Slab + interval stats and geoms

Matthew Kay

2024-03-04

Introduction

This vignette describes the slab+interval geoms and stats in ggdist. This is a flexible family of stats and geoms designed to make plotting distributions (such as priors and posteriors in Bayesian models, or even sampling distributions from other models) straightforward, and support a range of useful plots, including intervals, eye plots (densities + intervals), CCDF bar plots (complementary cumulative distribution functions + intervals), gradient plots, and histograms.

Setup

The following libraries are required to run this vignette:

library(dplyr)
library(tidyr)
library(distributional)
library(ggdist)
library(ggplot2)
library(patchwork)

theme_set(theme_ggdist())

Roadmap: The slabinterval meta-geometry

ggdist has a pantheon of geoms and stats that stem from a common root: geom_slabinterval() and stat_slabinterval(). These geoms consist of a “slab” (say, a density or a CDF), one or more intervals, and a point summary. These components may be computed in a number of different ways, and different variants of the geom will or will not include all components.

The base geom_slabinterval() uses a variety of custom aesthetics to create the composite geometry:

Depending on whether you want a horizontal or vertical orientation, you can provide ymin and ymax instead of xmin and xmax. By default, some aesthetics (e.g., fill, color, size, alpha) set properties of multiple sub-geometries at once. For example, the color aesthetic by default sets both the color of the point and the interval, but can also be overridden by point_color or interval_color to set the color of each sub-geometry separately.

geom_slabinterval() is most useful when paired with stat_slabinterval(), which will automatically calculate intervals, densities, and cumulative distribution functions, and maps these onto endpoints of the interval sub-geometry or the thickness of the slab sub-geometry.

The scaling of slab thickness is determined by a combination of the geometry’s height/width, its scale, the normalize parameter, and any thickness scales added to the plot (such as scale_thickness_shared()). For a comprehensive discussion and examples of slab scaling and normalization, see the thickness scale article.

Using geom_slabinterval() and stat_slabinterval() directly is not always advisable: they are highly configurable on their own, but this configurability requires remembering a number of combinations of options to use. For quick plotting, ggdist contains a number of pre-configured, easier-to-remember shortcut stats and geoms built on top of the slabinterval:

• Shortcut geoms, starting with geom_, are meant to be used on already-summarized data: geom_pointinterval() and geom_interval() (for data summarized into intervals) and geom_slab() (for data summarized into function values, like densities or cumulative distribution functions).

• Shortcut stats, starting with stat_, which compute relevant summaries (densities, CDFs, points, and/or intervals) before forwarding the summaries to their geom. Some have geom counterparts (e.g. stat_interval() corresponds to geom_interval(), except the former applies to sample data and the latter to already-summarized data). Many of these stats do not currently have geom counterparts (e.g. stat_ccdfinterval()), as they are primarily differentiated based on what kind of statistical summary they compute. If you’ve already computed a function (such as a density or CDF), you can just use geom_slabinterval() directly. These stats can be used on two types of data, depending on what aesthetic mappings you provide:

  • Sample data; e.g. draws from a data distribution, bootstrap distribution, Bayesian posterior distribution (or any other distribution, really). To use the stats on sample data, map sample values onto the x or y aesthetic.

  • Distribution objects and analytical distributions. To use the stats on this type of data, you must use the xdist, or ydist aesthetics, which take distributional objects, posterior::rvar() objects, or distribution names (e.g. "norm", which refers to the Normal distribution provided by the dnorm/pnorm/qnorm functions).

All slabinterval geoms can be plotted horizontally or vertically. Depending on how aesthetics are mapped, they will attempt to automatically determine the orientation; if this does not produce the correct result, the orientation can be overridden by setting orientation = "horizontal" or orientation = "vertical".

We’ll start with one of the most common existing use cases for these kinds geoms: eye plots.

Eye plots and half-eye plots

On sample data

Eye plots combine densities (as violins) with intervals to give a more detailed picture of uncertainty than is available just by looking at intervals.

For these first few demos we’ll use these data:

set.seed(1234)
df = tribble(
  ~group, ~subgroup, ~value,
  "a",          "h", rnorm(1000, mean = 5),
  "b",          "h", rnorm(1000, mean = 7, sd = 1.5),
  "c",          "h", rnorm(1000, mean = 8),
  "c",          "i", rnorm(1000, mean = 9),
  "c",          "j", rnorm(1000, mean = 7)
) %>%
  unnest(value)

We can summarize it at the group level using a “half-eye” plot, which combines a density plot with intervals (ignoring subgroups for now):

df %>%
  ggplot(aes(y = group, x = value)) +
  stat_halfeye() +
  ggtitle("stat_halfeye() (or stat_slabinterval())")

We can use the side parameter to more finely control where the slab (in this case, the density) is drawn; stat_eye() is also a shortcut for stat_slabinterval(side = "both"), as it creates “eye” plots:

p = df %>%
  ggplot(aes(x = group, y = value)) +
  theme(panel.background = element_rect(color = "grey70"))

(
  p + stat_slabinterval(side = "left") +
    labs(title = "stat_slabinterval()", subtitle = "side = 'left'")
) + (
  p + stat_slabinterval(side = "both") +
    labs(subtitle = "side = 'both'")
) + (
  p + stat_slabinterval(side = "right") +
    labs(subtitle = "side = 'right'")
)

Note how the above chart was drawn vertically instead of horizontally: all slabinterval geoms automatically detect their orientation based on the input data. For example, because we used a factor on the x axis above, the geoms were be drawn along the other axis (the y axis). If automatic detection of the desired axis fails, you can specify it manually; e.g. with stat_halfeye(orientation = 'vertical') or stat_halfeye(orientation = 'horizontal').

