devtools::install_github("wilkelab/ungeviz")Hands-on Exercise 4c: Visualizing Uncertainty
1 Getting Started
In this exercise, we will use the following our R packages.
tidyverse, a family of R packages for data science process,
plotly for creating interactive plot,
gganimate for creating animation plot,
DT for displaying interactive html table,
crosstalk for for implementing cross-widget interactions (currently, linked brushing and filtering), and
ggdist for visualising distribution and uncertainty.
The code chunk below uses p_load() of pacman package to check if these packages are installed in the computer and load them onto your working R environment.
pacman::p_load(ungeviz, plotly, crosstalk,
DT, ggdist, ggridges,
colorspace, gganimate, tidyverse)The code chunk below imports exam_data.csv into R environment by using read_csv() function of readr package.
exam <- read.csv("data/Exam_data.csv")The code chunk below uses summary()to summarize the data.
summary(exam) ID CLASS GENDER RACE
Length:322 Length:322 Length:322 Length:322
Class :character Class :character Class :character Class :character
Mode :character Mode :character Mode :character Mode :character
ENGLISH MATHS SCIENCE
Min. :21.00 Min. : 9.00 Min. :15.00
1st Qu.:59.00 1st Qu.:58.00 1st Qu.:49.25
Median :70.00 Median :74.00 Median :65.00
Mean :67.18 Mean :69.33 Mean :61.16
3rd Qu.:78.00 3rd Qu.:85.00 3rd Qu.:74.75
Max. :96.00 Max. :99.00 Max. :96.00 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.
Important
- Don’t confuse the uncertainty of a point estimate with the variation in the sample
In this section, you will learn how to plot error bars of maths scores by race by using data provided in exam tibble data frame.
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))
Things to learn from the code chunk above
group_by()of dplyr package is used to group the observation by RACE,summarise()is used to compute the count of observations, mean, standard deviationmutate()is used to derive standard error of Maths by RACE, andthe output is save as a tibble data table called my_sum.
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
The below plot shows the standard error bars of mean maths score by race.
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 race")
Things to learn from the code chunk above
The error bars are computed by using the formula mean+/-se.
For
geom_point(), it is important to indicate stat=“identity”.
2.2 Plotting confidence interval of point estimates
The below plot shows 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")
Things to learn from the code chunk above
The confidence intervals are computed by using the formula mean+/-1.96*se.
The error bars is sorted by using the average maths scores.
labs()argument of ggplot2 is used to change the x-axis label.
2.3 Visualizing the uncertainty of point estimates with interactive error bars
In this section, we will show 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 Visualizing 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.
Code
exam %>%
ggplot(aes(x = RACE,
y = MATHS)) +
stat_pointinterval(.width = 0.95,
.point = median,
.interval = qi) +
labs(title = "Visualizing confidence intervals of mean math score",
subtitle = "Mean Point + Multiple-interval plot")
In the code chunk below, stat_gradientinterval() of ggdist is used to build a visual for displaying distribution of maths scores by race.
Code
exam %>%
ggplot(aes(x = RACE,
y = MATHS)) +
stat_gradientinterval(
fill = "skyblue",
show.legend = TRUE
) +
labs(
title = "Visualizing confidence intervals of mean math score",
subtitle = "Gradient + interval plot")
4 Visualizing Uncertainty with Hypothetical Outcome Plots (HOPs)
Launch the application in R
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() +
transition_states(.draw, 1, 3)