From c0639d1d9c8fca9b3959b74336ac59557a6a146f Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Wed, 15 Nov 2023 17:21:59 -0500 Subject: [PATCH] rebuild work on Ch 03 --- 03-multivariate_plots.qmd | 68 ++++++++++++++++++-- R/common.R | 1 + R/penguin/peng-ggplot.R | 2 +- R/penguin/peng-mosaic.R | 18 ++++++ R/penguin/penguin-colors.R | 2 +- bib/pkgs.bib | 8 +++ bib/pkgs.txt | 2 + child/03-data-ellipse.qmd | 35 ++++++---- docs/03-multivariate_plots.html | 100 ++++++++++++++++++++++------- docs/90-references.html | 3 + docs/figs/fig-peng-ggdensity-1.png | Bin 285276 -> 284720 bytes docs/figs/fig-peng-ggpairs1-1.png | Bin 0 -> 949901 bytes docs/figs/fig-peng-mosaic-1.png | Bin 0 -> 152607 bytes docs/index.html | 4 +- docs/search.json | 8 +-- figs/fig-peng-ggdensity-1.png | Bin 285276 -> 284720 bytes figs/fig-peng-ggpairs1-1.png | Bin 0 -> 949901 bytes figs/fig-peng-mosaic-1.png | Bin 0 -> 152607 bytes 18 files changed, 200 insertions(+), 51 deletions(-) create mode 100644 R/penguin/peng-mosaic.R create mode 100644 docs/figs/fig-peng-ggpairs1-1.png create mode 100644 docs/figs/fig-peng-mosaic-1.png create mode 100644 figs/fig-peng-ggpairs1-1.png create mode 100644 figs/fig-peng-mosaic-1.png diff --git a/03-multivariate_plots.qmd b/03-multivariate_plots.qmd index 12c8c123..77420a5d 100644 --- a/03-multivariate_plots.qmd +++ b/03-multivariate_plots.qmd @@ -399,7 +399,11 @@ The most basic version is provided by `pairs()` in base R. When one variable is considered as an outcome or response, it is usually helpful to put this in the first row and column. For the `Prestige` data, in addition to income and education, we also have a measure of % women in each occupational category. -Plotting these together gives @fig-prestige-pairs. + +Plotting these together gives @fig-prestige-pairs. In such plots, the diagonal cells +give labels for the variables, but they are also a guide to interpreting what is shown. +In each row, say row 2 for `income`, income is the vertical $y$ variable in plots against other +variables. In each column, say column 3 for `education`, education is the horizonal $x$ variable. ```{r} #| label: fig-prestige-pairs @@ -413,14 +417,23 @@ pairs(~ prestige + income + education + women, The plots in the first row show what we have seen before for the relations between prestige and income and education, adding to those the plot of prestige vs. % women. Plots in the first column show the same data, but with $x$ and $y$ interchanged. -A more feature-rich version is provided by `car::scatterplotMatrix()` which +But this basic `pairs()` plot is very limited. A more feature-rich version is provided by `car::scatterplotMatrix()` which can add the regression lines, loess smooths and data ellipses for each -pair. The diagonal panels show density curves for the distribution of each -variable; for example, the distribution of education appears to be multi-modal +pair, as shown in @fig-prestige-spm1. + +The diagonal panels show density curves for the distribution of each +variable; for example, the distribution of `education` appears to be multi-modal and that of `women` shows that most of the occupations have a low percentage -of women. The combination of the regression line with the loess smoothed +of women. + +The combination of the regression line with the loess smoothed curve, but without their confidence envelopes, provides about the right amount of detail to take in at a glance where the relations are non-linear. +We've already seen (@fig-Prestige-scatterplot-income1) +the non-linear relation between prestige and income +(row 1, column 2) when occupational type is ignored. +But all relations with income in column 2 are non-linear, reinforcing +our idea (@sec-log-scale) that effects of income should be assessed on a log scale. ```{r} #| label: fig-prestige-spm1 @@ -497,7 +510,7 @@ have similar size and shape in most of the plots. From the boxplots, we can also see that `r colorize("Adelie", "orange")` penguins have shorter bill lengths than the others, while `r colorize("Gentoo", "green")` penguins have smaller bill depth, but longer flippers and are heavier -than r colorize("Chinstrap", "purple")` and `r colorize("Adelie", "orange")` +than `r colorize("Chinstrap", "purple")` and `r colorize("Adelie", "orange")` penguins. @@ -517,7 +530,7 @@ peng.mod <- lm(cbind(bill_length, bill_depth, flipper_length, body_mass) ~ speci Hypothesis-error (HE) plots, described in @sec-vis-mlm provide a better summary of the evidence for the MANOVA test of differences among means on all variables together. These give an $\mathbf{H}$ ellipse reflecting the differences among means, to be compared with -an $\mathbf{E}$ ellipse reflecting