The side parameter works for horizontal geoms as well. "top" and "right" are considered synonyms, as are "bottom" and "left"; either form works with both horizontal and vertical versions of the geoms:

p = df %>%
  ggplot(aes(x = value, y = group)) +
  theme(panel.background = element_rect(color = "grey70"))

(
  # side = "left" would give the same result
  p + stat_slabinterval(side = "left") +
    ggtitle("stat_slabinterval()") + labs(subtitle = "side = 'bottom'")
) + (
  p + stat_slabinterval(side = "both") + labs(subtitle = "side = 'both'")
) + (
  # side = "right" would give the same result
  p + stat_slabinterval(side = "right") + labs(subtitle = "side = 'top'")
)

The slabinterval geoms support dodging through the standard mechanism of position = "dodge". Unlike with geom_violin(), densities in groups that are not dodged (here, ‘a’ and ‘b’) have the same area and max width as those in groups that are dodged (‘c’):

df %>%
  ggplot(aes(x = group, y = value, fill = subgroup)) +
  stat_eye(position = "dodge") +
  ggtitle("stat_eye(position = 'dodge')")

Dodging works whether geoms are horizontal or vertical.

On analytical distributions

The same set of (half-)eye plot stats designed for sample data described above can be used on analytical distributions or distribution vectors by using the xdist/ydist aesthetics instead of x/y. These stats accept specifications for distributions in one of two ways:

Using distribution vectors from the distributional package or posterior::rvar() objects: this format uses aesthetics as follows:

• xdist, ydist, or dist: a distribution vector or posterior::rvar() produced by functions such as distributional::dist_normal(), distributional::dist_beta(), posterior::rvar_rng(), etc.

Using distribution names as character vectors: this is an older, soft-deprecated format included for backwards-compatibility, but generally not recommended in new code. This format uses aesthetics as follows:

• xdist, ydist, or dist: the name of the distribution, following R’s naming scheme. This is a string which should have "p", "q", and "d" functions defined for it: e.g., “norm” is a valid distribution name because the pnorm(), qnorm(), and dnorm() functions define the CDF, quantile function, and density function of the Normal distribution.
• args or arg1, …, arg9: arguments for the distribution. If you use args, it should be a list column where each element is a list containing arguments for the distribution functions; alternatively, you can pass the arguments directly using arg1, …, arg9.

For example, here are a variety of normal distributions describing the same data from the previous section:

dist_df = tribble(
  ~group, ~subgroup, ~mean, ~sd,
  "a",          "h",     5,   1,
  "b",          "h",     7,   1.5,
  "c",          "h",     8,   1,
  "c",          "i",     9,   1,
  "c",          "j",     7,   1
)

We can use the distributional::dist_normal() function to construct a vector of normal distributions from these means and standard deviations, and map it to the ydist aesthetic, which sets the distributions drawn along the y axis:

dist_df %>%
  ggplot(aes(x = group, ydist = dist_normal(mean, sd), fill = subgroup)) +
  stat_eye(position = "dodge") +
  ggtitle("stat_eye(position = 'dodge')", "aes(ydist = dist_normal(mean, sd))")

Distributional vectors, combined with the xdist and ydist aesthetics, make it easy to visualize a variety of distributions. E.g., here are some Beta distributions:

data.frame(alpha = seq(5, 100, length.out = 10)) %>%
  ggplot(aes(y = alpha, xdist = dist_beta(alpha, 10))) +
  stat_halfeye() +
  labs(
    title = "stat_halfeye()",
    subtitle = "aes(xdist = dist_beta(alpha, 10), y = alpha)",
    x = "Beta(alpha,10) distribution"
  )

If you want to plot all of these on top of each other (instead of stacked), you could turn off plotting of the interval to make the plot easier to read using stat_slabinterval(show_interval = FALSE, ...). A shortcut for stat_slabinterval(show_interval = FALSE, ...) is stat_slab(). We’ll also turn off the fill color with fill = NA to make the stacking easier to see, and use outline color to show the value of alpha:

data.frame(alpha = seq(5, 100, length.out = 10)) %>%
  ggplot(aes(xdist = dist_beta(alpha, 10), color = alpha)) +
  stat_slab(fill = NA) +
  coord_cartesian(expand = FALSE) +
  scale_color_viridis_c() +
  labs(
    title = "stat_slab()",
    subtitle = "aes(xdist = dist_beta(alpha, 10), color = alpha)",
    x = "Beta(alpha,10) distribution",
    y = NULL
  )

Visualizing frequentist uncertainty

Distributional vectors also make it easy to visualize frequentist confidence distributions, which are often Normal or Student’s t distributions. For examples of this, see vignette("freq-uncertainty-vis").

