---
title: "Dots + interval stats and geoms"
author: "Matthew Kay"
date: "`r Sys.Date()`"
output: 
  rmarkdown::html_vignette:
    toc: true
    df_print: kable
vignette: >
  %\VignetteIndexEntry{Dots + interval stats and geoms}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---
  
```{r, child="children/chunk_options.txt"}
```

## Introduction
  
This vignette describes the dots+interval geoms and stats in `ggdist`. This is a flexible sub-family of stats and geoms designed to make plotting dotplots straightforward. In particular, it supports a selection of useful layouts (including the classic Wilkinson layout, a weave layout, and a beeswarm layout) and can automatically select the dot size so that the dotplot stays within the bounds of the plot.

## Setup
  
The following libraries are required to run this vignette:
  
```{r setup, message = FALSE, warning = FALSE}
library(dplyr)
library(tidyr)
library(distributional)
library(ggdist)
library(ggplot2)
library(patchwork)

theme_set(theme_ggdist())
```

```{r hidden_options, include=FALSE}
.old_options = options(width = 100)
```


## Anatomy of `geom_dotsinterval()`

The `dotsinterval` family of geoms and stats is a sub-family of slabinterval (see `vignette("slabinterval")`), where the "slab" is a collection of dots forming a dotplot and the interval is a summary point (e.g., mean, median, mode) with an arbitrary number of intervals.

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

```{r dotsinterval_components, echo=FALSE, fig.height=4.15, fig.width=6.5}
red_ = "#d95f02"
green_ = "#1b9e77"
blue_ = "#7570b3"

bracket_ = function(..., x, xend = x, y, yend = y, color = red_) {
  annotate("segment",
    arrow = arrow(angle = 90, ends = "both", length = unit(3, "points")),
    color = color, linewidth = 0.75,
    x = x, xend = xend, y = y, yend = yend,
    ...
  )
}
thickness_ = function(x) dnorm(x,4,1) * 0.9 / dnorm(4,4,1)
refline_ = function(..., x, xend = x, y, yend = y, color = red_, linetype = "solid", alpha = 0.5) {
  annotate("segment",
    color = color, linetype = linetype, alpha = alpha, linewidth = 0.75,
    x = x, xend = xend, y = y, yend = yend,
    ...
  )
}
label_ = function(..., hjust = 0, color = red_) {
  annotate("text",
    color = color, hjust = hjust, lineheight = 1,
    size = 3.25,
    ...
  )
}
arrow_ = function(..., curvature = 0, x, xend = x, y, yend = y) {
  annotate("curve",
    color = red_, arrow = arrow(angle = 45, length = unit(3, "points"), type = "closed"),
    curvature = curvature,
    x = x, xend = xend, y = y, yend = yend
  )
}


tibble(dist = dist_normal(4, 1.2)) %>%
  ggplot(aes(y = 0, xdist = dist)) +

  geom_hline(yintercept = 0:1, color = "gray95") +

  stat_dotsinterval(
    aes(linewidth = NULL),
    slab_color = "gray50",
    .width = 1 - 2*pnorm(-1, sd = 1.2),
    fill = "gray75",
    point_size = 5,
    shape = 22,
    slab_shape = 21,
    stroke = 1.5,
    linewidth = 5,
    slab_linewidth = 1.5
  ) +

  # height
  refline_(x = 0, xend = 8.4, y = 1) +
  bracket_(x = 8.4, y = 0, yend = 1) +
  label_(label = "height", x = 8.6, y = 1) +

  # scale
  refline_(x = 4, xend = 8.6, y = 0.9) +
  bracket_(x = 8.6, y = 0, yend = 0.9) +
  label_(label = "scale = 0.9", x = 8.8, y = 0.9) +

  # slab line properties
  label_(x = 2.5, y = 0.7,
    label = 'slab_color = "gray50"\nslab_linewidth = 1.5',
    vjust = 1, hjust = 1
  ) +
  arrow_(x = 2.52, xend = 3, y = 0.67, yend = thickness_(3.1) + 0.03, curvature = -0.2) +

  # slab fill
  label_(x = 5.5, y = 0.7,
    label = 'slab_fill = fill = "gray75"\nslab_alpha = alpha = 1\nslab_shape = 21',
    vjust = 1
  ) +
  arrow_(x = 5.48, xend = 4.81, y = 0.67, yend = thickness_(3.1) + 0.01, curvature = 0.2) +

  # xmin, x, xmax
  arrow_(x = 2.65, xend = 3, y = -0.1, yend = -0.01, curvature = -0.2) +
  label_(x = 2.7, y = -0.1, label = "xmin", hjust = 1, vjust = 1) +
  arrow_(x = 4, y = -0.1, yend = -0.05) +
  label_(x = 4, y = -0.1, label = "x", hjust = 0.5, vjust = 1) +
  arrow_(x = 5.35, xend = 5, y = -0.1, yend = -0.01, curvature = 0.2) +
  label_(x = 5.3, y = -0.1, label = "xmax", hjust = 0, vjust = 1) +

  # interval properties
  label_(x = 3.5, y = -0.2,
    label = paste0(
      'interval_color = color = "black"\n',
      'interval_alpha = alpha = 1\n',
      'interval_linetype = linetype = "solid"\n',
      'linewidth = size = 5'
    ),
    vjust = 1, hjust = 1
  ) +
  arrow_(x = 3.3, xend = 3.4, y = -0.18, yend = -0.015, curvature = -0.1) +

  # point properties
  label_(x = 4.5, y = -0.2,
    label = paste0(
      'point_fill = fill = "gray75"\n',
      'point_color = color = "black"\n',
      'point_alpha = alpha = 1\n',
      'point_size = size = 5\nshape = 22\nstroke = 1.5'
    ),
    vjust = 1, hjust = 0
  ) +
  arrow_(x = 4.55, xend = 4.2, y = -0.18, yend = -0.03, curvature = 0.2) +

  coord_cartesian(xlim = c(-1, 10), ylim = c(-0.6, 1)) +
  labs(subtitle = "Properties of geom_dotsinterval", x = NULL, y = NULL)
```