within-group variation. +an $\mathbf{E}$ ellipse reflecting within-group variation and a visual test of significance A related question is "how well are the penguin species distinguished by these body size measures?" Here, the relevant model is linear discriminant analysis (LDA), where `species` plays the role of the response in the model, @@ -547,6 +560,47 @@ _Discrete Data Analysis with R_ [@FriendlyMeyer:2016:DDAR] and the **vcdExtra** package for mosaic plots and mosaic matrices. **TODO** Mosaic matrix of species, island & sex. +For example, we can tabulate the distributions of penguin species by sex and the island +where they were observed using `xtabs()`. `ftable()` prints this three-way table more compactly. + +```{r peng-table} +# use better labels for sex +peng <- peng |> + mutate(sex = factor(sex, labels = c("Female", "Male"))) +peng.table <- xtabs(~ species + sex + island, data = peng) + +ftable(peng.table) +``` + +We can see immediately that the penguin species differ by island: +only Adelie were observed on all three islands; Biscoe Island had no Chinstraps +and Dream Island had no Gentoos. + +`vcd::pairs()` produces all pairwise mosaic plots, as shown in @fig-peng-mosaic. +The diagonal panels show the one-way +frequencies by width of the divided bars. Each off-diagonal panel shows the bivariate +counts, breaking down each column variable by splitting the bars in proportion to a +second variable. Consequently, the frequency of each cell is represented by its' area. +The purpose is to show the pattern of association between each pair, +and so, the tiles in the mosaic are shaded according to the signed residual +in a simple $\chi^2$ test for association--- `r colorize("blue", "blue")` +where the observed frequency is greater than expected under independence, and +`r colorize("red", "red")` where it is less than expected. + + +```{r} +#| label: fig-peng-mosaic +#| fig-width: 7 +#| fig-height: 7 +#| out-width: "100%" +#| fig-cap: "Mosaic pairs plot for the combinations of species, sex and island. ..." +library(vcd) +pairs(peng.table, shade = TRUE) +``` + +The shading patterns in cells (1,3) and (3,1) of @fig-peng-mosaic show what we've seen before in the table of frequencies: The distribution of species varies across island. Row 2 and column 2 +show that there is sex is roughly proportional among species and islands. + The next step, by John Emerson and others [@Emerson-etal:2013] was to recognize that combinations of continuous and discrete, categorical variables could be plotted diff --git a/R/common.R b/R/common.R index b7d1521e..b0404e85 100644 --- a/R/common.R +++ b/R/common.R @@ -104,6 +104,7 @@ $\\newcommand*{\\diag}[1]{\\ensuremath{\\mathrm{diag}\\, #1}}$ "lattice", "datasauRus", "vcd", + "vcdExtra", "palmerpenguins") # write list of packages used at end of every chapter diff --git a/R/penguin/peng-ggplot.R b/R/penguin/peng-ggplot.R index d16162ac..ba46bc45 100644 --- a/R/penguin/peng-ggplot.R +++ b/R/penguin/peng-ggplot.R @@ -10,7 +10,7 @@ library(ggdensity) library(patchwork) load(here::here("data", "peng.RData")) -str(peng) +#str(peng) source("R/penguin-colors.R") diff --git a/R/penguin/peng-mosaic.R b/R/penguin/peng-mosaic.R new file mode 100644 index 00000000..6537886a --- /dev/null +++ b/R/penguin/peng-mosaic.R @@ -0,0 +1,18 @@ +#' --- +#' title: Penguins data, mosaic plots +#' --- + +load(here::here("data", "peng.RData")) +source("R/penguin-colors.R") + +library(vcdExtra) + +# change levels of sex +peng <- peng |> + mutate(sex = factor(sex, labels = c("Female", "Male"))) + +peng.table <- xtabs(~ species + sex + island, data = peng) + +ftable(peng.table) + +pairs(peng.table, shade = TRUE) diff --git a/R/penguin/penguin-colors.R b/R/penguin/penguin-colors.R index 12335f5d..505daabe 100644 --- a/R/penguin/penguin-colors.R +++ b/R/penguin/penguin-colors.R @@ -45,7 +45,7 @@ theme_penguins <- function(shade=c("medium", "light", "dark"), ...) { shade = match.arg(shade) list(scale_color_penguins(shade=shade), scale_fill_penguins(shade=shade) - ) + ) } diff --git a/bib/pkgs.bib b/bib/pkgs.bib index 9f1fa31a..19957625 100644 --- a/bib/pkgs.bib +++ b/bib/pkgs.bib @@ -350,6 +350,14 @@ @Manual{R-tidyverse } +@Manual{R-vcdExtra, + title = {vcdExtra: vcd Extensions and Additions}, + author = {Michael Friendly}, + year = {2023}, + note = {R package version 0.8-5}, + url = {https://friendly.github.io/vcdExtra/}, +} + @Manual{R-VisCollin, title = {VisCollin: Visualizing Collinearity Diagnostics}, author = {Michael Friendly}, diff --git a/bib/pkgs.txt b/bib/pkgs.txt index 82e4617c..9372d2f1 100644 --- a/bib/pkgs.txt +++ b/bib/pkgs.txt @@ -34,11 +34,13 @@ ggdensity ggplot2 graphics grDevices +grid methods patchwork