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Hypothetical outcome plots (HOPs) and quantile dotplots for proportions

Here is a quick example of two frequency-framing approaches to visualizing the uncertainty in a proportion: hypothetical outcome plots (HOPs), which are useful when you are using a medium that supports animation, and quantile dotplots, which are useful when you are using a medium that does not support animation.

Setup

The following libraries are needed:

library(tidyverse)
library(modelr)
library(rstanarm)
library(tidybayes)
library(gganimate)     # devtools::install_github("thomasp85/gganimate")
library(ggstance)
library(forcats)

theme_set(
  theme_light() +
  theme(panel.grid = element_blank())
)

Data

We’ll use some count data to illustrate:

df = data_frame(
  group = c("A","B","C"),
  count = c(100, 50, 30),
  proportion = count / sum(count)
)
df
## # A tibble: 3 x 3
##   group count proportion
##   <chr> <dbl>      <dbl>
## 1 A       100      0.556
## 2 B        50      0.278
## 3 C        30      0.167

Model

One possible model for this data is as follows (N.B. this makes some strong assumptions about how the data were generated for the purposes of an example, your mileage may vary!):

m = stan_glm(count ~ group, family = poisson, data = df)

Hypothetical outcome plots (HOPs)

Given that model, we could construct a HOPs (Hullman, Resnick, and Adar 2015; Kale et al. 2019) bar chart illustrating the posterior distribution for the proportion in each group:

n_hops = 100

p = df %>%
  data_grid(group) %>%
  add_fitted_draws(m, n = n_hops) %>%
  group_by(.draw) %>%
  mutate(proportion = .value / sum(.value)) %>%
  ggplot(aes(y = group, x = proportion)) +
  geom_colh(fill = "gray75") +
  geom_point(data = df, color = "red") +
  annotate("text", y = "C", x = .5, label = "Observed proportion", hjust = 0, color = "red") +
  annotate("segment", y = "C", yend = "C", x = .18, xend = .49, linetype = "dashed", color = "red") +
  annotate("text", y = 2.7, x = .5, label = "Posterior distribution for proportion", hjust = 0,
    color = "gray35") +
  annotate("segment", y = 2.7, yend = 2.7, x = .1, xend = .49, linetype = "dashed", color = "gray75") +
  xlim(0,1) +
  transition_states(.draw, transition_length = 1, state_length = 1)

animate(p, nframes = n_hops * 2, width = 600, height = 300)

Quantile dotplots

If animation were not available (e.g. in a print medium), an alternative might be a quantile dotplot (Kay et al. 2016; Fernandes et al. 2018):

observed_label_data = data_frame(
  group = "C",
  label = "Observed proportion",
  x = .18, xend = .44, y = .55
)
dotplot_label_data = data_frame(
  group = "C",
  label = "100 approximately equally likely proportions",
  x = .18, xend = .44, y = .3
)


df %>%
  data_grid(group) %>%
  add_fitted_draws(m) %>%
  group_by(.draw) %>%
  mutate(proportion = .value / sum(.value)) %>%
  group_by(group) %>%
  do(data_frame(proportion = quantile(.$proportion, ppoints(100)))) %>%
  ggplot(aes(x = proportion)) +
  geom_dotplot(binwidth = .01, fill = "gray65", color = NA) +
  facet_grid(fct_rev(group) ~ .) +
  geom_text(aes(xend + .01, y, label = label), data = observed_label_data, hjust = 0, color = "red") +
  geom_segment(aes(x, y, xend = xend, yend = y), data = observed_label_data,
    linetype = "dashed", color = "red") +
  geom_vline(aes(xintercept = proportion), data = df, color = "red") +
  geom_text(aes(xend + .01, y, label = label), data = dotplot_label_data, hjust = 0, color = "gray35") +
  geom_segment(aes(x, y, xend = xend, yend = y), data = dotplot_label_data,
    linetype = "dashed", color = "gray65") +
  xlim(0,1) +
  ylab(NULL) +
  scale_y_continuous(breaks = NULL)

References

Fernandes, Michael, Logan Walls, Sean Munson, Jessica Hullman, and Matthew Kay. 2018. “Uncertainty Displays Using Quantile Dotplots or CDFs Improve Transit Decision-Making.” Conference on Human Factors in Computing Systems - CHI ’18. https://doi.org/10.1145/3173574.3173718.

Hullman, Jessica, Paul Resnick, and Eytan Adar. 2015. “Hypothetical Outcome Plots Outperform Error Bars and Violin Plots for Inferences about Reliability of Variable Ordering.” PloS One 10 (11). Public Library of Science. https://doi.org/10.1371/journal.pone.0142444.

Kale, Alex, Francis Nguyen, Matthew Kay, and Jessica Hullman. 2019. “Hypothetical Outcome Plots Help Untrained Observers Judge Trends in Ambiguous Data.” Transactions on Visualization and Computer Graphics.

Kay, Matthew, Tara Kola, Jessica R Hullman, and Sean A Munson. 2016. “When (ish) is My Bus? User-centered Visualizations of Uncertainty in Everyday, Mobile Predictive Systems.” Proceedings of the 2016 CHI Conference on Human Factors in Computing Systems - CHI ’16, 5092–5103. https://doi.org/10.1145/2858036.2858558.