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. 

Due to its relationship to the `geom_slabinterval()` family, aesthetics specific
to the "dots" sub-geometry are referred to with the prefix `slab_`. When using
the standalone `geom_dots()` geometry, it is not necessary to use these custom
aesthetics:

```{r dots_components, echo=FALSE, fig.height=3.04, fig.width=6.5}
tibble(dist = dist_normal(4, 1.2)) %>%
  ggplot(aes(y = 0, xdist = dist)) +

  geom_hline(yintercept = 0:1, color = "gray95") +

  stat_dots(
    aes(linewidth = NULL),
    color = "gray50",
    fill = "gray75",
    linewidth = 1.5,
    shape = 21
  ) +

  # height
  refline_(x = 0, xend = 8.4, y = 1) +
  bracket_(x = 8.4, y = 0, yend = 1) +
  label_(label = "height", x = 8.6, y = 1) +

  # scale
  refline_(x = 4, xend = 8.6, y = 0.9) +
  bracket_(x = 8.6, y = 0, yend = 0.9) +
  label_(label = "scale = 0.9", x = 8.8, y = 0.9) +

  # slab line properties
  label_(x = 2.5, y = 0.7,
    label = 'color = "gray50"\nlinewidth = 1.5',
    vjust = 1, hjust = 1
  ) +
  arrow_(x = 2.52, xend = 3, y = 0.67, yend = thickness_(3.1) + 0.03, curvature = -0.2) +

  # slab fill
  label_(x = 5.5, y = 0.7,
    label = 'fill = "gray75"\nalpha = 1\nshape = 21',
    vjust = 1
  ) +
  arrow_(x = 5.48, xend = 4.81, y = 0.67, yend = thickness_(3.1) + 0.01, curvature = 0.2) +

  coord_cartesian(xlim = c(-1, 10), ylim = c(-0.05, 1)) +
  labs(subtitle = "Properties of geom_dots", x = NULL, y = NULL)
```

`geom_dotsinterval()` is often most useful when paired with `stat_dotsinterval()`, which will automatically calculate points and intervals and map these onto endpoints of the interval sub-geometry.

`stat_dotsinterval()` and `stat_dots()` 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](https://pkg.mitchelloharawild.com/distributional/) objects, `posterior::rvar()` objects, or distribution names (e.g. `"norm"`, which refers to the Normal distribution provided by the `dnorm/pnorm/qnorm` functions). When used on analytical distributions (e.g. `distributional::dist_normal()`), the `quantiles` argument determines the number of quantiles used (and therefore the number of dots shown); the default is `100`.

All `dotsinterval` 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"`.


