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#### Description

Bayesian analysis + tidy data + geoms (R package)

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# 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
geom
s (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")
• 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 n;
int n_condition;
int condition[n];
real response[n];
}
parameters {
real overall_mean;
vector[n_condition] condition_zoffset;
real response_sd;
real 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 %>%
head(15)  # just show the first few rows

## # A tibble: 15 x 6
## # Groups:   condition [1]
##    condition condition_mean .chain .iteration .draw response_sd
##
##  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 %>%
ggplot(aes(x = condition_mean, y = condition)) +
stat_eye()


<!-- -->

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

m %>%
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 %>%
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 %>%
median_qi(condition_mean)

## # A tibble: 5 x 7
##   condition condition_mean .lower .upper .width .point .interval
##
## 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(conf.int = TRUE) %>%
mutate(model = "OLS")
linear_results

## # A tibble: 5 x 8
##   condition estimate    df conf.low conf.high statistic  p.value model
##
## 1 A            0.182    45   -0.167     0.530      1.05 3.00e- 1 OLS
## 2 B            1.01     45    0.665     1.36       5.85 5.13e- 7 OLS
## 3 C            1.87     45    1.53      2.22      10.8  4.15e-14 OLS
## 4 D            1.03     45    0.678     1.38       5.93 3.97e- 7 OLS
## 5 E           -0.935    45   -1.28     -0.586     -5.40 2.41e- 6 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 %>%
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
##
## 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 %>%
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)) %>%
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
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) %>%
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 2.3.0, https://mjskay.github.io/tidybayes/. DOI: 10.5281/zenodo.1308151.