Visualizing priors

A particularly good use of the xdist/ydist aesthetics is to visualize priors. For example, with brms you can specify priors using the brms::prior() function, which creates data frames with a "prior" column indicating the name of the prior distribution as a string. E.g., one might set some priors on the betas and the standard deviation in a model with something like this:

# NB these priors are made up!
priors = c(
  prior(normal(1, 0.5), class = b),
  prior(gamma(2, 2), class = phi),
  # lb = 0 sets a lower bound of 0, i.e. a half-Normal distribution
  prior(normal(0, 1), class = sigma, lb = 0)
)
priors

##            prior class coef group resp dpar nlpar   lb ub
## 1 normal(1, 0.5)     b                            <NA> NA
## 2    gamma(2, 2)   phi                            <NA> NA
## 3   normal(0, 1) sigma                               0 NA

The parse_dist() function can make it easier to visualize these: it takes in string specifications like those produced by brms — "normal(0,1)" and "lognormal(0,1)" above — and translates them into .dist, .args, and .dist_obj columns:

priors %>%
  parse_dist(prior)

##            prior class coef group resp dpar nlpar   lb ub .dist    .args         .dist_obj
## 1 normal(1, 0.5)     b                            <NA> NA  norm 1.0, 0.5      norm(1, 0.5)
## 2    gamma(2, 2)   phi                            <NA> NA gamma     2, 2       gamma(2, 2)
## 3   normal(0, 1) sigma                               0 NA  norm     0, 1 norm(0, 1)[0,Inf]

Notice that it also automatically translates some common distribution names (e.g. “normal”) into their equivalent R function names ("norm"). It also creates a .dist_obj vector using distributional::dist_wrap(). This distribution vector respects truncation bounds set by the lb and ub columns output by brms::prior(), as on the half-Normal prior for the sigma parameter. The .dist_obj vector can be assigned to the xdist or ydist aesthetic in ggdist:

priors %>%
  parse_dist(prior) %>%
  ggplot(aes(y = paste(class, "~", format(.dist_obj)), xdist = .dist_obj)) +
  stat_halfeye(subguide = subguide_inside(position = "right", title = "density")) +
  labs(
    title = "stat_halfeye()",
    subtitle = "with parse_dist() and brms::prior() to show priors",
    x = NULL,
    y = NULL
  )

This example also demonstrates the use of subguides to label the thickness axis. For more on subguides, see the documentation for the subguide_axis() function, and for more on scaling of the thickness aesthetic, see the thickness article.

The format() function in format(.dist_obj) generates a string containing a human-readable name for the distribution for labeling purposes.

Sharing thickness scaling across geometries

In some cases, such as visualizing priors and posteriors, it can be helpful to use multiple geometries (e.g. one for prior and one for posterior). By default, normalization/scaling of slab thicknesses is controlled by geometries, not by a scale function. This allows various functionality not otherwise possible, such as (1) allowing different geometries to have different thickness scales and (2) allowing the user to control at what level of aggregation (panels, groups, the entire plot, etc) thickness scaling is done via the normalize parameter to [geom_slabinterval()].

To override this default behavior and make separate geometries use a shared thickness scale, add scale_thickness_shared() to the plot. The difference is illustrated below:

prior_post = data.frame(
  prior = dist_normal(0, 1),
  posterior = dist_normal(0.1, 0.5)
)

separate_scale_plot = prior_post %>%
  ggplot() +
  stat_halfeye(aes(xdist = posterior)) +
  stat_slab(aes(xdist = prior), fill = NA, color = "red") +
  labs(
    subtitle = "default: no shared thickness scale"
  )

shared_scale_plot = prior_post %>%
  ggplot() +
  stat_halfeye(aes(xdist = posterior)) +
  stat_slab(aes(xdist = prior), fill = NA, color = "#e41a1c") +
  scale_thickness_shared() +
  labs(subtitle = "with scale_thickness_shared()")

separate_scale_plot + shared_scale_plot + plot_annotation(title = "prior (slab) + posterior (halfeye)")

With scale_thickness_shared() applied, both densities have the same area under their curves. Further details of scaling of the thickness aesthetic are discussed in the thickness article

Scale transformations of densities

The stat_slabinterval() family also adjusts densities appropriately when scale transformations are applied. For example, here is a log-Normal distribution plotted on a log scale:

data.frame(dist = dist_lognormal(log(10), 2*log(10))) %>%
  ggplot(aes(xdist = dist)) +
  stat_halfeye() +
  scale_x_log10(breaks = 10^seq(-5,7, by = 2))

As expected, a log-Normal density plotted on the log scale appears Normal. The Jacobian correction for the scale transformation is applied to the density so that the correct density is shown on the log scale. Internally, ggdist attempts to do symbolic differentiation on scale transformation functions (and if that fails, uses numerical differentiation) to calculate the Jacobian so that the stat_slabinterval() family works generically across the different scale transformations supported by ggplot.

Summing up eye plots: stat_[half]eye

All of the stats in this section follow the naming scheme stat_[half]eye, where adding half to the name to yields half-eyes (density plots) instead of eyes (violins).

Like the remaining shortcut stats, these stats also follow these conventions:

• Map sample values to x or y to use the stats on sample data.
• Use the xdist, ydist, and args aesthetics for analytical distributions or distributions contained in vector objects, such as distributional or posterior::rvar() objects.

Histogram + interval plots

In some cases you might prefer histograms to density plots. stat_histinterval() provides an alternative to stat_halfeye() that uses histograms instead of densities; it is roughly equivalent to stat_slabinterval(density = "histogram"):

p = df %>%
  ggplot(aes(x = group, y = value)) +
  theme(panel.background = element_rect(color = "grey70"))

ph = df %>%
  ggplot(aes(y = group, x = value)) +
  theme(panel.background = element_rect(color = "grey70"))

(
  p + stat_histinterval() + labs(title = "stat_histinterval()", subtitle = "horizontal")
) + (
  ph + stat_histinterval() + labs(subtitle = "vertical")
)

You can use the slab_color aesthetic to show the outline of the bars. By default the outlines are only drawn along the tops of the bars, as typical tasks with histograms involve area estimation, so the outlines between bars are not strictly necessary and may be distracting. However, if you wish to include those outlines, you can set outline_bars = TRUE:

(
  ph + stat_histinterval(slab_color = "gray45", outline_bars = FALSE) +
    labs(title = "stat_histinterval", subtitle = "outline_bars = FALSE (default)")
) + (
  ph + stat_histinterval(slab_color = "gray45", outline_bars = TRUE) +
    labs(subtitle = "outline_bars = TRUE")
)

Histograms of analytical distributions

While stat_histinterval() will not produce histograms of continuous analytical distributions, the stat_slabinterval() family will automatically detect discrete distributions supplied on the xdist and ydist aesthetics and plot them using stepped histograms instead of densities. As with stat_histinterval(), you can choose whether or not to draw outlines between bars of the histogram using outline_bars = TRUE or FALSE (the default is FALSE).

