Hands-on Exercise 4.3: Visualising Uncertainty

1 Getting Started

1.1 Install and loading R packages.

devtools::install_github("wilkelab/ungeviz")

pacman::p_load(ungeviz, plotly, crosstalk, DT, ggdist, ggridges, colorspace, gganimate, tidyverse)

1.2 Importing the data

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

2 Visualizing the uncertainty of point estimates: 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.

Firstly, 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))

Next, the 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

2.1 Plotting standard error bars of point estimates

Now we are ready to 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")

2.2 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")

2.3 Visualizing the uncertainty of point estimates with interactive error bars

Learning how to plot 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))

3 Visualising Uncertainty: ggdist package

ggdist is an R package that provides a flexible set of ggplot2 geoms and stats designed especially for visualising distributions and uncertainty.

It 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).

3.1 Visualizing the uncertainty of point estimates: ggdist methods

In the code chunk below, 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")

For example, in the code chunk below the following arguments are used:

• width = 0.95

• point = median

• interval = qi

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")

3.2 Visualizing the uncertainty of point estimates: ggdist methods

Makeover the plot on previous slide by showing 95% and 99% confidence intervals.

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")

exam %>%
  ggplot(aes(x = RACE, y = MATHS)) +
  stat_pointinterval(
    .width = c(0.95, 0.99),
    .point = median,
    .interval = qi
  ) +
  labs(
    title = "Visualising confidence intervals of median math score",
    subtitle = "Median Point + Multiple-interval plot"
  )

3.3 Visualizing the uncertainty of point estimates: ggdist methods

In the code chunk below, stat_gradientinterval() of ggdist is used to build a visual for displaying distribution of maths scores by race.

exam %>%
  ggplot(aes(x = RACE, 
             y = MATHS)) +
  stat_gradientinterval(   
    fill = "skyblue",      
    show.legend = TRUE     
  ) +                        
  labs(
    title = "Visualising confidence intervals of mean math score",
    subtitle = "Gradient + interval plot")

3.4 Visualising Uncertainty with Hypothetical Outcome Plots (HOPs)

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)

3.5 Visualising Uncertainty with Hypothetical Outcome Plots (HOPs)

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() + 
  transition_states(.draw, 1, 3)