## Controlling dot layout

Size and layout of dots in the dotplot are controlled by four parameters: 
`scale`, `binwidth`, `dotsize`, and `stackratio`.

```{r layout_params, echo=FALSE, fig.height=3.7, fig.width=6}
data.frame(x = c(.4, .7, .7, 1, 1, 1)) %>%
  ggplot(aes(x = x)) +

  geom_hline(yintercept = 0:1, color = "gray95") +

  # binwidth
  refline_(x = seq(.25, 1.15, by = .3), y = -0.025, yend = 0.9, color = green_) +
  bracket_(x = .25, xend = .55, y = -0.025, color = green_) +
  label_(
    label = "binwidth = NA\n=> binwidth = 0.3\n(auto-selected so that\n the tallest stack is \u2264 scale)",
    x = 0.55, y = -0.08, vjust = 1, hjust = 1, color = green_
  ) +

  geom_dots(scale = 0.9, dotsize = 1, alpha = 0.5) +

  # height
  refline_(x = 0, xend = 2, y = 1) +
  bracket_(x = 2, y = 0, yend = 1) +
  label_(label = "height", x = 2.05, y = 1) +

  # scale
  refline_(x = 0.25, xend = 2.1, y = 0.9) +
  bracket_(x = 2.1, y = 0, yend = 0.9) +
  label_(label = "scale = 0.9", x = 2.15, y = 0.9) +

  # stackratio
  refline_(x = 1, xend = 1.3, y = c(.15, .45)) +
  bracket_(x = 1.3, y = .15, yend = .45) +
  label_(label = "stackratio = 1", x = 1.35, y = .3) +

  # dotsize
  refline_(x = c(.85, 1.15), y = 0.15, yend = -0.025, color = blue_, linetype = "22", alpha = 1) +
  bracket_(x = .85, xend = 1.15, y = -0.025, color = blue_) +
  label_(
    label = "dotsize = 1\n(relative to binwidth)",
    x = 0.85, y = -0.08, vjust = 1, hjust = 0, color = blue_
  ) +

  scale_x_continuous(limits = c(-0.1, 2.35)) +
  scale_y_continuous(limits = c(-0.35, 1)) +
  coord_fixed() +
  labs(subtitle = "Layout parameters for dots geoms", x = NULL, y = NULL)
```

- `scale`: If `binwidth` is not set (is `NA`), then the `binwidth` is determined
automatically so that the height of the highest stack of dots is less than `scale`.
The default value of `scale`, 0.9, ensures there is a small gap between dotplots
when multiple dotplots are drawn.

- `binwidth`: The width of the bins used to lay out the dots:
  - `NA` (default): Use `scale` to determine bin width.
  - A single numeric or `unit()`: the exact bin width to use. If it is `numeric`, 
    the bin width is expressed in data units; use `unit()` to specify the width
    in terms of screen coordinates (e.g. `unit(0.1, "npc")` would make the bin width
    0.1 *normalized parent coordinates*, which would be 10% of the plot width.)
  - A 2-vector of numerics or `unit()`s giving an acceptable minimum and maximum
    width. The automatic bin width algorithm will attempt to find the largest
    bin width between these two values that also keeps the tallest stack of dots
    shorter than `scale`.

- `dotsize`: The size of the dots as a percentage of `binwidth`. The default value
  is `1.07` rather than `1`. This value was chosen largely by trial and error, to
  find a value that gives nice-looking layouts with circular dots on continuous
  distributions, accounting for the fact that a slight overlap of dots tends to 
  give a nicer apparent visual distance between adjacent stacks than the precise
  value of `1`.
  
- `stackratio`: The distance between the centers of dots in a stack as a proportion
  of the height of each dot. `stackratio = 1`, the default, mean dots will just
  touch; `stackratio < 1` means dots will overlap each other, and `stackratio > 1`
  means dots will have gaps between them.

## Side

The `side` aesthetic allows you to adjust the positioning and
direction of the dots:

* `"top"`, `"right"`, or `"topright"`: draw the dots on the top or on the right, depending on `orientation`
* `"bottom"`, `"left"`, or `"bottomleft"`: draw the dots on the bottom or on the left, depending on `orientation`
* `"topleft"`: draw the dots on top or on the left, depending on `orientation`
* `"bottomright"`: draw the dots on the bottom or on the right, depending on `orientation`
* `"both"`: draw the dots mirrored, as in a "beeswarm" plot.

When `orientation = "horizontal"`, this yields:

```{r horizontal_side, fig.width = small_width, fig.height = small_width/2}
set.seed(1234)
x = rnorm(100)

side_plot = function(...) {
  expand.grid(
    x = x,
    side = c("topright", "both", "bottomleft"),
    stringsAsFactors = FALSE
  ) %>%
    ggplot(aes(side = side, ...)) +
    geom_dots() +
    facet_grid(~ side, labeller = "label_both") +
    labs(x = NULL, y = NULL) +
    theme(panel.border = element_rect(color = "gray75", fill = NA))
}
side_plot(x = x) +
  labs(title = "Horizontal geom_dots() with different values of side") +
  scale_y_continuous(breaks = NULL)
```

When `orientation = "vertical"`, this yields:

```{r vertical_side, fig.width = small_width, fig.height = small_width/2}
side_plot(y = x) +
  labs(title = "Vertical geom_dots() with different values of side") +
  scale_x_continuous(breaks = NULL)
```

## Layout

The `layout` parameter allows you to adjust the algorithm used to place dots:

* `"bin"` (default): places dots on the off-axis at the midpoint of their bins as in the classic Wilkinson dotplot. This maintains the alignment of rows and columns in the dotplot. This layout is slightly different from the classic Wilkinson algorithm in that: (1) it nudges bins slightly to avoid overlapping bins and (2) if the input data are symmetrical it will return a symmetrical layout.
* `"weave"`: uses the same basic binning approach of "bin", but places dots in the off-axis at their actual positions (modulo overlaps, which are nudged out of the way). This maintains the alignment of rows but does not align dots within columns.
* `"hex"`: uses the same basic binning approach of "bin", but alternates placing dots `+binwidth/4` or `-binwidth/4` in the off-axis from the bin center. This allows hexagonal packing by setting a `stackratio` less than `1` (something like `0.9` tends to work).
* "swarm": uses the `"compactswarm"` layout from `beeswarm::beeswarm()`. Does not maintain alignment of rows or columns, but can be more compact and neat looking, especially for sample data (as opposed to quantile dotplots of theoretical distributions, which may look better with `"bin"`, `"weave"`, or `"hex"`).

