pacman::p_load(ggstatsplot, tidyverse)Hands-on Exercise 4
4a. Visual Statistical Analysis
4.1 Learning Outcome
In this hands-on exercise, we will gain hands-on experience on using:
ggstatsplot package to create visual graphics with rich statistical information,
performance package to visualise model diagnostics, and
parameters package to visualise model parameters
4.2 Visual Statistical Analysis with ggstatsplot
ggstatsplot is an extension of ggplot2 package for creating graphics with details from statistical tests included in the information-rich plots themselves. - To provide alternative statistical inference methods by default. - To follow best practices for statistical reporting. For all statistical tests reported in the plots, the default template abides by the APA gold standard for statistical reporting. For example, here are results from a robust t-test:
4.3 Getting started
4.3.1 Installing and launching R packages
In this exercise, ggstatsplot and tidyverse will be used.
4.3.2 Importing data
exam <- read_csv("data/Exam_data.csv")Rows: 322 Columns: 7
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (4): ID, CLASS, GENDER, RACE
dbl (3): ENGLISH, MATHS, SCIENCE
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.4.3.3 One-sample test: gghistostats() method
In the code chunk below, gghistostats() is used to to build an visual of one-sample test on English scores.
set.seed(1234)
gghistostats(
data = exam,
x = ENGLISH,
type = "bayes",
test.value = 60,
xlab = "English scores"
)
4.3.4 Unpacking the Bayes Factor
A Bayes factor is the ratio of the likelihood of one particular hypothesis to the likelihood of another. It can be interpreted as a measure of the strength of evidence in favor of one theory among two competing theories.
That’s because the Bayes factor gives us a way to evaluate the data in favor of a null hypothesis, and to use external information to do so. It tells us what the weight of the evidence is in favor of a given hypothesis.
When we are comparing two hypotheses, H1 (the alternate hypothesis) and H0 (the null hypothesis), the Bayes Factor is often written as B10. It can be defined mathematically as
- The Schwarz criterion is one of the easiest ways to calculate rough approximation of the Bayes Factor.
ggbetweenstats(
data = exam,
x = GENDER,
y = MATHS,
type = "np",
messages = FALSE
)
4.3.5 How to interpret Bayes Factor
A Bayes Factor can be any positive number. One of the most common interpretations is this one—first proposed by Harold Jeffereys (1961) and slightly modified by Lee and Wagenmakers in 2013:
4.3.6 Two-sample mean test: ggbetweenstats()
In the code chunk below, ggbetweenstats() is used to build a visual for two-sample mean test of Maths scores by gender.
ggbetweenstats(
data = exam,
x = GENDER,
y = MATHS,
type = "np",
messages = FALSE
)
Default information: - statistical details - Bayes Factor - sample sizes - distribution summary
4.3.7 Oneway ANOVA Test: ggbetweenstats() method
In the code chunk below, ggbetweenstats() is used to build a visual for One-way ANOVA test on English score by race.
ggbetweenstats(
data = exam,
x = RACE,
y = ENGLISH,
type = "p",
mean.ci = TRUE,
pairwise.comparisons = TRUE,
pairwise.display = "s",
p.adjust.method = "fdr",
messages = FALSE
)
- “ns” → only non-significant
- “s” → only significant
- “all” → everything
4.3.7.1 ggbetweenstats - Summary of tests
4.3.8 Significant Test of Correlation: ggscatterstats()
In the code chunk below, ggscatterstats() is used to build a visual for Significant Test of Correlation between Maths scores and English scores.
ggscatterstats(
data = exam,
x = MATHS,
y = ENGLISH,
marginal = FALSE,
)
4.3.9 Significant Test of Association (Depedence) : ggbarstats() methods
In the code chunk below, the Maths scores is binned into a 4-class variable by using cut().
exam1 <- exam %>%
mutate(MATHS_bins =
cut(MATHS,
breaks = c(0,60,75,85,100))
)In this code chunk below ggbarstats() is used to build a visual for Significant Test of Association
ggbarstats(exam1,
x = MATHS_bins,
y = GENDER)
4.4 visualising Models
In this section, we will learn how to visualize model diagnostic and model parameters by using parameters package.
