dbl>  <dbl>  <dbl>  <dbl> <chr>  <chr>    
## 1 A                  0.199 -0.142  0.549   0.95 median qi       
## 2 B                  1.01   0.651  1.34    0.95 median qi       
## 3 C                  1.84   1.48   2.19    0.95 median qi       
## 4 D                  1.02   0.681  1.37    0.95 median qi       
## 5 E                 -0.890 -1.23  -0.529   0.95 median qi

Comparison to other models via compatibility with `broom`

Translation functions like ggdist::to_broom_names(), ggdist::from_broom_names(), ggdist::to_ggmcmc_names(), etc. can be used to translate between common tidy format data frames with different naming schemes. This makes it easy, for example, to compare points summaries and intervals between tidybayes output and models that are supported by broom::tidy.

For example, let’s compare against ordinary least squares (OLS) regression:

linear_results = 
  lm(response ~ condition, data = ABC) %>% 
  emmeans(~ condition) %>% 
  tidy() %>%
  mutate(model = "OLS")
linear_results

## # A tibble: 5 x 7
##   condition estimate std.error    df conf.low conf.high model
##   <fct>        <dbl>     <dbl> <dbl>    <dbl>     <dbl> <chr>
## 1 A            0.182     0.173    45   -0.167     0.530 OLS  
## 2 B            1.01      0.173    45    0.665     1.36  OLS  
## 3 C            1.87      0.173    45    1.53      2.22  OLS  
## 4 D            1.03      0.173    45    0.678     1.38  OLS  
## 5 E           -0.935     0.173    45   -1.28     -0.586 OLS

Using ggdist::to_broom_names(), we’ll convert the output from median_qi (which uses names .lower and .upper) to use names from broom (conf.low and conf.high) so that comparison with output from broom::tidy is easy:

bayes_results = m %>%
  spread_draws(condition_mean[condition]) %>%
  median_qi(estimate = condition_mean) %>%
  to_broom_names() %>%
  mutate(model = "Bayes")
bayes_results

## # A tibble: 5 x 8
##   condition estimate conf.low conf.high .width .point .interval model
##   <chr>        <dbl>    <dbl>     <dbl>  <dbl> <chr>  <chr>     <chr>
## 1 A            0.199   -0.142     0.549   0.95 median qi        Bayes
## 2 B            1.01     0.651     1.34    0.95 median qi        Bayes
## 3 C            1.84     1.48      2.19    0.95 median qi        Bayes
## 4 D            1.02     0.681     1.37    0.95 median qi        Bayes
## 5 E           -0.890   -1.23     -0.529   0.95 median qi        Bayes

This makes it easy to bind the two results together and plot them:

bind_rows(linear_results, bayes_results) %>%
  ggplot(aes(y = condition, x = estimate, xmin = conf.low, xmax = conf.high, color = model)) +
  geom_pointinterval(position = position_dodge(width = .3))

Shrinkage towards the overall mean is visible in the Bayesian results.

Compatibility with broom::tidy also gives compatibility with dotwhisker::dwplot:

bind_rows(linear_results, bayes_results) %>%
  rename(term = condition) %>%
  dotwhisker::dwplot()

Posterior prediction and complex custom plots

The tidy data format returned by spread_draws also facilitates additional computation on variables followed by the construction of more complex custom plots. For example, we can generate posterior predictions easily, and use the .width argument (passed internally to median_qi) to generate any number of intervals from the posterior predictions, then plot them alongside point summaries and the data:

m %>%
  spread_draws(condition_mean[condition], response_sd) %>%
  mutate(prediction = rnorm(n(), condition_mean, response_sd)) %>%
  ggplot(aes(y = condition)) +
  
  # posterior predictive intervals
  stat_interval(aes(x = prediction), .width = c(.5, .8, .95)) +
  scale_color_brewer() +
  
  # median and quantile intervals of condition mean
  stat_pointinterval(aes(x = condition_mean), .width = c(.66, .95), position = position_nudge(y = -0.2)) +
  
  # data
  geom_point(aes(x = response), data = ABC)

This plot shows 66% and 95% quantile credible intervals of posterior median for each condition (point + black line); 95%, 80%, and 50% posterior predictive intervals (blue); and the data.

Fit curves

For models that support it (like rstanarm and brms models), We can also use the add_fitted_draws or add_predicted_draws functions to generate posterior fits or predictions. Combined with the functions from the modelr package, this makes it easy to generate fit curves.