stats tidyr utils +vcd base bayestestR car diff --git a/child/03-data-ellipse.qmd b/child/03-data-ellipse.qmd index d8f29b6b..98f0f125 100644 --- a/child/03-data-ellipse.qmd +++ b/child/03-data-ellipse.qmd @@ -272,7 +272,8 @@ scatterplot(prestige ~ education, data=Prestige, ``` -#### Plotting on a log scale +#### Plotting on a log scale {#sec-log-scale} + A typical remedy for the non-linear relationship of income to prestige is to plot income on a log scale. This usually makes sense, and expresses a belief that a **multiple** of or **percentage increase** in income has a constant impact on prestige, as opposed to the **additive** interpretation for income itself. @@ -360,13 +361,14 @@ higher occupational category. A different plot entails a different story. #| echo: false #| fig-align: center #| out-width: "80%" -#| fig-cap: "Penguin species observed in the Palmer Archipelago. Image: Allison Horst" +#| fig-cap: "Penguin species observed in the Palmer Archipelago. This is a cartoon, but it illustrates some features of penguin body size measurements, and the colors typically used for species. Image: Allison Horst" knitr::include_graphics("images/penguins-horst.png") ``` The `penguins` dataset from the **palmerpenguins** package [@R-palmerpenguins] provides further instructive examples of plots and analyses of multivariate data. The data consists of measurements of body size (flipper length, body mass, bill length and depth) of 344 penguins collected at the [Palmer Research Station](https://pallter.marine.rutgers.edu/) in Antartica. + There were three different species of penguins (Adélie, Chinstrap & Gentoo) collected from 3 islands in the Palmer Archipelago between 2007--2009 [@Gorman2014]. The purpose was to examine differences in size or appearance of these species, @@ -398,9 +400,11 @@ use `ggplot2` for these plots. I'll be using the penguins data quite a lot, so it is useful to set up custom colors like those used in @fig-penguin-species. These are shades of: -Adelie: `r colorize("orange", "orange")`, -Chinstrap: `r colorize("purple", "purple")`, and -Gentoo: `r colorize("green", "green")`. To use these in `ggplot2` I define a function +* `r colorize("Adelie", "orange")`: `r colorize("orange", "orange")`, +* `r colorize("Chinstrap", "purple")`: `r colorize("purple", "purple")`, and +* Gentoo: `r colorize("green", "green")`. + +To use these in `ggplot2` I define a function `peng.colors()` that allows shades of light, medium and dark and then functions `scale_*_penguins()` for color and fill. @@ -441,13 +445,16 @@ scale_colour_penguins <- function(shade=c("medium", "light", "dark"), ...){ scale_color_penguins <- scale_colour_penguins ``` -This is used to define a `theme_penguins` that I use to simply change the color and fill scales +This is used to define a `theme_penguins()` function that I use to simply change the color and fill scales for plots below. ```{r} -theme_penguins <- list( - scale_color_penguins(shade="dark"), - scale_fill_penguins(shade="dark")) +theme_penguins <- function(shade=c("medium", "light", "dark"), ...) { + shade = match.arg(shade) + list(scale_color_penguins(shade=shade), + scale_fill_penguins(shade=shade) + ) +} ``` @@ -468,7 +475,7 @@ ggplot(peng, geom_smooth(method = "loess", formula = y ~ x, linewidth = 1.5, se = FALSE, alpha=0.1) + stat_ellipse(geom = "polygon", level = 0.95, alpha = 0.2) + - theme_penguins + + theme_penguins("dark") + theme(legend.position = c(0.85, 0.15)) ``` @@ -495,11 +502,11 @@ ggplot(peng, stat_ellipse(geom = "polygon", level = 0.95, alpha = 0.2) + stat_ellipse(geom = "polygon", level = 0.68, alpha = 0.2) + stat_ellipse(geom = "polygon", level = 0.40, alpha = 0.2) + - theme_penguins + + theme_penguins("dark") + theme(legend.position = c(0.85, 0.15)) ``` -#### Nonparamteric bivariate density plots +#### Nonparamtric bivariate density plots While I emphasize data ellipses (because I like their beautiful geometry), other visual summaries of the bivariate density are possible and often useful. @@ -541,7 +548,7 @@ p1 <- ggplot(peng, geom_density_2d(linewidth = 1.1, bins = 8) + ggtitle("geom_density_2d") + theme_bw(base_size = 14) + - theme_penguins + + theme_penguins() + theme(legend.position = c(0.85, 0.15)) p2 <- ggplot(peng, @@ -551,7 +558,7 @@ p2 <- ggplot(peng, geom_hdr(probs = c(0.95, 0.68, 0.4), show.legend = FALSE) + ggtitle("ggdensity::geom_hdr") + theme_bw(base_size = 14) + - theme_penguins + + theme_penguins() + theme(legend.position = "none") p1 + p2 diff --git a/docs/03-multivariate_plots.html b/docs/03-multivariate_plots.html index f531362c..f7bb2767 100644 --- a/docs/03-multivariate_plots.html +++ b/docs/03-multivariate_plots.html @@ -708,7 +708,7 @@