- Toyota Corolla case study will be used. The purpose of study is to build a model to discover factors affecting prices of used-cars by taking into consideration a set of explanatory variables.
4.5 Getting Started
4.6 Installing and loading the required libraries
pacman::p_load(readxl, performance, parameters, see)4.6.1 Importing Excel file: readxl methods
In the code chunk below, read_xls() of readxl package is used to import the data worksheet of ToyotaCorolla.xls workbook into R.
car_resale <- read_xls("data/ToyotaCorolla.xls",
"data")
car_resale# A tibble: 1,436 × 38
Id Model Price Age_08_04 Mfg_Month Mfg_Year KM Quarterly_Tax Weight
<dbl> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 81 TOYOTA … 18950 25 8 2002 20019 100 1180
2 1 TOYOTA … 13500 23 10 2002 46986 210 1165
3 2 TOYOTA … 13750 23 10 2002 72937 210 1165
4 3 TOYOTA… 13950 24 9 2002 41711 210 1165
5 4 TOYOTA … 14950 26 7 2002 48000 210 1165
6 5 TOYOTA … 13750 30 3 2002 38500 210 1170
7 6 TOYOTA … 12950 32 1 2002 61000 210 1170
8 7 TOYOTA… 16900 27 6 2002 94612 210 1245
9 8 TOYOTA … 18600 30 3 2002 75889 210 1245
10 44 TOYOTA … 16950 27 6 2002 110404 234 1255
# ℹ 1,426 more rows
# ℹ 29 more variables: Guarantee_Period <dbl>, HP_Bin <chr>, CC_bin <chr>,
# Doors <dbl>, Gears <dbl>, Cylinders <dbl>, Fuel_Type <chr>, Color <chr>,
# Met_Color <dbl>, Automatic <dbl>, Mfr_Guarantee <dbl>,
# BOVAG_Guarantee <dbl>, ABS <dbl>, Airbag_1 <dbl>, Airbag_2 <dbl>,
# Airco <dbl>, Automatic_airco <dbl>, Boardcomputer <dbl>, CD_Player <dbl>,
# Central_Lock <dbl>, Powered_Windows <dbl>, Power_Steering <dbl>, …Notice that the output object car_resale is a tibble data frame.
4.6.2 Multiple Regression Model using lm()
The code chunk below is used to calibrate a multiple linear regression model by using lm() of Base Stats of R.
model <- lm(Price ~ Age_08_04 + Mfg_Year + KM +
Weight + Guarantee_Period, data = car_resale)
model
Call:
lm(formula = Price ~ Age_08_04 + Mfg_Year + KM + Weight + Guarantee_Period,
data = car_resale)
Coefficients:
(Intercept) Age_08_04 Mfg_Year KM
-2.637e+06 -1.409e+01 1.315e+03 -2.323e-02
Weight Guarantee_Period
1.903e+01 2.770e+01 4.6.3 Model Diagnostic: checking for multicolinearity:
In the code chunk, check_collinearity() of performance package.
check_collinearity(model)# Check for Multicollinearity
Low Correlation
Term VIF VIF 95% CI Increased SE Tolerance Tolerance 95% CI
KM 1.46 [ 1.37, 1.57] 1.21 0.68 [0.64, 0.73]
Weight 1.41 [ 1.32, 1.51] 1.19 0.71 [0.66, 0.76]
Guarantee_Period 1.04 [ 1.01, 1.17] 1.02 0.97 [0.86, 0.99]
High Correlation
Term VIF VIF 95% CI Increased SE Tolerance Tolerance 95% CI
Age_08_04 31.07 [28.08, 34.38] 5.57 0.03 [0.03, 0.04]
Mfg_Year 31.16 [28.16, 34.48] 5.58 0.03 [0.03, 0.04]check_c <- check_collinearity(model)
plot(check_c)Variable `Component` is not in your data frame :/
4.6.4 Model Diagnostic: checking normality assumption
In the code chunk, check_normality() of performance package.