When `side` is `"top"`, these layouts look like this:

```{r layout_top, fig.width = small_width, fig.height = small_height}
layout_plot = function(layout, side, ...) {
  data.frame(
    x = x
  ) %>%
    ggplot(aes(x = x)) +
    geom_dots(layout = layout, side = side, stackratio = if (layout == "hex") 0.9 else 1) +
    labs(
      subtitle = paste0("layout = ", deparse(layout), if (layout == "hex") " with stackratio = 0.9"),
      x = NULL,
      y = NULL
    ) +
    scale_y_continuous(breaks = NULL) +
    theme(panel.border = element_rect(color = "gray75", fill = NA))
}

(layout_plot("bin", side = "top") + layout_plot("hex", side = "top")) /
  (layout_plot("weave", side = "top") + layout_plot("swarm", side = "top")) +
  plot_annotation(title = 'geom_dots() layouts with side = "top"')
```

When `side` is `"both"`, these layouts look like this:

```{r layout_both, fig.width = small_width, fig.height = small_height}
(layout_plot("bin", side = "both") + layout_plot("hex", side = "both")) /
  (layout_plot("weave", side = "both") + layout_plot("swarm", side = "both")) +
  plot_annotation(title = 'geom_dots() layouts with side = "both"')
```

### Beeswarm plots

Thus, it is possible to create beeswarm plots by using `geom_dots()`
with `side = "both"`:

```{r beeswarm_bin, fig.width = small_width, fig.height = small_height}
set.seed(1234)

abc_df = tibble(
  value = rnorm(300, mean = c(1,2,3), sd = c(1,2,2)),
  abc = rep(c("a", "b", "c"), 100)
)

abc_df %>%
  ggplot(aes(x = abc, y = value)) +
  geom_dots(side = "both") +
  ggtitle('geom_dots(side = "both")')
```

`side = "both"` also tends to work well with the `"hex"` and `"swarm"` layouts for 
more classic-looking "beeswarm" plots:

```{r beeswarm_hex, fig.width = small_width, fig.height = small_height}
abc_df %>%
  ggplot(aes(x = abc, y = value)) +
  geom_dots(side = "both", layout = "hex", stackratio = 0.92) +
  ggtitle('geom_dots(side = "both", layout = "hex")')
```

The combination of `binwidth = unit(1.5, "mm")` and `overflow = "compress"` (see the 
section on large samples, below) can be used to set the dot size to a specific size
while guaranteeing the layout stays within the bounds of the geom. 
This combination is used by two shortcut geoms, `geom_swarm()` and `geom_weave()`,
which use the `"swarm"` and `"weave"` layouts respectively. These also use 
`side = "both"`, and are intended to make it easy to create good-looking beeswarm 
plots *without* manually tweaking settings:

```{r geom_weave, fig.width = small_width, fig.height = small_height}
set.seed(1234)

swarm_data = tibble(
  y = rnorm(300, c(1,4)),
  g = rep(c("a","b"), 150)
)

swarm_plot = swarm_data %>%
  ggplot(aes(x = g, y = y)) +
  geom_swarm(linewidth = 0, alpha = 0.75) +
  labs(title = "geom_swarm()")

weave_plot = swarm_data %>%
  ggplot(aes(x = g, y = y)) +
  geom_weave(linewidth = 0, alpha = 0.75) +
  labs(title = "geom_weave()")

swarm_plot + weave_plot
```

## Varying `color`, `fill`, `shape`, and `linewidth`

Aesthetics like `color`, `fill`, `shape`, and `linewidth` can be varied over the dots.
For example, we can vary the `fill` aesthetic to create two
subgroups, and use `position = "dodge"` to dodge entire "swarms" at once so
the subgroups do not overlap. We'll also set `linewidth = 0` so that the default
gray outline is not drawn:

```{r beeswarm_dodge, fig.width = small_width, fig.height = small_height}
set.seed(12345)

abcc_df = tibble(
  value = rnorm(300, mean = c(1,2,3,4), sd = c(1,2,2,1)),
  abc = rep(c("a", "b", "c", "c"), 75),
  hi = rep(c("h", "h", "h", "i"), 75)
)

abcc_df %>%
  ggplot(aes(y = value, x = abc, fill = hi)) +
  geom_weave(position = "dodge", linewidth = 0, alpha = 0.75) +
  scale_fill_brewer(palette = "Dark2") +
  ggtitle(
    'geom_weave(position = "dodge")',
    'aes(fill = hi, shape = hi)'
  )
```

### Varying discrete aesthetics within dot groups

By default, if you assign a discrete variable to `fill`, color`, `shape`, etc it
will also be used in the `group` aesthetic to determine dot groups, which
are laid out separate (and can be dodged separately, as above).