Here is an example of histograms of analytical distributions that also shows a redundant encoding of the density by mapping the pdf computed variable onto fill (in addition to the default mapping onto thickness):

tibble(
  group = c("a","b","c","d","e"),
  lambda = c(13,7,4,3,2)
) %>%
  ggplot(aes(x = group)) +
  stat_slab(aes(ydist = dist_poisson(lambda), fill = after_stat(pdf))) +
  geom_line(aes(y = lambda, group = NA), linewidth = 1) +
  geom_point(aes(y = lambda), size = 2.5) +
  labs(fill = "Pr(y)") +
  ggtitle("stat_slab()", "aes(ydist = dist_poisson(lambda), fill = after_stat(pdf))")

This was inspired by an example from Isabella Ghement.

CCDF bar plots

Another (perhaps sorely underused) technique for visualizing distributions is cumulative distribution functions (CDFs) and complementary CDFs (CCDFs). These can be more effective for some decision-making tasks than densities or intervals, and require fewer assumptions to create from sample data than density plots.

For all of the examples above, both on sample data and analytical distributions, you can replace slabinterval with [c]cdfinterval to get a stat that creates a CDF or CCDF bar plot.

stat_ccdfinterval() is roughly equivalent to stat_slabinterval(aes(thickness = after_stat(1 - cdf)), justification = 0.5, side = "topleft", normalize = "none", expand = TRUE)

On sample data

The CCDF interval plots are probably more useful than the CDF interval plots in most cases, as the bars typically grow up from the baseline. For example, replacing stat_eye() with stat_ccdfinterval() in our previous subgroup plot produces CCDF bar plots:

df %>%
  ggplot(aes(x = group, y = value, fill = subgroup, group = subgroup)) +
  stat_ccdfinterval(position = "dodge") +
  ggtitle("stat_ccdfinterval(position = 'dodge')")

The extents of the bars are determined automatically by range of the data in the samples. However, for bar charts it is often good practice to draw the bars from a meaningful reference point (this point is often 0). You can use ggplot2::expand_limits() to ensure the bar is drawn down to 0. Let’s also adjust the position of the slab relative to the position of the interval using the justification parameter:

df %>%
  ggplot(aes(x = group, y = value, fill = subgroup)) +
  stat_ccdfinterval(position = "dodge", justification = 1) +
  expand_limits(y = 0) +
  coord_cartesian(expand = FALSE) +
  ggtitle("stat_ccdfinterval(position = 'dodge', justification = 1)")

All other parameters, like orientation and side, work in the same way it does with the basic stat_slabinterval().

On analytical distributions

As with other plot types, you can also use stat_ccdfinterval()/stat_cdfinterval() to visualize analytical distributions or distribution vectors, using the xdist or ydist aesthetic (see previous examples).

Summing up CDF bar plots

All of the stats in this section follow the naming scheme stat_[c]cdfinterval:

• Add c to the name to get CCDFs instead of CDFs.
• Use xdist/ydist instead of x/y to use the stats on analytical distributions or distribution vectors instead of sample data.
• It can be helpful to use expand_limits() to ensure meaningful reference points are included in the plot.

Gradient plots

An alternative approach to mapping density onto the thickness aesthetic of the slab is to instead map it onto its alpha value (i.e., opacity). This is what the stat_gradientinterval family does (actually, it uses slab_alpha, a variant of the alpha aesthetic, described below).

It is roughly equivalent to stat_slabinterval(aes(slab_alpha = after_stat(f)), thickness = 1, justification = 0.5).

On sample data

For example, replacing stat_eye() with stat_gradientinterval() produces gradient + interval plots:

df %>%
  ggplot(aes(x = group, y = value, fill = subgroup)) +
  stat_gradientinterval(position = "dodge") +
  labs(title = "stat_gradientinterval(position = 'dodge')")

stat_gradientinterval() maps density onto the slab_alpha aesthetic, which is a variant of the ggplot alpha scale that specifically targets alpha (opacity) values of the slab portion of geom_slabinterval(). This aesthetic has default ranges and limits that are a little different from the base ggplot alpha scale and which ensure that densities of 0 are mapped onto opacities of 0. You can use scale_slab_alpha_continuous() to adjust this scale’s settings.

Avoiding “choppy”-looking gradients

Depending on your graphics device, gradients may be “choppy” looking. You can fix this choppiness by setting fill_type = "gradient", which uses a gradient feature introduced in some graphics engines in R 4.1. If you use stat_gradientinterval() in R 4.1, you will receive a message suggesting you may want to explicitly set fill_type = "gradient" to improve output quality. If you are using R 4.2 or greater, you should not need to set fill_type = "gradient" as support for gradients can be auto-detected in that version, but you will get a warning message if you use stat_gradientinterval() with a graphics engine that does not support gradients.

df %>%
  ggplot(aes(x = group, y = value, fill = subgroup)) +
  stat_gradientinterval(position = "dodge", fill_type = "gradient") +
  labs(title = "stat_gradientinterval(position = 'dodge', fill_type = 'gradient')")

As of this writing, in R version 4.1 or greater the graphics devices that support gradients — i.e. device that support the grid::linearGradient() function — include pdf(), svg(), and png(type = "cairo"). See here for more about the changes to the R graphics engine.