+

3.1.4.4 Plotting on a log scale

A typical remedy for the non-linear relationship of income to prestige is to plot income on a log scale. This usually makes sense, and expresses a belief that a multiple of or percentage increase in income has a constant impact on prestige, as opposed to the additive interpretation for income itself.

For example, the slope of the linear regression line in Figure 3.11 is given by coef(lm(prestige ~ income, data=Prestige))[2] = 0.003. Multiplying this by 1000 says that a $1000 increase in income is associated with with an average increase of prestige of 2.9.

@@ -763,11 +763,12 @@

-
Figure 3.16: Penguin species observed in the Palmer Archipelago. Image: Allison Horst
+
Figure 3.16: Penguin species observed in the Palmer Archipelago. This is a cartoon, but it illustrates some features of penguin body size measurements, and the colors typically used for species. Image: Allison Horst
-

The penguins dataset from the palmerpenguins package (Horst, Hill, and Gorman 2022) provides further instructive examples of plots and analyses of multivariate data. The data consists of measurements of body size (flipper length, body mass, bill length and depth) of 344 penguins collected at the Palmer Research Station in Antartica. There were three different species of penguins (Adélie, Chinstrap & Gentoo) collected from 3 islands in the Palmer Archipelago between 2007–2009 (Gorman, Williams, and Fraser 2014). The purpose was to examine differences in size or appearance of these species, particularly differences among the sexes (sexual dimorphism) in relation to foraging and habitat.