If you override this behavior by setting `group` to `NA` (or to some other
variable you want to group dot layouts by), `geom_dotsinterval()` will leave
dots in data order within the layout but allow aesthetics to vary across them.

For example:

```{r beeswarm_shape_color_together, fig.width = small_width, fig.height = small_height}
abcc_df %>%
  ggplot(aes(y = value, x = abc, fill = hi, group = NA)) +
  geom_dots(linewidth = 0) +
  scale_color_brewer(palette = "Dark2") +
  ggtitle(
    'geom_dots()',
    'aes(fill = hi, group = NA)'
  )
```

By default, dot positions within bins for the `"bin"` layout are determined
by their data values (e.g. by the `y` values in the above chart). You can 
override this by passing a variable to the `order` aesthetic, which will set
the sort order within bins. This can be used to create "stacked" dotplots by
setting `order` to a discrete variable:

```{r beeswarm_shape_color_together_stacked, fig.width = small_width, fig.height = small_height}
abcc_df %>%
  ggplot(aes(y = value, x = abc, fill = hi, group = NA, order = hi)) +
  geom_dots(linewidth = 0) +
  scale_color_brewer(palette = "Dark2") +
  ggtitle(
    'geom_dots()',
    'aes(fill = hi, group = NA, order = hi)'
  )
```

### Varying continuous aesthetics within dot groups

Continuous variables can also be varied within groups. Since continuous variables
will not automatically set the `group` aesthetic, we can simply assign them to
the desired aesthetic we want to vary:

```{r beeswarm_shape_color_continuous, fig.width = small_width, fig.height = small_height}
abcc_df %>%
  arrange(hi) %>%
  ggplot(aes(y = value, x = abc, shape = abc, color = value)) +
  geom_dots() +
  ggtitle(
    'geom_dots()',
    'aes(color = value)'
  )
```

## Constraining dot size

When sample sizes can vary widely (and dynamically), it can be difficult to set
a reasonable dot size that works on all charts. In this case, it can be useful
to set constraints on the dot sizes picked by the automatic bin width selection
algorithm.

For example, on very large samples, dots may become smaller than desired. 
Consider the following increasingly large samples:

```{r increasing_samples, fig.width = med_width, fig.height = med_height}
set.seed(1234)

ns = c(50, 200, 500, 5000)
increasing_samples = data.frame(
  x = rgamma(sum(ns), 2, 2),
  n = rep(ns, ns)
)

increasing_samples %>%
  ggplot(aes(x = x)) +
  geom_dots() +
  facet_wrap(~ n) +
  labs(
    title = "geom_dots()",
    subtitle = "on large samples, dots may get too small"
  )
```

The dots become quite small on the 5000-dot dotplot, making it harder to read.

You can set constraints on the desired dot size / bin width by using the `binwidth` 
argument. To set a specific bin width, pass a single value; to set constraints,
pass a length-2 vector, where the first element is the min and the second the max. 
The min can be `0` and the max can be `Inf` if you only want to constrain the
other value (max or min, respectively). The bin width can be in data units 
(using `numeric` values) or in plotting units (using `grid::unit()`s).

For example, we could constrain the dot size to be greater than 1mm:

```{r increasing_samples_min_binwidth, fig.width = med_width, fig.height = med_height}
increasing_samples %>%
  ggplot(aes(x = x)) +
  geom_dots(binwidth = unit(c(1, Inf), "mm")) +
  facet_wrap(~ n) +
  labs(
    title = "geom_dots()",
    subtitle = 'binwidth = unit(c(1.5, Inf), "mm")'
  )
```

Notice how the dots now go off the page and we receive a warning with suggestions on
how to fix the layout. If we set `overflow = "compress"`, instead of overflowing,
the layout will compress the spacing between dots to keep them within the geometry's
bounds:

```{r increasing_samples_min_binwidth_compress, fig.width = med_width, fig.height = med_height}
increasing_samples %>%
  ggplot(aes(x = x)) +
  geom_dots(binwidth = unit(c(1, Inf), "mm"), overflow = "compress", alpha = 0.75) +
  facet_wrap(~ n) +
  labs(
    title = "geom_dots()",
    subtitle = 'binwidth = unit(c(1, Inf), "mm"), overflow = "compress"'
  )
```

These settings give reasonable displays in small sample sizes and scale up
to larger sample sizes without changing settings.