On analytical distributions

As with other plot types, you can also use stat_gradientinterval() to visualize analytical distributions or distribution vectors, using the xdist or ydist aesthetic (see previous examples).

Dotplots

The encodings thus far are continuous probability encodings: they map probabilities or probability densities onto aesthetics like x/y position or alpha transparency. An alternative is discrete or frequency-framing uncertainty visualizations, such as dotplots and quantile dotplots. Dotplots represent distributions by showing each data point, and quantile dotplots extend this idea to analytical distributions by showing quantiles from the distribution as a number of discrete possible outcomes.

On sample data

For example, replacing stat_halfeye() with stat_dots() produces dotplots. With so many dots here, the outlines mask the fill, so it makes sense to map subgroup to the outline color of the dots as well:

df %>%
  ggplot(aes(x = group, y = value, fill = subgroup, color = subgroup)) +
  stat_dots(position = "dodgejust") +
  labs(
    title = "stat_dots()",
    subtitle = "aes(fill = subgroup, color = subgroup))"
  )

Unlike the base ggplot2::geom_dotplot() geom, ggdist::geom_dots() automatically determines a bin width to ensure that the dot stacks fit within the available space. You can set the binwidth parameter manually to override this.

Quantile dotplots

The above plots are a bit hard to read due to the large number of dots. Particularly when summarizing posterior distributions or predictive distributions, which may have thousands of data points, it can make sense to plot a smaller number of dots (say 20, 50 or 100) that are representative of the full sample. One such approach is to plot quantiles, thereby creating quantile dotplots, which can help people make better decisions under uncertainty (Kay 2016, Fernandes 2018).

The quantiles argument to stat_dots constructs a quantile dotplot with the specified number of quantiles. Here is one with 50 quantiles, so each dot represents approximately a 2% (1/50) chance. We’ll turn off outline color too (color = NA):

df %>%
  ggplot(aes(x = group, y = value, fill = subgroup)) +
  stat_dots(position = "dodgejust", quantiles = 50, color = NA) +
  labs(title = "stat_dots(quantiles = 50)")

For more on dotplots, see vignette("dotsinterval")

Custom plots

The slabinterval family of stats and geoms is designed to be very flexible. Most of the shortcut geoms above can be created simply by setting particular combinations of options and aesthetic mappings using the basic geom_slabinterval() and stat_slabinterval(). Some useful combinations do not have specific shortcut geoms currently, but can be created manually with only a bit of additional effort.

Gradients of alpha, color, and fill

Two aesthetics of particular use for creating custom geoms are slab_alpha, which changes the alpha transparency of the slab portion of the geom, slab_color, which changes its outline color, and fill, which changes its fill color. All of these aesthetics can be mapped to variables along the length of the geom (that is, the color does not have to be constant over the entire geom), which allows you to create gradients or to highlight meaningful regions of the data (amongst other things). You can also employ the ggdist-specific color_ramp and fill_ramp aesthetics to create custom gradients with outline and fill colors, as demonstrated later in this section.

Note: The examples of gradients in this section use the (optional) experimental setting fill_type = "gradient". If you do not have R greater than 4.1.0 or are not using a supported graphics device, the output may be blank; in this case, omit this option. Gradients can be produced without this option but they may not look as nice.

CCDF Gradients

By default, stat_ccdfinterval() maps the output of the evaluated function (in its case, the CCDF) onto the thickness aesthetic of the slabinterval geom, which determines how thick the slab is. This is the equivalent of setting aes(thickness = after_stat(f)). However, we could instead create a CCDF gradient plot, a sort of mashup of a CCDF barplot and a density gradient plot, by mapping after_stat(f) onto the slab_alpha aesthetic instead, and setting thickness to a constant (1):

df %>%
  ggplot(aes(x = group, y = value, fill = subgroup)) +
  stat_ccdfinterval(aes(slab_alpha = after_stat(f)),
    thickness = 1, position = "dodge", fill_type = "gradient"
  ) +
  expand_limits(y = 0) +
  # plus coord_cartesian so there is no space between bars and axis
  coord_cartesian(expand = FALSE) +
  ggtitle("stat_ccdfinterval(thickness = 1)", "aes(slab_alpha = after_stat(f))")

If this approach were applied to bins in a histogram, where each bin had some uncertainty associated with its height, the result would be a so-called fuzzygram (Haber and Wilkinson 1982).

Highlighting and other combinations

The ability to map arbitrary variables onto fill or outline colors within a slab allows you to easily highlight sub-regions of a plot. Taking the earlier example of visualizing priors, we can add a mapping to the fill aesthetic to highlight a region of interest, say ±1.5:

priors = tibble(
  dist = c(dist_normal(0, 1), dist_student_t(3, 0, 1))
)

priors %>%
  ggplot(aes(y = format(dist), xdist = dist)) +
  stat_halfeye(aes(fill = after_stat(abs(x) < 1.5))) +
  ggtitle("stat_halfeye()", "aes(fill = after_stat(abs(x) < 1.5)))") +
  # we'll use a nicer palette than the default for highlighting:
  scale_fill_manual(values = c("gray85", "skyblue"))

