Hands On Exercise 4 - Visualise Uncertainty

Author

You Ting QUEK

Published

May 1, 2024

Modified

May 2, 2024

Learning Objectives

Visualising uncertainty is relatively new in statistical graphics. In this chapter, you will gain hands-on experience on creating statistical graphics for visualising uncertainty. By the end of this chapter you will be able:

  • to plot statistics error bars by using ggplot2,

  • to plot interactive error bars by combining ggplot2, plotly and DT,

  • to create advanced by using ggdist, and

  • to create hypothetical outcome plots (HOPs) by using ungeviz package.

Loading the packages

pacman::p_load(ungeviz, plotly, crosstalk,
               DT, ggdist, ggridges,
               colorspace, gganimate, tidyverse)
devtools::install_github("wilkelab/ungeviz")

Importing data

exam <- read_csv("data/Exam_data.csv")

Visualizing the uncertainty of point estimates using ggplot2 methods

A point estimate is a single number, such as a mean. Uncertainty, on the other hand, is expressed as standard error, confidence interval, or credible interval.

The code chunk below will be used to derive the necessary summary statistics.

my_sum <- exam %>%
  group_by(RACE) %>%
  summarise(
    n=n(),
    mean=mean(MATHS),
    sd=sd(MATHS)
    ) %>%
  mutate(se=sd/sqrt(n-1))
Tip

  • group_by() of dplyr package is used to group the observation by RACE,

  • summarise() is used to compute the count of observations, mean, standard deviation

  • mutate() is used to derive standard error of Maths by RACE, and

  • the output is save as a tibble data table called my_sum.

code chunk below will be used to display my_sum tibble data frame in an html table format.

knitr::kable(head(my_sum), format = 'html')
RACE n mean sd se
Chinese 193 76.50777 15.69040 1.132357
Indian 12 60.66667 23.35237 7.041005
Malay 108 57.44444 21.13478 2.043177
Others 9 69.66667 10.72381 3.791438

Plot the standard error bars of mean maths score by race as shown below.

ggplot(my_sum) +
  geom_errorbar(
    aes(x=RACE, 
        ymin=mean-se, 
        ymax=mean+se), 
    width=0.2, 
    colour="black", 
    alpha=0.9, 
    size=0.5) +
  geom_point(aes
           (x=RACE, 
            y=mean), 
           stat="identity", 
           color="red",
           size = 1.5,
           alpha=1) +
  ggtitle("Standard error of mean maths score by rac")

Plotting confidence interval of point estimates

Instead of plotting the standard error bar of point estimates, we can also plot the confidence intervals of mean maths score by race.

ggplot(my_sum) +
  geom_errorbar(
    aes(x=reorder(RACE, -mean), 
        ymin=mean-1.96*se, 
        ymax=mean+1.96*se), 
    width=0.2, 
    colour="black", 
    alpha=0.9, 
    size=0.5) +
  geom_point(aes
           (x=RACE, 
            y=mean), 
           stat="identity", 
           color="red",
           size = 1.5,
           alpha=1) +
  labs(x = "Maths score",
       title = "95% confidence interval of mean maths score by race")

Visualizing the uncertainty of point estimates with interactive error bars

Plotting the interactive error bars for the 99% confidence interval of mean maths score by race as shown in the figure below.

shared_df = SharedData$new(my_sum)

bscols(widths = c(4,8),
       ggplotly((ggplot(shared_df) +
                   geom_errorbar(aes(
                     x=reorder(RACE, -mean),
                     ymin=mean-2.58*se, 
                     ymax=mean+2.58*se), 
                     width=0.2, 
                     colour="black", 
                     alpha=0.9, 
                     size=0.5) +
                   geom_point(aes(
                     x=RACE, 
                     y=mean, 
                     text = paste("Race:", `RACE`, 
                                  "<br>N:", `n`,
                                  "<br>Avg. Scores:", round(mean, digits = 2),
                                  "<br>95% CI:[", 
                                  round((mean-2.58*se), digits = 2), ",",
                                  round((mean+2.58*se), digits = 2),"]")),
                     stat="identity", 
                     color="red", 
                     size = 1.5, 
                     alpha=1) + 
                   xlab("Race") + 
                   ylab("Average Scores") + 
                   theme_minimal() + 
                   theme(axis.text.x = element_text(
                     angle = 45, vjust = 0.5, hjust=1)) +
                   ggtitle("99% Confidence interval of average /<br>maths scores by race")), 
                tooltip = "text"), 
       DT::datatable(shared_df, 
                     rownames = FALSE, 
                     class="compact", 
                     width="100%", 
                     options = list(pageLength = 10,
                                    scrollX=T), 
                     colnames = c("No. of pupils", 
                                  "Avg Scores",
                                  "Std Dev",
                                  "Std Error")) %>%
         formatRound(columns=c('mean', 'sd', 'se'),
                     digits=2))

Visualising Uncertainty with ggdist2 packages

  • ggdist2 is designed for both frequentist and Bayesian uncertainty visualization, taking the view that uncertainty visualization can be unified through the perspective of distribution visualization:

  • for frequentist models, one visualises confidence distributions or bootstrap distributions (see vignette(“freq-uncertainty-vis”));

  • for Bayesian models, one visualises probability distributions (see the tidybayes package, which builds on top of ggdist).

Visualizing the uncertainty of point estimates: ggdist methods

Using stat_pointinterval() of ggdist is used to build a visual for displaying distribution of maths scores by race.

exam %>%
  ggplot(aes(x = RACE, 
             y = MATHS)) +
  stat_pointinterval() +
  labs(
    title = "Visualising confidence intervals of mean math score",
    subtitle = "Mean Point + Multiple-interval plot")

This function however comes with many arguments and some interesting ones are as follows:

.width = 0.95 .point = median .interval = qi (quantile interval, qi; highest-density interval, hdi; or highest-density continuous interval, hdci) .inherit.aes = If FALSE, overrides the default aesthetics, rather than combining with them. This is most useful for helper functions that define both data and aesthetics and shouldn’t inherit behaviour from the default plot specification, e.g. borders().

exam %>%
  ggplot(aes(x = RACE, y = MATHS)) +
  stat_pointinterval(.width = 0.95,
  .point = median,
  .interval = qi) +
  labs(
    title = "Visualising confidence intervals of median math score",
    subtitle = "Median Point + Multiple-interval plot")

Visualizing the uncertainty of point estimates: ggdist methods

exam %>%
  ggplot(aes(x = RACE, 
             y = MATHS)) +
  stat_pointinterval(
    show.legend = FALSE) +   
  labs(
    title = "Visualising confidence intervals of mean math score",
    subtitle = "Mean Point + Multiple-interval plot")

Visualising Uncertainty with Hypothetical Outcome Plots (HOPs)

Step 1:

devtools::install_github("wilkelab/ungeviz")

Step 2: Launch the app in R

library(ungeviz)
ggplot(data = exam, 
       (aes(x = factor(RACE), y = MATHS))) +
  geom_point(position = position_jitter(
    height = 0.3, width = 0.05), 
    size = 0.4, color = "#0072B2", alpha = 1/2) +
  geom_hpline(data = sampler(25, group = RACE), height = 0.6, color = "#D55E00") +
  theme_bw() + 
  # `.draw` is a generated column indicating the sample draw
  transition_states(.draw, 1, 3)