## On discrete distributions

The dots family includes a variety of features to make visualizing discrete and categorical
distributions easier. These distributions can be hard to visualize under the default settings
if the dots become very small:

```{r discrete_dots_too_small, fig.width = small_width, fig.height = small_height}
set.seed(1234)
abcd_df = tibble(
  x = sample(c("a", "b", "c", "d"), 1000, replace = TRUE, prob = c(0.27, 0.6, 0.03, 0.005)),
  g = rep(c("a","b"), 500)
)

abcd_df %>%
  ggplot(aes(x = x)) +
  geom_dots() +
  scale_y_continuous(breaks = NULL) +
  labs(
    title = "geom_dots()",
    subtitle = "on a large discrete sample"
  )
```

The automatic bin width algorithm selects a dot size that is very small in order to ensure
the tallest bin fits in the plot, but this means the dots are hard to see.

Bar-like layouts can be achieved by using `layout = "bar"`:

```{r discrete_dots_bar, fig.width = small_width, fig.height = small_height}
abcd_df %>%
  ggplot(aes(x = x, fill = g, order = g)) +
  geom_dots(layout = "bar", group = NA, color = NA) +
  scale_y_continuous(breaks = NULL) +
  labs(
    title = 'geom_dots(aes(fill = g), layout = "bar", group = NA)',
    subtitle = "on a large discrete sample"
  )
```

Notice how we set `group = NA` to override the default `ggplot2` behavior of 
grouping data by all discrete variables. This allows the layout to be calculated 
taking all groups into account.

We can also use the `smooth` parameter to improve the display of discrete distributions,
for which `geom_dots()` supports a handful of *smoothers*. These all correspond to 
functions that start with `smooth_`, like `smooth_bounded()`, `smooth_unbounded()`, and `smooth_discrete()`, and can be applied either by passing the suffix as a string 
(e.g. `smooth = "bounded"`) or by passing the function itself, to set specific options
on it (e.g. `smooth = smooth_bounded(adjust = 0.5)`).

`smooth_discrete()` applies a kernel density smoother whose default bandwidth is 
less than the distances between bins. We can use the `kernel` argument (passed to
`density_bounded()`; the same kernels from `stats::density()` are available)
to change the shape of the bins. 

For example, using the `"epanechnikov"` (parabolic) kernel along with `side = "both"`,
we can create lozenge-like shapes. We'll abbreviate the kernel `"ep"` to save typing
out `"epanechnikov"` (partial matching is allowed):

```{r discrete_dots_ep, fig.width = small_width, fig.height = small_height}
abcd_df %>%
  ggplot(aes(x = x)) +
  geom_dots(smooth = smooth_discrete(kernel = "ep"), side = "both") +
  scale_y_continuous(breaks = NULL) +
  labs(
    title = 'geom_dots(smooth = smooth_discrete(kernel = "ep"), side = "both")',
    subtitle = "on a large discrete sample"
  )
```


## On analytical distributions

Like the `stat_slabinterval()` family, `stat_dotsinterval()` and `stat_dots()`
support using both sample data (via `x` and `y` aesthetics) or analytical distributions
(via the `xdist` and `ydist` aesthetics). For analytical distributions, these stats 
accept specifications for distributions in one of two ways:

1. **Using distribution names as character vectors**: 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`.

2. **Using distribution vectors from the [distributional](https://pkg.mitchelloharawild.com/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.

For example, here are a variety of distributions:

```{r dotsinterval_dist, fig.width = small_width, fig.height = small_height}
dist_df = tibble(
  dist = c(dist_normal(1,0.25), dist_beta(3,3), dist_gamma(5,5)),
  dist_name = format(dist)
)

dist_df %>%
  ggplot(aes(y = dist_name, xdist = dist)) +
  stat_dotsinterval(subguide = 'integer') +
  ggtitle(
    "stat_dotsinterval(subguide = 'integer')",
    "aes(y = dist_name, xdist = dist)"
  )
```

This example also shows the use of sub-guides to label dot counts. See the documentation
of `subguide_axis()` and its shortcuts (particularly `subguide_integer()` and `subguide_count()`)
for more examples.

Analytical distributions are shown by default using 100 quantiles, sometimes
referred to as a *quantile dotplot*, which can help people make better decisions under uncertainty ([Kay 2016](https://doi.org/10.1145/2858036.2858558), [Fernandes 2018](https://doi.org/10.1145/3173574.3173718)). 
This can be changed using the `quantiles` argument. For example, we can plot the same
distributions again using 1000 quantiles. We'll also make use of `point_interval` to plot
the mode and highest-density continuous intervals (instead of the default median and quantile
intervals; see `point_interval()`).