+

The penguins dataset from the palmerpenguins package (Horst, Hill, and Gorman 2022) provides further instructive examples of plots and analyses of multivariate data. The data consists of measurements of body size (flipper length, body mass, bill length and depth) of 344 penguins collected at the Palmer Research Station in Antartica.

+

There were three different species of penguins (Adélie, Chinstrap & Gentoo) collected from 3 islands in the Palmer Archipelago between 2007–2009 (Gorman, Williams, and Fraser 2014). The purpose was to examine differences in size or appearance of these species, particularly differences among the sexes (sexual dimorphism) in relation to foraging and habitat.

Here I use a slightly altered version of the dataset, peng, renaming variables to remove the units, making factors of character variables and deleting a few cases with missing data.

data(penguins, package = "palmerpenguins")
@@ -795,7 +796,8 @@ 

#> $ year : int [1:333] 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007 ...

There are quite a few variables to choose for illustrating data ellipses in scatterplots. Here I focus on the measures of their bills, bill_length and bill_depth (indicating curvature) and show how to use ggplot2 for these plots.

-

I’ll be using the penguins data quite a lot, so it is useful to set up custom colors like those used in Figure 3.16. These are shades of: Adelie: orange, Chinstrap: purple, and Gentoo: green. To use these in ggplot2 I define a function peng.colors() that allows shades of light, medium and dark and then functions scale_*_penguins() for color and fill.

+

I’ll be using the penguins data quite a lot, so it is useful to set up custom colors like those used in Figure 3.16. These are shades of: * Adelie: orange, * Chinstrap: purple, and * Gentoo: green.

+

To use these in ggplot2 I define a function peng.colors() that allows shades of light, medium and dark and then functions scale_*_penguins() for color and fill.

Code
peng.colors <- function(shade=c("medium", "light", "dark")) {
   shade = match.arg(shade)
@@ -831,11 +833,14 @@ 

scale_color_penguins <- scale_colour_penguins

-

This is used to define a theme_penguins that I use to simply change the color and fill scales for plots below.

+

This is used to define a theme_penguins() function that I use to simply change the color and fill scales for plots below.

-
theme_penguins <- list(
-  scale_color_penguins(shade="dark"),
-  scale_fill_penguins(shade="dark"))
+
theme_penguins <- function(shade=c("medium", "light", "dark"), ...) {
+  shade = match.arg(shade)
+  list(scale_color_penguins(shade=shade),
+       scale_fill_penguins(shade=shade)
+      )
+}

An initial plot using ggplot2 shown in Figure 3.17 uses color and point shape to distinguish the three penguin species. I annotate the plot of points using the linear regression lines, loess smooths to check for non-linearity and 95% data ellipses to show precision of the linear relation.

@@ -848,7 +853,7 @@

geom_smooth(method = "loess", formula = y ~ x, linewidth = 1.5, se = FALSE, alpha=0.1) + stat_ellipse(geom = "polygon", level = 0.95, alpha = 0.2) + - theme_penguins + + theme_penguins("dark") + theme(legend.position = c(0.85, 0.15))

@@ -867,7 +872,7 @@

stat_ellipse(geom = "polygon", level = 0.95, alpha = 0.2) + stat_ellipse(geom = "polygon", level = 0.68, alpha = 0.2) + stat_ellipse(geom = "polygon", level = 0.40, alpha = 0.2) + - theme_penguins + + theme_penguins("dark") + theme(legend.position = c(0.85, 0.15))

@@ -876,8 +881,8 @@

-3.1.4.7 Nonparamteric bivariate density plots

+

+3.1.4.7 Nonparamtric bivariate density plots

While I emphasize data ellipses (because I like their beautiful geometry), other visual summaries of the bivariate density are possible and often useful.