Let’s fit a slightly naive model to miles per gallon versus horsepower in the mtcars dataset:

m_mpg = brm(
  mpg ~ log(hp), 
  data = mtcars, 
  family = lognormal,

  file = "README_models/m_mpg.rds" # cache model (can be removed)  
)

Now we will use modelr::data_grid, tidybayes::add_predicted_draws(), and ggdist::stat_lineribbon() to generate a fit curve with multiple probability bands:

mtcars %>%
  data_grid(hp = seq_range(hp, n = 101)) %>%
  add_predicted_draws(m_mpg) %>%
  ggplot(aes(x = hp, y = mpg)) +
  stat_lineribbon(aes(y = .prediction), .width = c(.99, .95, .8, .5), color = "#08519C") +
  geom_point(data = mtcars, size = 2) +
  scale_fill_brewer()

ggdist::stat_lineribbon(aes(y = .prediction), .width = c(.99, .95, .8, .5)) is one of several shortcut geoms that simplify common combinations of tidybayes functions and ggplot geoms. It is roughly equivalent to the following:

  stat_summary(
    aes(y = .prediction, fill = forcats::fct_rev(ordered(stat(.width))), group = -stat(.width)), 
    geom = "ribbon", point_interval = median_qi, fun.args = list(.width = c(.99, .95, .8, .5))
  ) +
  stat_summary(aes(y = .prediction), fun.y = median, geom = "line", color = "red", size = 1.25)

Because this is all tidy data, if you wanted to build a model with interactions among different categorical variables (say a different curve for automatic and manual transmissions), you can easily generate predictions faceted over that variable (say, different curves for different transmission types). Then you could use the existing faceting features built in to ggplot to plot them.

Such a model might be:

m_mpg_am = brm(
  mpg ~ log(hp) * am, 
  data = mtcars, 
  family = lognormal,

  file = "README_models/m_mpg_am.rds" # cache model (can be removed)  
)

Then we can generate and plot predictions as before (differences from above are highlighted as comments):

mtcars %>%
  data_grid(hp = seq_range(hp, n = 101), am) %>%    # add am to the prediction grid
  add_predicted_draws(m_mpg_am) %>%
  ggplot(aes(x = hp, y = mpg)) +
  stat_lineribbon(aes(y = .prediction), .width = c(.99, .95, .8, .5), color = "#08519C") +
  geom_point(data = mtcars) +
  scale_fill_brewer() +
  facet_wrap(~ am)                                  # facet by am

Or, if you would like overplotted posterior fit lines, you can instead use tidybayes::add_fitted_draws() to get draws from fit lines (instead of predictions), select some reasonable number of them (say n = 100), and then plot them:

mtcars %>%
  data_grid(hp = seq_range(hp, n = 200), am) %>%
  add_fitted_draws(m_mpg_am, n = 100) %>%         # sample 100 fits from the posterior
  ggplot(aes(x = hp, y = mpg)) +
  geom_line(aes(y = .value, group = .draw), alpha = 1/20, color = "#08519C") +
  geom_point(data = mtcars) +
  facet_wrap(~ am)

Animated hypothetical outcome plots (HOPs) can also be easily constructed by using gganimate:

set.seed(12345)
ndraws = 50

p = mtcars %>%
  data_grid(hp = seq_range(hp, n = 50), am) %>%
  add_fitted_draws(m_mpg_am, n = ndraws) %>%
  ggplot(aes(x = hp, y = mpg)) +
  geom_line(aes(y = .value, group = .draw), color = "#08519C") +
  geom_point(data = mtcars) +
  facet_wrap(~ am, labeller = label_both) +
  transition_states(.draw, 0, 1) +
  shadow_mark(past = TRUE, future = TRUE, alpha = 1/20, color = "gray50")

animate(p, nframes = ndraws, fps = 2.5, width = 672, height = 480, res = 100, dev = "png", type = "cairo")

See vignette("tidybayes") for a variety of additional examples and more explanation of how it works.

Feedback, issues, and contributions

I welcome feedback, suggestions, issues, and contributions! Contact me at [email protected]. If you have found a bug, please file it here with minimal code to reproduce the issue. Pull requests should be filed against the dev branch.

tidybayes grew out of helper functions I wrote to make my own analysis pipelines tidier. Over time it has expanded to cover more use cases I have encountered, but I would love to make it cover more!

Citing `tidybayes`

Matthew Kay (2020). tidybayes: Tidy Data and Geoms for Bayesian Models. R package version 2.1.1, https://mjskay.github.io/tidybayes/. DOI: 10.5281/zenodo.1308151.