We'll also highlight some intervals by coloring the dots.
Like with the `stat_slabinterval()` family, computed variables from the interval
sub-geometry (`level` and `.width`) are available to the dots/slab sub-geometry,
and correspond to the smallest interval containing that dot. We can use these
to color dots according to the interval containing them (we'll also use the
`"weave"` layout since it maintains x positions better than the `"bin"` layout):

```{r dotsinterval_dist_1000_level_color, fig.width = small_width, fig.height = small_height}
dist_df %>%
  ggplot(aes(y = dist_name, xdist = dist, slab_fill = after_stat(level))) +
  stat_dotsinterval(quantiles = 1000, point_interval = mode_hdci, layout = "weave", slab_color = NA) +
  scale_color_manual(values = scales::brewer_pal()(3)[-1], aesthetics = "slab_fill") +
  ggtitle(
    "stat_dotsinterval(quantiles = 1000, point_interval = mode_hdci)",
    "aes(y = dist_name, xdist = dist, slab_fill = after_stat(level))"
  )
```

When summarizing sample distributions
with `stat_dots()`/`stat_dotsinterval()` (e.g. samples from Bayesian posteriors),
one can also use the `quantiles` argument, though it is not on by default.


### Varying continuous aesthetics with analytical distributions

While varying discrete aesthetics works similarly with `stat_dotsinterval()`/`stat_dots()`
as it does with `geom_dotsinterval()`/`geom_dots()`, varying continuous aesthetics within
dot groups typically requires mapping the continuous aesthetic *after* the stats
are computed. This is because the stat (at least for analytical distributions) must
first generate the quantiles before properties of those quantiles can be mapped to
aesthetics.

Thus, because it relies upon generated variables from the stat, you can use the
`after_stat()` or `stage()` functions from `ggplot2` to map those variables. For example:

```{r dotsinterval_dist_color, fig.width = small_width, fig.height = small_height}
dist_df %>%
  ggplot(aes(y = dist_name, xdist = dist, slab_color = after_stat(x))) +
  stat_dotsinterval(slab_shape = 19, quantiles = 500) +
  scale_color_distiller(aesthetics = "slab_color", guide = "colorbar2") +
  ggtitle(
    "stat_dotsinterval(slab_shape = 19, quantiles = 500)",
    'aes(slab_color = after_stat(x)) +\nscale_color_distiller(aesthetics = "slab_color", guide = "colorbar2")'
  )
```

This example also demonstrates the use of sub-geometry scales: the `slab_`-prefixed
aesthetics `slab_color` and `slab_shape` must be used to target the color and shape
of the slab ("slab" here refers to the stack of dots) when using `geom_dotsinterval()`
and `stat_dotsinterval()` to disambiguate between the point/interval and the dot stack.
When using `stat_dots()`/`geom_dots()` this is not necessary.

Also note the use of `scale_color_distiller()`, a base ggplot2 color scale, with the
`slab_color` aesthetic by setting the `aesthetics` and `guide` properties (the latter
is necessary because the default `guide = "colorbar"` will not work with non-standard
color aesthetics).

### Thresholds

Another potentially useful application of post-stat aesthetic computation is to
apply thresholds on a dotplot, coloring points on one side of a line differently.
However, the default dotplot layout, `"bin"`, can cause dots to be on the wrong
side of a cutoff when coloring dots within dotplots. Thus it can be useful when
plotting thresholds to use the `"weave"` or `"swarm"` layouts, which tend to 
position dots closer to their true `x` positions, rather than at bin centers:

```{r dist_dots_weave, fig.width = small_width, fig.height = small_height}
ab_df = tibble(
  ab = c("a", "b"),
  mean = c(5, 7),
  sd = c(1, 1.5)
)

ab_df %>%
  ggplot(aes(y = ab, xdist = dist_normal(mean, sd), fill = after_stat(x < 6))) +
  stat_dots(position = "dodge", color = NA, layout = "weave") +
  labs(
    title = 'stat_dots(layout = "weave")',
    subtitle = "aes(fill = after_stat(x < 6))"
  ) +
  geom_vline(xintercept = 6, alpha = 0.25) +
  scale_x_continuous(breaks = 2:10)
```


## Rain cloud 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. We'll also
scale the halfeye slab thickness by `n` (the number of observations in each group)
so that the area of each slab represents sample size (and looks similar to
the total area of its corresponding dotplot).