For a single variable, stats::density() and ggplot2::geom_density() calculate a smoothed estimate of the density using nonparametric kernel methods (Silverman 1986) whose smoothness is controlled by a bandwidth parameter, analogous to the span in a loess smoother. This idea extends to two (and more) variables (Scott 1992). For bivariate data, MASS::kde2d() estimates the density on a square \(n \times n\) grid over the ranges of the variables.

ggplot2 provides geom_density_2d() which uses MASS::kde2d() and displays these as contours— horizontal slices of the 3D surface at equally-spaced heights and projects these onto the 2D plane. The ggdensity package (Otto and Kahle 2023) extends this with geom_hdr(), computing the high density regions that bound given levels of probability and maps these to the alpha transparency aesthetic. A method argument allows you to specify various nonparametric (method ="kde" is the default) and parametric (method ="mvnorm" gives normal data ellipses) ways to estimate the underlying bivariate distribution.

@@ -892,7 +897,7 @@

geom_density_2d(linewidth = 1.1, bins = 8) + ggtitle("geom_density_2d") + theme_bw(base_size = 14) + - theme_penguins + + theme_penguins() + theme(legend.position = c(0.85, 0.15)) p2 <- ggplot(peng, @@ -902,7 +907,7 @@

geom_hdr(probs = c(0.95, 0.68, 0.4), show.legend = FALSE) + ggtitle("ggdensity::geom_hdr") + theme_bw(base_size = 14) + - theme_penguins + + theme_penguins() + theme(legend.position = "none") p1 + p2 @@ -916,7 +921,8 @@

3.2 Scatterplot matrices

Going beyond bivariate scatterplots, a pairs plot (or scatterplot matrix) displays all possible \(p \times p\) pairs of \(p\) variables in a matrix-like display where variables \((x_i, x_j)\) are shown in a plot for row \(i\), column \(j\). This idea, due to Hartigan (1975), uses small multiple plots, so that the eye can easily scan across a row or down a column to see how a given variable is related to all the others.

-

The most basic version is provided by pairs() in base R. When one variable is considered as an outcome or response, it is usually helpful to put this in the first row and column. For the Prestige data, in addition to income and education, we also have a measure of % women in each occupational category. Plotting these together gives Figure 3.20.

+

The most basic version is provided by pairs() in base R. When one variable is considered as an outcome or response, it is usually helpful to put this in the first row and column. For the Prestige data, in addition to income and education, we also have a measure of % women in each occupational category.

+

Plotting these together gives Figure 3.20. In such plots, the diagonal cells give labels for the variables, but they are also a guide to interpreting what is shown. In each row, say row 2 for income, income is the vertical \(y\) variable in plots against other variables. In each column, say column 3 for education, education is the horizonal \(x\) variable.

pairs(~ prestige + income + education + women,
       data=Prestige)
@@ -928,7 +934,9 @@

\(x\) and \(y\) interchanged.

-

A more feature-rich version is provided by car::scatterplotMatrix() which can add the regression lines, loess smooths and data ellipses for each pair. The diagonal panels show density curves for the distribution of each variable; for example, the distribution of education appears to be multi-modal and that of women shows that most of the occupations have a low percentage of women. The combination of the regression line with the loess smoothed curve, but without their confidence envelopes, provides about the right amount of detail to take in at a glance where the relations are non-linear.

+

But this basic pairs() plot is very limited. A more feature-rich version is provided by car::scatterplotMatrix() which can add the regression lines, loess smooths and data ellipses for each pair, as shown in Figure 3.21.

+

The diagonal panels show density curves for the distribution of each variable; for example, the distribution of education appears to be multi-modal and that of women shows that most of the occupations have a low percentage of women.

+

The combination of the regression line with the loess smoothed curve, but without their confidence envelopes, provides about the right amount of detail to take in at a glance where the relations are non-linear. We’ve already seen (Figure 3.11) the non-linear relation between prestige and income (row 1, column 2) when occupational type is ignored. But all relations with income in column 2 are non-linear, reinforcing our idea (Section 3.1.4.4) that effects of income should be assessed on a log scale.

scatterplotMatrix(~ prestige + income + education + women,
   data=Prestige,
@@ -979,7 +987,7 @@ 

Adelie penguins have shorter bill lengths than the others, while Gentoo penguins have smaller bill depth, but longer flippers and are heavier than Chinstrap and Adelie penguins.