model1 <- lm(Price ~ Age_08_04 + KM +
Weight + Guarantee_Period, data = car_resale)check_n <- check_normality(model1)plot(check_n)
4.6.5 Model Diagnostic: Check model for homogeneity of variances
In the code chunk, check_heteroscedasticity() of performance package.
check_h <- check_heteroscedasticity(model1)plot(check_h)
4.6.6 Model Diagnostic: Complete check
We can also perform the complete check by using check_model().
check_model(model1)
4.6.7 Visualising Regression Parameters: see methods
In the code below, plot() of see package and parameters() of parameters package is used to visualise the parameters of a regression model.
plot(parameters(model1))
4.6.8 Visualising Regression Parameters: ggcoefstats() methods
In the code below, ggcoefstats() of ggstatsplot package to visualise the parameters of a regression model.
ggcoefstats(model1,
output = "plot")
4b. Visualizing Uncertainty
4.1 Learning Outcome
4.2 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
pacman::p_load(tidyverse, plotly, crosstalk, DT, ggdist, gganimate)exam <- read_csv("data/Exam_data.csv")Rows: 322 Columns: 7
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (4): ID, CLASS, GENDER, RACE
dbl (3): ENGLISH, MATHS, SCIENCE
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.4.2.1 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.
my_sum <- exam %>%
group_by(RACE) %>%
summarise(
n=n(),
mean=mean(MATHS),
sd=sd(MATHS)
) %>%
mutate(se=sd/sqrt(n-1))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 |
4.2.2 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.
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")Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
ℹ Please use `linewidth` instead.
4.2.3 Visualizing the uncertainty of point estimates: ggplot2 methods
Note
Plot the 95% confidence interval of mean maths score by race. The error bars should be sorted by the average maths scores.
4.2.4 Visualizing the uncertainty of point estimates with interactive error bars
Note
Plot interactive error bars for the 99% confidence interval of mean maths score by race.
Warning in geom_point(aes(x = RACE, y = mean, text = paste("Race:", RACE, :
Ignoring unknown aesthetics: text4.3 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).
4.3.1 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")
4.3.2 Visualizing the uncertainty of point estimates: ggdist methods
The below chart shows the confidence interval.
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")
4.3.3 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")Warning: fill_type = "gradient" is not supported by the current graphics device.
- Falling back to fill_type = "segments".
- If you believe your current graphics device *does* support
fill_type = "gradient" but auto-detection failed, set that option
explicitly and consider reporting a bug.
- See help("geom_slabinterval") for more information.
4.4 Visualising Uncertainty with Hypothetical Outcome Plots (HOPs)
Step 1: Installing ungeviz package
devtools::install_github("wilkelab/ungeviz")Skipping install of 'ungeviz' from a github remote, the SHA1 (aeae12b0) has not changed since last install.
Use `force = TRUE` to force installationStep 2: Launch the application 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)Warning in geom_hpline(data = sampler(25, group = RACE), height = 0.6, color =
"#D55E00"): Ignoring unknown parameters: `height`Warning: Using the `size` aesthetic in this geom was deprecated in ggplot2 3.4.0.
ℹ Please use `linewidth` in the `default_aes` field and elsewhere instead.
4.5 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)Warning in geom_hpline(data = sampler(25, group = RACE), height = 0.6, color =
"#D55E00"): Ignoring unknown parameters: `height`
4c. Funnel Plots for Fair Comparisons
4.1 Overview
Funnel plot is a specially designed data visualisation for conducting unbiased comparison between outlets, stores or business entities. By the end of this hands-on exercise, you will gain hands-on experience on:
- plotting funnel plots by using funnelPlotR package,
- plotting static funnel plot by using ggplot2 package, and
- plotting interactive funnel plot by using both plotly R and ggplot2 packages.