We could also combine these aesthetics arbitrarily. Here is a (probably not very useful) eye plot + gradient plot combination, with the portion of the distribution above 1 highlighted:

priors %>%
  ggplot(aes(y = format(dist), xdist = dist)) +
  stat_eye(aes(slab_alpha = after_stat(f), fill = after_stat(x > 1)), fill_type = "gradient") +
  ggtitle(
    "stat_eye(fill_type = 'gradient')",
    "aes(slab_alpha = after_stat(f), fill = after_stat(x > 1)))"
  ) +
  # we'll use a nicer palette than the default for highlighting:
  scale_fill_manual(values = c("gray75", "skyblue"))

Mashups with Correll and Gleicher-style gradients

We can also take advantage of the fact that all slabinterval stats also supply cdf and pdf aesthetics to create charts that make use of both the CDF and the PDF in their aesthetic mappings. For example, we could create Correll & Gleicher-style gradient plots by fading the tails outside of the 95% interval in proportion to \(|1 - 2F(x)|\) (where \(F(x)\) is the CDF):

priors %>%
  ggplot(aes(y = format(dist), xdist = dist)) +
  stat_gradientinterval(aes(slab_alpha = after_stat(-pmax(abs(1 - 2*cdf), .95))),
    fill_type = "gradient"
  ) +
  scale_slab_alpha_continuous(guide = "none") +
  ggtitle(
    "stat_gradientinterval(fill_type = 'gradient')",
    "aes(slab_alpha = after_stat(-pmax(abs(1 - 2*cdf), .95)))"
  )

We could also do a mashup of faded-tail gradients with violin plots by starting with an eye plot and then using the generated cdf aesthetic to fade the tails, producing plots like those in Helske et al.:

priors %>%
  ggplot(aes(y = format(dist), xdist = dist)) +
  stat_eye(aes(slab_alpha = after_stat(-pmax(abs(1 - 2*cdf), .95))), fill_type = "gradient") +
  scale_slab_alpha_continuous(guide = "none") +
  ggtitle(
    "stat_eye(fill_type = 'gradient')",
    "aes(slab_alpha = after_stat(-pmax(abs(1 - 2*cdf), .95)))"
  )

A related idea is one from Tukey: rather than visually emphasizing where a value is likely, emphasize where it is unlikely. While Tukey used a visual representation showing both pointwise and simultaneous intervals, for this example we will do something a bit different, inverting the faded-tails function from Correll & Gleicher to create bars that “block out” the regions of low likelihood:

dist_df %>%
  ggplot(aes(x = group, ydist = dist_normal(mean, sd), fill = subgroup)) +
  stat_slab(
    aes(
      thickness = after_stat(pmax(0, abs(1 - 2*cdf) - .95)),
      fill_ramp = after_stat(pmax(0, abs(1 - 2*cdf) - .95))
    ),
    side = "both", position = "dodge", fill_type = "gradient"
  ) +
  labs(
    title = 'stat_slab(side = "both")',
    subtitle = paste0(
      "aes(fill = subgroup,\n       ",
      "fill_ramp and thickness = after_stat(pmax(0, abs(1 - 2*cdf) - .95)))"
    )
  ) +
  guides(fill_ramp = "none") +
  coord_cartesian(expand = FALSE)

Thanks to a Jessica Hullman for suggesting the Tukey paper that inspired this idea.

Densities filled according to intervals

Another common chart type involves filling in the interior of a halfeye plot according to some intervals. Here, we can use the fact that computed variables from the interval sub-geometry are made available to the slab sub-geometry and vice versa.

For example, within the slab sub-geometry, the .width and level computed variables correspond to the smallest intervals that contain the x value at that portion of the slab. Thus, we can map .width or level onto the slab fill:

df %>%
  ggplot(aes(y = group, x = value)) +
  stat_halfeye(aes(fill = after_stat(level))) +
  # na.translate = FALSE drops the unnecessary NA from the legend, which covers
  # slab values outside the intervals. An alternative would be to use
  # na.value = ... to set the color for values outside the intervals.
  scale_fill_brewer(na.translate = FALSE) +
  labs(
    title = "stat_halfeye()",
    subtitle = "aes(fill = after_stat(level))",
    fill = "interval"
  )

(Note: in previous versions of ggdist, using cut_cdf_qi() was the recommended way to achieve this affect. That function still exists for backwards compatibility, but mapping level or .width is now the recommended approach, as it generalizes to other interval types, such as highest-density intervals — see later.)

To apply the color scale to all values outside the intervals, one option is to split stat_halfeye() into its constituent parts (stat_slab() and stat_pointinterval()), then include a “100%” interval in .width:

df %>%
  ggplot(aes(y = group, x = value)) +
  stat_slab(aes(fill = after_stat(level)), .width = c(.66, .95, 1)) +
  stat_pointinterval() +
  scale_fill_brewer() +
  labs(
    title = "stat_slab()",
    subtitle = "aes(fill = after_stat(level), .width = c(.66, .95, 1))",
    fill = "interval"
  )

If we change the interval type used, the resulting .width and level computed variables change correspondingly, allowing us to highlight other types of intervals besides quantile intervals; for example, highest-density intervals:

qi_plot = data.frame(dist = dist_beta(10, 2)) %>%
  ggplot(aes(xdist = dist)) +
  stat_halfeye(aes(fill = after_stat(level)), point_interval = median_qi, .width = c(.5, .8, .95)) +
  scale_fill_brewer(na.value = "gray95") +
  labs(subtitle = "stat_halfeye(aes(fill = after_stat(level)), point_interval = median_qi)")

hdi_plot = data.frame(dist = dist_beta(10, 2)) %>%
  ggplot(aes(xdist = dist)) +
  stat_halfeye(aes(fill = after_stat(level)), point_interval = mode_hdci, .width = c(.5, .8, .95)) +
  scale_fill_brewer(na.value = "gray95") +
  labs(subtitle = "stat_halfeye(aes(fill = after_stat(level)), point_interval = mode_hdci)")

qi_plot /
  hdi_plot

Annotating slabs with spikes

geom_spike() and stat_spike() make it straightforward to apply custom “spike” annotations to slabs. The easiest way to use spikes is to use stat_spike() and pass it a numeric position or a function giving numeric position(s) at which you wish to place a spike (or a list of these). If passed a function, the function will be applied to the distributional or posterior::rvar() object used internally to represent the distribution.

