Hands-on Exercise 04b - Visualising Uncertainty

Author

Ong Chae Hui

1. Visualizing the uncertainty of point estimates

  • A point estimate is a single number, such as a mean.
  • Uncertainty is expressed as standard error, confidence interval, or credible interval
  • Important:
    • Don’t confuse the uncertainty of a point estimate with the variation in the sample

2. Getting Started

2.1. Installing and Loading the required R Packages

In this exercise using Exam_data, we will be using tidyverse, plotly, crosstalk, DT, ggdist and gganimate.

Code 
pacman::p_load(tidyverse, plotly, crosstalk, DT, ggdist, gganimate)

2.2. Importing Data (Exam_data)

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

2.3. Visualizing the uncertainty of point estimates: ggplot2 methods

The code chunk below performs the followings:

  • group the observation by RACE,
  • computes the count of observations, mean, standard deviation and standard error of Maths by RACE, and
  • save the output as a tibble data table called my_sum.
Code 
my_sum <- exam %>%
  group_by(RACE) %>%
  summarise(
    n=n(),
    mean=mean(MATHS),
    sd=sd(MATHS)
    ) %>%
  mutate(se=sd/sqrt(n-1))

my_sum
# A tibble: 4 × 5
  RACE        n  mean    sd    se
  <chr>   <int> <dbl> <dbl> <dbl>
1 Chinese   193  76.5  15.7  1.13
2 Indian     12  60.7  23.4  7.04
3 Malay     108  57.4  21.1  2.04
4 Others      9  69.7  10.7  3.79

Next, the code chunk below will

Code 
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

2.4. Visualizing the uncertainty of point estimates: ggplot2 methods

The code chunk below is used to reveal the standard error of mean maths score by race.

Code 
ggplot(my_sum) +
  geom_errorbar(
    aes(x=RACE, 
        ymin=mean-se, 
        ymax=mean+se), 
    width=0.2, 
    colour="black", 
    alpha=0.9, 
    linewidth=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 race")

2.5. Visualizing the uncertainty of point estimates: ggplot2 methods

Plotting the 95% confidence interval of mean maths score by race. The error bars are sorted by the average maths scores.

Code 
my_sum2 <- exam %>%
  group_by(RACE) %>%
  summarise(
    n=n(),
    mean=mean(MATHS),
    sd=sd(MATHS)
    ) %>%
  mutate(se=sd/sqrt(n-1)) %>%
  mutate(ci95= qt(c(0.05, 0.95), length(n) - 1) * se) %>%
  mutate(ci99= qt(c(0.01, 0.99), length(n) - 1) * se)

my_sum2$RACE = with(my_sum2, reorder(RACE, -mean))

ggplot(my_sum2) +
  geom_errorbar(
    aes(x=RACE, 
        ymin=mean-ci95, 
        ymax=mean+ci95), 
    width=0.2, 
    colour="black", 
    alpha=0.9, 
    linewidth=0.5) +
  geom_point(aes
           (x=RACE, 
            y=mean), 
           stat="identity", 
           color="red",
           size = 1.5,
           alpha=1) +
  ggtitle("95% Confidence Interval of mean maths score by race")

2.6. Visualizing the uncertainty of point estimates with interactive error bars

Interactive error bars for the 99% confidence interval of mean maths score by race.

Code 
colnames(my_sum) <- c('Race', 'No. of pupils','Avg Scores','Std Dev','Std Error')
colnames(my_sum2) <- c('Race', 'No. of pupils','Avg Scores','Std Dev','Std Error', '95% CI', '99% CI')

DT::datatable(my_sum, class= "compact")
Code 
d <- highlight_key(my_sum)

p <- ggplot(my_sum2) +
      geom_errorbar(
        aes(x=Race, 
            ymin=`Avg Scores`-`99% CI`, 
            ymax=`Avg Scores`+`99% CI`), 
        width=0.2, 
        colour="black", 
        alpha=0.9, 
        linewidth=0.5) +
      geom_point(aes
               (x=Race, 
                y=`Avg Scores`, 
                text=paste("N=",`No. of pupils`,"<br>99% CI=",`99% CI`)), 
               stat="identity", 
               color="red",
               size = 1.5,
               alpha=1) +
      ggtitle("99% Confidence Interval of \n mean maths score by race")


gg <- highlight(ggplotly(p), tooltip="text")
#                "plotly_selected")  

crosstalk::bscols(gg,               
                  DT::datatable(d), 
                  widths = 5)

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.

NOTE: This function comes with many arguments, refer to the syntax reference here for more detail.

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

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

3.2. Visualizing the uncertainty of point estimates: ggdist methods

Showing the plots with 95% and 99% confidence intervals.

Code 
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")

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.

NOTE: This function comes with many arguments, refer to the syntax reference here for more detail.

Code 
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")

4. Visualising Uncertainty with Hypothetical Outcome Plots (HOPs)

Step 1: Installing ungeviz package (only need to perform this step once1)

Code 
# devtools::install_github("wilkelab/ungeviz")

Step 2: Launch the application in R

Code 
library(ungeviz)
Code 
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)

5. Visualising Uncertainty with Hypothetical Outcome Plots (HOPs)

Code 
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)