4.2 Installing and Launching R Packages
In this exercise, four R packages will be used. They are:
- readr for importing csv into R.
- FunnelPlotR for creating funnel plot.
- ggplot2 for creating funnel plot manually.
- knitr for building static html table.
- plotly for creating interactive funnel plot.
pacman::p_load(tidyverse, FunnelPlotR, plotly, knitr)4.3 Importing Data
In this section, COVID-19_DKI_Jakarta will be used. The data was downloaded from Open Data Covid-19 Provinsi DKI Jakarta portal. For this hands-on exercise, we are going to compare the cumulative COVID-19 cases and death by sub-district (i.e. kelurahan) as at 31st July 2021, DKI Jakarta.
The code chunk below imports the data into R and save it into a tibble data frame object called covid19.
covid19 <- read_csv("data/COVID-19_DKI_Jakarta.csv") %>%
mutate_if(is.character, as.factor)Rows: 267 Columns: 7
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (3): City, District, Sub-district
dbl (4): Sub-district ID, Positive, Recovered, Death
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.4.4 FunnelPlotR methods
FunnelPlotR package uses ggplot to generate funnel plots. It requires a numerator (events of interest), denominator (population to be considered) and group. The key arguments selected for customisation are:
- limit: plot limits (95 or 99).
- label_outliers: to label outliers (true or false).
- Poisson_limits: to add Poisson limits to the plot.
- OD_adjust: to add overdispersed limits to the plot.
- xrange and yrange: to specify the range to display for axes, acts like a zoom function.
- Other aesthetic components such as graph title, axis labels etc.
4.4.1 FunnelPlotR methods: The basic plot
The code chunk below plots a funnel plot.
funnel_plot(
numerator = covid19$Positive,
denominator = covid19$Death,
group = covid19$`Sub-district`
)
A funnel plot object with 267 points of which 0 are outliers.
Plot is adjusted for overdispersion. Things to learn from the code chunk above.
- group in this function is different from the scatterplot. Here, it defines the level of the points to be plotted i.e. Sub-district, District or City. If Cityc is chosen, there are only six data points.
- By default, data_typeargument is “SR”.
- limit: Plot limits, accepted values are: 95 or 99, corresponding to 95% or 99.8% quantiles of the distribution.
4.4.2 FunnelPlotR methods: Makeover 1
The code chunk below plots a funnel plot.
funnel_plot(
numerator = covid19$Death,
denominator = covid19$Positive,
group = covid19$`Sub-district`,
data_type = "PR", #<<
xrange = c(0, 6500), #<<
yrange = c(0, 0.05) #<<
)Warning: The `xrange` argument deprecated; please use the `x_range` argument
instead. For more options, see the help: `?funnel_plot`Warning: The `yrange` argument deprecated; please use the `y_range` argument
instead. For more options, see the help: `?funnel_plot`
A funnel plot object with 267 points of which 7 are outliers.
Plot is adjusted for overdispersion. Things to learn from the code chunk above. + data_type argument is used to change from default “SR” to “PR” (i.e. proportions). + xrange and yrange are used to set the range of x-axis and y-axis
4.4.3 FunnelPlotR methods: Makeover 2
The code chunk below plots a funnel plot.
funnel_plot(
numerator = covid19$Death,
denominator = covid19$Positive,
group = covid19$`Sub-district`,
data_type = "PR",
xrange = c(0, 6500),
yrange = c(0, 0.05),
label = NA,
title = "Cumulative COVID-19 Fatality Rate by Cumulative Total Number of COVID-19 Positive Cases", #<<
x_label = "Cumulative COVID-19 Positive Cases", #<<
y_label = "Cumulative Fatality Rate" #<<
)Warning: The `xrange` argument deprecated; please use the `x_range` argument
instead. For more options, see the help: `?funnel_plot`Warning: The `yrange` argument deprecated; please use the `y_range` argument
instead. For more options, see the help: `?funnel_plot`
A funnel plot object with 267 points of which 7 are outliers.