This means that point estimates (e.g., mean(), median(), Mode()), quantiles (quantile()), and interval estimates (qi(), hdci(), hdi()) can be provided to stat_spike() directly. This makes it easy to modify the previous example to highlight how medians and quantile intervals differ from modes and highest-density intervals in terms of their densities:

qi_plot_spikes = data.frame(dist = dist_beta(10, 2)) %>%
  ggplot(aes(xdist = dist)) +
  stat_slab(aes(fill = after_stat(level)), point_interval = median_qi, .width = c(.5, .95)) +
  # stat_spike(at = c(median, qi)) would also work, but this demonstrates how
  # to re-label the names of the `at` computed variable and use it in an
  # aesthetic mapping by mapping it to `linetype`
  stat_spike(aes(linetype = after_stat(at)), at = c("median", "interval (qi)" = qi)) +
  scale_fill_brewer(na.value = "gray95") +
  scale_thickness_shared() +
  labs(subtitle = "stat_slab() + stat_spike(at = c(median, qi))")

hdi_plot_spikes = data.frame(dist = dist_beta(10, 2)) %>%
  ggplot(aes(xdist = dist)) +
  stat_slab(aes(fill = after_stat(level)), point_interval = mode_hdi, .width = c(.5, .95)) +
  stat_spike(aes(linetype = after_stat(at)), at = c("mode" = Mode, "interval (hdi)" = hdi)) +
  scale_fill_brewer(na.value = "gray95") +
  scale_thickness_shared() +
  labs(subtitle = "stat_slab() + stat_spike(at = c(Mode, hdi))")

qi_plot_spikes /
  hdi_plot_spikes

Note the use of scale_thickness_shared(), which ensures that the thickness values for the slabs and the thickness values for the spikes (which determine their heights) use a shared scale, so they line up correctly.

Using color ramps for fill and color aesthetics

ggdist supplies color_ramp (or colour_ramp) and fill_ramp aesthetics which can be used to vary (“ramp”) the outline or fill colors smoothly from a base color (default "white") to whatever color the geometry would otherwise have.

Taking the above example with interval-filled slabs, we could use the fill_ramp aesthetic instead of the fill aesthetic to set the slab color based on the interval it is in. We could then vary the base fill color separately from the interval based on another column in the original data table, such as the subgroup column:

df %>%
  ggplot(aes(y = group, x = value)) +
  stat_halfeye(
    aes(fill = subgroup, fill_ramp = after_stat(level)),
    .width = c(.50, .80, .95),
    # NOTE: we use position = "dodgejust" (a dodge that respects the
    # justification of intervals relative to slabs) instead of
    # position = "dodge" here because it ensures the topmost slab does
    # not extend beyond the plot limits
    position = "dodgejust"
  ) +
  # a range from 1 down to 0.2 ensures the fill goes dark to light inside-out
  # and doesn't get all the way down to white (0) on the lightest color
  scale_fill_ramp_discrete(na.translate = FALSE) +
  labs(
    title = "stat_halfeye(position = 'dodgejust')",
    subtitle = "aes(fill = subgroup, fill_ramp = after_stat(level))",
    fill_ramp = "interval"
  )

We could similarly use stat_interval() with the color_ramp aesthetic to vary subgroup color separately from the whiteness of the intervals. Here, level is a variable generated by all stats in the stat_slabinterval() family which contains the level of the generated intervals, as an ordered factor.

dist_df %>%
  ggplot(aes(x = group, ydist = dist_normal(mean, sd), color = subgroup)) +
  stat_interval(aes(color_ramp = after_stat(level)), position = "dodge") +
  labs(
    title = "stat_interval()",
    subtitle = "aes(color = subgroup, color_ramp = after_stat(level))"
  )

See help("scale_color_ramp") for more information on the color ramp aesthetics/scales.

Raindrop plots

Barrowman and Myers proposed an alternative to density-based eye plots (such as created by stat_eye() by default) called raindrop plots. In these, the thickness of the slab is proportional to log(pdf) instead of pdf, and is bounded within the 95% interval. We can construct a function that uses the pdf and .width computed variables to give a thickness proportional to log(pdf) within the 95% interval, and use it to create raindrop plots.