We'll use a subsample of of the data to show how it might look on a reasonably-sized
dataset.

```{r halfeye_dotplot, fig.width = small_width, fig.height = small_height}
set.seed(12345) # for reproducibility

tibble(
  abc = rep(c("a", "b", "b", "c"), 50),
  value = rnorm(200, c(1, 8, 8, 3), c(1, 1.5, 1.5, 1))
) %>%
  ggplot(aes(y = abc, x = value, fill = abc)) +
  stat_slab(aes(thickness = after_stat(pdf*n)), scale = 0.7) +
  stat_dotsinterval(side = "bottom", scale = 0.7, slab_linewidth = NA) +
  scale_fill_brewer(palette = "Set2") +
  ggtitle(
    paste0(
      'stat_slab(aes(thickness = after_stat(pdf*n)), scale = 0.7) +\n',
      'stat_dotsinterval(side = "bottom", scale = 0.7, slab_linewidth = NA)'
    ),
    'aes(fill = abc)'
  )
```

## Dotplots with Monte Carlo Standard Error

A specialized variant of `geom_dots()`, `geom_blur_dots()`, supports visualizing
dotplots with blur applied to each dot. `stat_mcse_dots()` uses `geom_blur_dots()`
with `posterior::mcse_quantile()` to show the error in each quantile of a quantile
dotplot:

```{r mcse_blur_dots, fig.width=med_width, fig.height=med_height, warning=FALSE, eval=requireNamespace("posterior", quietly = TRUE) && getRversion() >= "4.1"}
increasing_samples %>%
  ggplot(aes(x = x)) +
  stat_mcse_dots(quantiles = 100) +
  facet_wrap(~ n) +
  labs(
    title = "stat_mcse_dots(quantiles = 100)",
    subtitle = "Monte Carlo Standard Error of each quantile shown as blur"
  )
```

Custom blur functions can be selected using the `blur` parameter, including the
built-in `blur_interval()`, which draws an interval with a default width of 95%:

```{r mcse_interval_dots, fig.width=med_width, fig.height=med_height, warning=FALSE, eval=requireNamespace("posterior", quietly = TRUE) && getRversion() >= "4.1"}
increasing_samples %>%
  ggplot(aes(x = x)) +
  stat_mcse_dots(quantiles = 100, blur = "interval") +
  facet_wrap(~ n) +
  labs(
    title = 'stat_mcse_dots(quantiles = 100, blur = "interval")',
    subtitle = "Monte Carlo Standard Error of each quantile shown as 95% intervals"
  )
```


## Logit dotplots

To demonstrate another useful plot type, the *logit dotplot* (courtesy [Ladislas Nalborczyk](https://lnalborczyk.github.io/post/glm/)), we'll fit a 
logistic regression to some data on the petal length of the *Iris versicolor* 
and *Iris virginica* flowers.

First, we'll demo varying the `side` aesthetic to create two dotplots that are
"facing" each other: `scale_side_mirrored()` will set the `side` aesthetic to 
`"top"` or `"bottom"` if two categories are assigned to `side`". We also adjust 
the `scale` so that the dots don't overlap:

```{r iris_v, fig.width = med_width, fig.height = med_height}
iris_v = iris %>%
  filter(Species != "setosa")

iris_v %>%
  ggplot(aes(x = Petal.Length, y = Species, side = Species)) +
  geom_dots(scale = 0.5) +
  scale_side_mirrored(guide = "none") +
  ggtitle(
    "geom_dots(scale = 0.5)",
    'aes(side = Species) + scale_side_mirrored()'
  )
```

This can also be accomplished by setting side directly and omitting
`scale_side_mirrored()`; e.g. via `aes(side = ifelse(Species == "virginica", "bottom", "top"))`.

Now we fit a logistic regression predicting species based on petal length:

```{r m_iris_v}
m = glm(Species == "virginica" ~ Petal.Length, data = iris_v, family = binomial)
m
```

Then we can overlay a fit line as a `stat_lineribbon()` (see `vignette("lineribbon")`)
on top of the mirrored dotplots to create a *logit dotplot*:

```{r logit_dotplot, fig.width = med_width, fig.height = med_height/1.5}
# construct a prediction grid for the fit line
prediction_grid = with(iris_v,
  data.frame(Petal.Length = seq(min(Petal.Length), max(Petal.Length), length.out = 100))
)

prediction_grid %>%
  bind_cols(predict(m, ., se.fit = TRUE)) %>%
  mutate(
    # distribution describing uncertainty in log odds
    log_odds = dist_normal(fit, se.fit),
    # inverse-logit transform the log odds to get
    # distribution describing uncertainty in Pr(Species == "virginica")
    p_virginica = dist_transformed(log_odds, plogis, qlogis)
  ) %>%
  ggplot(aes(x = Petal.Length)) +
  geom_dots(
    aes(y = as.numeric(Species == "virginica"), side = Species),
    scale = 0.4,
    data = iris_v
  ) +
  stat_lineribbon(
    aes(ydist = p_virginica), alpha = 1/4, fill = "#08306b"
  ) +
  scale_side_mirrored(guide = "none") +
  coord_cartesian(ylim = c(0, 1)) +
  labs(
    title = "logit dotplot: geom_dots() with stat_lineribbon()",
    subtitle = 'aes(side = Species) + scale_side_mirrored()',
    x = "Petal Length",
    y = "Pr(Species = virginica)"
  )
```



```{r reset_options, include=FALSE}
options(.old_options)
```