Plot is adjusted for overdispersion. Things to learn from the code chunk above.
- label = NA argument is to removed the default label outliers feature.
- title argument is used to add plot title.
- x_label and y_label arguments are used to add/edit x-axis and y-axis titles.
4.5 Funnel Plot for Fair Visual Comparison: ggplot2 methods
In this section, you will gain hands-on experience on building funnel plots step-by-step by using ggplot2. It aims to enhance you working experience of ggplot2 to customise speciallised data visualisation like funnel plot.
4.5.1 Computing the basic derived fields
To plot the funnel plot from scratch, we need to derive cumulative death rate and standard error of cumulative death rate.
df <- covid19 %>%
mutate(rate = Death / Positive) %>%
mutate(rate.se = sqrt((rate*(1-rate)) / (Positive))) %>%
filter(rate > 0)Next, the fit.mean is computed by using the code chunk below.
fit.mean <- weighted.mean(df$rate, 1/df$rate.se^2)4.5.2 Calculate lower and upper limits for 95% and 99.9% CI
The code chunk below is used to compute the lower and upper limits for 95% confidence interval.
number.seq <- seq(1, max(df$Positive), 1)
number.ll95 <- fit.mean - 1.96 * sqrt((fit.mean*(1-fit.mean)) / (number.seq))
number.ul95 <- fit.mean + 1.96 * sqrt((fit.mean*(1-fit.mean)) / (number.seq))
number.ll999 <- fit.mean - 3.29 * sqrt((fit.mean*(1-fit.mean)) / (number.seq))
number.ul999 <- fit.mean + 3.29 * sqrt((fit.mean*(1-fit.mean)) / (number.seq))
dfCI <- data.frame(number.ll95, number.ul95, number.ll999,
number.ul999, number.seq, fit.mean)4.5.3 Plotting a static funnel plot
In the code chunk below, ggplot2 functions are used to plot a static funnel plot.
p <- ggplot(df, aes(x = Positive, y = rate)) +
geom_point(aes(label=`Sub-district`),
alpha=0.4) +
geom_line(data = dfCI,
aes(x = number.seq,
y = number.ll95),
size = 0.4,
colour = "grey40",
linetype = "dashed") +
geom_line(data = dfCI,
aes(x = number.seq,
y = number.ul95),
size = 0.4,
colour = "grey40",
linetype = "dashed") +
geom_line(data = dfCI,
aes(x = number.seq,
y = number.ll999),
size = 0.4,
colour = "grey40") +
geom_line(data = dfCI,
aes(x = number.seq,
y = number.ul999),
size = 0.4,
colour = "grey40") +
geom_hline(data = dfCI,
aes(yintercept = fit.mean),
size = 0.4,
colour = "grey40") +
coord_cartesian(ylim=c(0,0.05)) +
annotate("text", x = 1, y = -0.13, label = "95%", size = 3, colour = "grey40") +
annotate("text", x = 4.5, y = -0.18, label = "99%", size = 3, colour = "grey40") +
ggtitle("Cumulative Fatality Rate by Cumulative Number of COVID-19 Cases") +
xlab("Cumulative Number of COVID-19 Cases") +
ylab("Cumulative Fatality Rate") +
theme_light() +
theme(plot.title = element_text(size=12),
legend.position = c(0.91,0.85),
legend.title = element_text(size=7),
legend.text = element_text(size=7),
legend.background = element_rect(colour = "grey60", linetype = "dotted"),
legend.key.height = unit(0.3, "cm"))Warning in geom_point(aes(label = `Sub-district`), alpha = 0.4): Ignoring
unknown aesthetics: labelp
4.5.4 Interactive Funnel Plot: plotly + ggplot2
The funnel plot created using ggplot2 functions can be made interactive with ggplotly() of plotly r package.
fp_ggplotly <- ggplotly(p,
tooltip = c("label",
"x",
"y"))
fp_ggplotly