@@ -995,7 +1003,7 @@

peng.mod <- lm(cbind(bill_length, bill_depth, flipper_length, body_mass) ~ species, 
                data=peng)

-

Hypothesis-error (HE) plots, described in Chapter 9 provide a better summary of the evidence for the MANOVA test of differences among means on all variables together. These give an \(\mathbf{H}\) ellipse reflecting the differences among means, to be compared with an \(\mathbf{E}\) ellipse reflecting within-group variation.

+

Hypothesis-error (HE) plots, described in Chapter 9 provide a better summary of the evidence for the MANOVA test of differences among means on all variables together. These give an \(\mathbf{H}\) ellipse reflecting the differences among means, to be compared with an \(\mathbf{E}\) ellipse reflecting within-group variation and a visual test of significance

A related question is “how well are the penguin species distinguished by these body size measures?” Here, the relevant model is linear discriminant analysis (LDA), where species plays the role of the response in the model,

peng.lda <- MASS:lda( species ~ cbind(bill_length, bill_depth, flipper_length, body_mass), 
@@ -1006,14 +1014,59 @@ 

3.2.1 Generalized pairs plots

-

When a dataset contains one or more discrete variables, the traditional pairs plot provides cannot cope, using only color and/or point symbols to represent categorical variables. In the context of mosaic displays and loglinear models, representing \(n\)-way frequency tables by rectangular tiles depicting cell frequencies, I (Friendly 1994) proposed an analog of the scatterplot matrix using mosaic plots for each pair of variables. The vcd package (Meyer, Zeileis, and Hornik 2023) implements very general pairs() methods for "table" objects. See my book Discrete Data Analysis with R (Friendly and Meyer 2016)

+

When a dataset contains one or more discrete variables, the traditional pairs plot cannot cope, using only color and/or point symbols to represent categorical variables. In the context of mosaic displays and loglinear models, representing \(n\)-way frequency tables by rectangular tiles depicting cell frequencies, I (Friendly 1994) proposed an analog of the scatterplot matrix using mosaic plots for each pair of variables. The vcd package (Meyer, Zeileis, and Hornik 2023) implements very general pairs() methods for "table" objects. See my book Discrete Data Analysis with R (Friendly and Meyer 2016) and the vcdExtra (Friendly 2023) package for mosaic plots and mosaic matrices.

+

TODO Mosaic matrix of species, island & sex. For example, we can tabulate the distributions of penguin species by sex and the island where they were observed using xtabs(). ftable() prints this three-way table more compactly.

+
+
# use better labels for sex
+peng <- peng |>
+  mutate(sex = factor(sex, labels = c("Female", "Male")))
+peng.table <- xtabs(~ species + sex + island, data = peng)
+
+ftable(peng.table)
+#>                  island Biscoe Dream Torgersen
+#> species   sex                                 
+#> Adelie    Female            22    27        24
+#>           Male              22    28        23
+#> Chinstrap Female             0    34         0
+#>           Male               0    34         0
+#> Gentoo    Female            58     0         0
+#>           Male              61     0         0
+
+

We can see immediately that the penguin species differ by island: only Adelie were observed on all three islands; Biscoe Island had no Chinstraps and Dream Island had no Gentoos.

+

vcd::pairs() produces all pairwise mosaic plots, as shown in Figure 3.24. The diagonal panels show the one-way frequencies by width of the divided bars. Each off-diagonal panel shows the bivariate counts, breaking down each column variable by splitting the bars in proportion to a second variable. Consequently, the frequency of each cell is represented by its’ area. The purpose is to show the pattern of association between each pair, and so, the tiles in the mosaic are shaded according to the signed residual in a simple \(\chi^2\) test for association— blue where the observed frequency is greater than expected under independence, and red where it is less than expected.

+
+
library(vcd)
+pairs(peng.table, shade = TRUE)
+
+
+

+
Figure 3.24: Mosaic pairs plot for the combinations of species, sex and island. …
+
+
+
+

The shading patterns in cells (1,3) and (3,1) of Figure 3.24 show what we’ve seen before in the table of frequencies: The distribution of species varies across island. Row 2 and column 2 show that there is sex is roughly proportional among species and islands.