Barrowman and Myers apply this technique with a 95% raindrop superimposed on a 99% raindrop, which we can replicate:

priors %>%
  ggplot(aes(y = format(dist), xdist = dist)) +
  # must also use normalize = "groups" because min(log(pdf)) will be different for each dist
  stat_slab(
    aes(thickness = after_stat(ifelse(.width <= 0.99, log(pdf), NA))),
    normalize = "groups", fill = "gray85", .width = .99, side = "both"
  ) +
  stat_eye(
    aes(thickness = after_stat(ifelse(.width <= 0.95, log(pdf), NA))),
    normalize = "groups"
  ) +
  ggtitle(
    'stat_eye(normalize = "groups")',
    paste0(
      "with aes(thickness = after_stat(ifelse(.width <= 0.95, log(pdf), NA)))\n",
      "and aes(thickness = after_stat(ifelse(.width <= 0.99, log(pdf), NA)))"
    )
  )

Creating ridge plots

When plotting densities (as in stat_halfeye(), stat_slab(), etc) it can be useful to overplot many densities simultaneously, an approach sometimes called ridge plots (e.g. as in the ggridges package). This can be done by setting scale or height to a value greater than 1. Setting height is often the best approach as it will correctly adjust plot boundaries (unless you need to use position = "dodge", in which case you should use scale and adjust plot boundaries manually).

set.seed(1234)

ridges_df = data.frame(
  group = letters[7:1],
  x = rnorm(700, mean = 1:7, sd = 2)
)

ridges_df %>%
  ggplot(aes(y = group, x = x)) +
  stat_slab(height = 2, color = "black") +
  ggtitle("stat_slab(height = 2, color = 'black')")

Depending on if it makes sense for your data (for example, if the scale is unbounded), you may also wish to adjust the density and trim parameters. The default density, density_bounded(), estimates the bounds of the distribution, which is useful if your data has natural boundaries (e.g., is restricted to be positive). But if you know the underlying distribution is unbounded, you can set density = "unbounded". You may also want to set trim to FALSE to ensure the densities smoothly go down to 0, rather than being cut off at the limits of the raw data. Combining both of these with expand = TRUE will make each slab expand itself to the limits of the x axis.

We’ll use density, trim, and expand along with a combination of fill and fill_ramp to give each group on the y axis a different color and to vary the fill along the x axis in a way that provides a “softer” form of region of practical equivalence:

ridges_df %>%
  ggplot(aes(
    y = group, x = x,
    fill = group, fill_ramp = after_stat(abs(x)),
    color_ramp = after_stat(-dnorm(x, 0, 2))
  )) +
  stat_slab(
    height = 2, color = "gray15",
    expand = TRUE, trim = FALSE, density = "unbounded",
    fill_type = "gradient",
    show.legend = FALSE
  ) +
  geom_vline(xintercept = 0, color = "gray85", linetype = "dashed") +
  ggtitle(
    'stat_slab(height = 2, color = "black", expand = TRUE, trim = FALSE)',
    'aes(fill = group, fill_ramp = after_stat(abs(x)), color_ramp = after_stat(-dnorm(x, 0, 2)))'
  ) +
  scale_fill_viridis_d()

We use a tighter ramp on color compared to fill (via -dnorm() instead of abs()) because we want the outlines to quickly ramp back to black outside of 0 so that they have sufficient contrast against the slabs when they overlap.

Varying side, scale, and justification within geoms

The side, scale, and justification parameters can also be varied within all geoms in the geom_slabinterval() family, allowing (for example) different groups to hang above or below the interval:

dist_df %>%
  filter(subgroup == "h") %>%
  mutate(side = c("top", "both", "bottom")) %>%
  ggplot(aes(y = group, xdist = dist_normal(mean, sd), side = side)) +
  stat_dotsinterval(scale = 2/3) +
  labs(
    title = 'stat_dotsinterval(scale = 2/3)',
    subtitle = 'aes(xdist = dist_normal(mean, sd), side = c("top","both","bottom"))'
  ) +
  coord_cartesian()

Multiple slabs and intervals in composite plots

Sometimes you may want to include multiple different types of slabs in the same plot in order to take advantage of the features each slab type provides. For example, people often combine densities with dotplots to show the underlying datapoints that go into a density estimate, creating so-called “rain cloud” plots.

To use multiple slab geometries together, you can use the side parameter to change which side of the interval a slab is drawn on and set the scale parameter to something around 0.5 (by default it is 0.9) so that the two slabs do not overlap. Geoms can also be dodged together, as in this example using densities with quantile dotplots in subgroups. This example also shows how stat_pointinterval() can be repurposed to be used with other geoms; here to replace points with labels (the idea of replacing points with labels comes from Brenton Wiernik).

df %>%
  ggplot(aes(x = group, y = value, fill = subgroup)) +
  stat_slab(side = "left", scale = 0.5, position = "dodge") +
  stat_dotsinterval(scale = 0.5, quantiles = 100, position = "dodge") +
  stat_pointinterval(
    geom = "label",
    aes(label = paste0(group, subgroup)),
    .width = .5,  # set to a scalar to draw only one label instead of two
    position = position_dodge(width = 1),
    size = 3.5
  ) +
  labs(title = paste0(
    'stat_halfeye(side = "left") +\n',
    'stat_dotsinterval(quantiles = 100) +\n',
    'stat_pointinterval(geom = "label")'
  ))

When constructing composite plots it may be useful to position the slab and interval parts of the geometry separately. While some relative positioning of these geometries is supported by manipulating the justification parameter, if you want complete, separate control over positioning of intervals versus slabs, the simplest approach can be to specify those geometries separately.

For example, the following uses a separate specification of a stat_slab() and a stat_pointinterval() instead of a combined stat_slabinterval() in order to use position_dodge() on the intervals but not the slabs:

df %>%
  ggplot(aes(fill = group, color = group, x = value)) +
  stat_slab(alpha = .3) +
  stat_pointinterval(position = position_dodge(width = .4, preserve = "single")) +
  labs(
    title = "stat_slab() and stat_pointinterval()",
    subtitle = "with position_dodge() applied to the intervals",
    y = NULL
  ) +
  scale_y_continuous(breaks = NULL)

(Thanks to Brenton Wiernik for this example.)