The next step, by John Emerson and others (Emerson et al. 2013) was to recognize that combinations of continuous and discrete, categorical variables could be plotted in different ways.

  • two continuous variables can be shown as a standard scatterplot of points and/or bivariate density contours, or simply by numeric summaries such as a correlation value;
  • a pair of one continuous and one categorical variable can be shown as side-by-side boxplots or violin plots, histograms or density plots
  • two categorical variables could be shown in a mosaic plot or by grouped bar plots.
-

In the ggplot2 framework, these displays are implemented in the GGally package (Schloerke et al. 2021)

+

In the ggplot2 framework, these displays are implemented in the GGally package (Schloerke et al. 2021) in the ggpairs() function. This allows different plot types to be shown in the lower and upper triangles and in the diagonal cells of the plot matrix. As well, aesthetics such as color and shape can be used within the plots to distinguish groups directly. As illustrated below, you can define custom functions to control exactly what is plotted in any panel.

+

The basic, default plot shows scatterplots for pairs of continuous variables in the lower triangle and the values of correlations in the upper triangle. A combination of a discrete and continuous variable is plotted as histograms in the lower triangle and boxplots in the upper triangle. Figure 3.25 includes sex to illustrate the combinations.

+
+
ggpairs(peng, columns=c(3:6, 7),
+        aes(color=species, alpha=0.5),
+        progress = FALSE) +
+  theme_penguins()
+
+
+

+
Figure 3.25: Basic ggpairs() plot of penguin size variables and sex, stratified by species.
+
+
+
+

To my eye, printing the values of correlations in the upper triangle is often a waste of graphic space. But this example shows something peculiar and interesting if you look closely: In all pairs among the penguin size measurements, there are positive correlations within each species, as we can see in Figure 3.23. Yet in three of these panels, the overall correlation ignoring species is negative. For example the overall correlation between bill depth and flipper length is \(r = -0.579\) in row 2, column 3; the scatterplot in the diagonally opposite cell, row 3, column 2 shows the data. These cases, of differing signs for an overall correlation, ignoring a group variable and the within group correlations are examples of Simpson’s Paradox, explored later in Chapter XX.

+

The last row and column, for sex in Figure 3.25, provides an initial glance at the issue of sex differences among pengiun species that motivated the collection of these data. …

3.3 Parallel coordinate plots

As we have seen above, scatterplot matrices and generalized pairs plots extend data visualization to multivariate data, but these variables share one 2D space, and resolution decreases as the number of variable increase. You need a very large screen or sheet of paper to see more than, say 5-6 variables with any clarity.

@@ -1022,8 +1075,8 @@

-
#> 16  packages used here:
-#>  base, car, carData, corrgram, datasets, dplyr, GGally, ggdensity, ggplot2, graphics, grDevices, methods, patchwork, stats, tidyr, utils
+
#> 18  packages used here:
+#>  base, car, carData, corrgram, datasets, dplyr, GGally, ggdensity, ggplot2, graphics, grDevices, grid, methods, patchwork, stats, tidyr, utils, vcd
@@ -1065,6 +1118,9 @@

Friendly, Michael. 1994. “Mosaic Displays for Multi-Way Contingency Tables.” Journal of the American Statistical Association 89: 190–200. http://www.jstor.org/stable/2291215. +
+———. 2023. vcdExtra: Vcd Extensions and Additions. https://friendly.github.io/vcdExtra/. +
Friendly, Michael, and David Meyer. 2016. Discrete Data Analysis with R: Visualization and Modeling Techniques for Categorical and Count Data. Boca Raton, FL: Chapman & Hall/CRC.
diff --git a/docs/90-references.html b/docs/90-references.html index 5805b331..f332c3b2 100644 --- a/docs/90-references.html +++ b/docs/90-references.html @@ -409,6 +409,9 @@

References

———. 2008. “The Golden Age of Statistical Graphics.” Statistical Science 23 (4): 502–35. https://doi.org/10.1214/08-STS268. +
+———. 2023. vcdExtra: Vcd Extensions and Additions. https://friendly.github.io/vcdExtra/. +
Friendly, Michael, and E. 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