more on Ch13

02-getting_started.qmd

@@ -185,7 +185,7 @@ knitr::include_graphics("images/DataSaurusDozen.gif")
 ::: {.content-visible when-format="pdf"}
 ```{r}
 #| label: fig-datasaurus2
-#| out-width: "90%"
+#| out-width: "100%"
 #| echo: false
 #| fig-cap: "Plots of the Dinosaur Dozen datasets. Source: [Selçuk Korkmaz on X](https://x.com/selcukorkmaz/status/1864583253253927156)"
 knitr::include_graphics("images/datasaurus-dozen.jpg")

12-eqcov.qmd

@@ -125,7 +125,8 @@ So, this tells us that the groups do not differ in variances on all variables ex
 ## Visualizing Levene's test {#sec-mlevene}
 
 To gain some insight into the problem of homogeneity of variance it is helpful how the situation looks in terms of data.
-For the Penguin data, it might be simplest just boxplots of the variables and try to see whether the widths of the
+For the Penguin data, it might be simplest just boxplots of the variables and try to see whether the 
+**widths** of the
 central 50% boxes seem to be the same, as in @fig-peng-boxplots.
 However, it is perceptually difficult to focus on differences with widths of
 the boxes within each panel when their centers also differ from group to group.
@@ -166,7 +167,9 @@ pengDevs <- colDevs(peng[, vars], peng$species, median) |>
   abs()
 ```
 
-as shown in @fig-peng-devplots.
+Making boxplot of the absolute deviations in @fig-peng-devplots your eye can now focus on the average
+value, shown by the median '|' line, because Levene's method is testing whether these differ
+across groups.
 
 ```{r}
 #| label: fig-peng-devplots
@@ -207,12 +210,29 @@ the within-group covariance **matrices** $\mathbf{\Sigma}_i$ are equal for all g
 $$
 \mathbf{\Sigma}_1 = \mathbf{\Sigma}_2 = \cdots = \mathbf{\Sigma}_g \; .
 $$
-This is much stronger than in the univariate case, because it also required that all the correlations between pairs of variables are the same for all
-groups. ...
+This is much stronger than in the univariate case, because it also requires that all the correlations between pairs of variables are the same for all groups. For example, in the case of two responses,
+we must assume:
+
+$$
+\begin{pmatrix} 
+\sigma_1^2             & \textsf{sym} \\ 
+\rho \sigma_1 \sigma_2 & \sigma_2^2   \\ 
+\end{pmatrix}_1 = 
+\begin{pmatrix} 
+\sigma_1^2             & \textsf{sym} \\ 
+\rho \sigma_1 \sigma_2 & \sigma_2^2   \\ 
+\end{pmatrix}_2 = \dots =
+\begin{pmatrix} 
+\sigma_1^2             & \textsf{sym} \\ 
+\rho \sigma_1 \sigma_2 & \sigma_2^2   \\ 
+\end{pmatrix}
+_g
+$$
 
-**Insert** formulas for 2 x 2 case
 
-**Insert** pairs covEllipses for penguins data
+
+
+<!-- **Insert** pairs covEllipses for penguins data -->
 
 To preview the main example, @fig-peng-covEllipse0 shows data ellipses for the
 main size variables in the `palmerpenguins::penguins` data.
@@ -222,39 +242,43 @@ To view the relations ...
 ```{r}
 #| label: fig-peng-covEllipse0
 #| fig-align: center
+#| fig-height: 5
+#| fig-width: 10
 #| out-width: "100%"
-#| code-fold: show
+#| code-fold: true
+#| code-summary: "See the code"
 #| fig-cap: "Data ellipses for bill length and bill depth in the penguins data, also showing the pooled covariance. Left: As is; right: centered at the grand means for easier comparison."
 op <- par(mar = c(4, 4, 1, 1) + .5,
           mfrow = c(c(1,2)))
 covEllipses(cbind(bill_length, bill_depth) ~ species, data=peng,
-            fill = TRUE,
-            fill.alpha = 0.1,
-            lwd = 3,
-            col = clr)
+  fill = TRUE,
+  fill.alpha = 0.1,
+  lwd = 3,
+  col = clr)
 
 covEllipses(cbind(bill_length, bill_depth) ~ species, data=peng,
-            center = TRUE, 
-            fill = c(rep(FALSE,3), TRUE), 
-            fill.alpha = .1, 
-            lwd = 3,
-            col = clr,
-            label.pos = c(1:3,0))
+  center = TRUE, 
+  fill = c(rep(FALSE,3), TRUE), 
+  fill.alpha = .1, 
+  lwd = 3,
+  col = clr,
+  label.pos = c(1:3,0))
 par(op)
 ```
 
-
+All pairs:
 ```{r}
 #| label: fig-peng-covEllipse-pairs
 #| fig-align: center
 #| out-width: "100%"
 #| code-fold: show
 #| fig-cap: "All pairwise covariance ellipses for the penguins data."
-covEllipses(peng[3:6], peng$species, 
-            variables=1:4,
-            pooled = FALSE,
-            fill=c(rep(FALSE,3), TRUE), 
-            fill.alpha=.1)
+clr <- c(peng.colors(), "black")
+covEllipses(peng[,3:6], peng$species, 
+  variables=1:4,
+  col = clr,
+  fill=TRUE, 
+  fill.alpha=.1)
 ```
 
 They covariance ellipses look pretty similar in size, shape and orientation.

R/penguin/penguins-eqcov.R

@@ -7,7 +7,6 @@ library(effects)
 library(heplots)
 library(candisc)
 
-# load(here::here("data", "peng.RData"))
 data(peng, package="heplots")
 source("R/penguin/penguin-colors.R")
 # use penguin colors
@@ -27,11 +26,17 @@ vars <- c("bill_length", "bill_depth", "flipper_length", "body_mass")
 
 # Multivariate levene test
 pengDevs <- abs(colDevs(peng[, vars], peng$species, median))
-#pengDevs <- data.frame(species = peng$species, pengDevs)
-
 dev.mod <- lm(pengDevs ~ peng$species)
 Anova(dev.mod)
 
+pengDevs <- data.frame(species = peng$species, pengDevs)
+dev.mod <- lm(cbind(bill_length, bill_depth, flipper_length, body_mass) ~ species, 
+              data=pengDevs)
+Anova(dev.mod)
+
+heplot(dev.mod)
+
+
 # box plots of deviations
 dev_long <- data.frame(species = peng$species, pengDevs) |> 
   pivot_longer(bill_length:body_mass, 

bib/pkgs.bib

@@ -45,7 +45,7 @@ @Manual{R-candisc
 @Manual{R-car,
   title = {car: Companion to Applied Regression},
   author = {John Fox and Sanford Weisberg and Brad Price},
-  year = {2023},
+  year = {2024},
   note = {R package version 3.1-3},
   url = {https://r-forge.r-project.org/projects/car/},
 }
@@ -90,6 +90,14 @@ @Manual{R-corrplot
   url = {https://github.com/taiyun/corrplot},
 }
 
+@Manual{R-datasauRus,
+  title = {datasauRus: Datasets from the Datasaurus Dozen},
+  author = {Colin Gillespie and Steph Locke and Rhian Davies and Lucy {D'Agostino McGowan}},
+  year = {2024},
+  note = {R package version 0.1.8},
+  url = {https://github.com/jumpingrivers/datasauRus},
+}
+
 @Manual{R-datawizard,
   title = {datawizard: Easy Data Wrangling and Statistical Transformations},
   author = {Indrajeet Patil and Etienne Bacher and Dominique Makowski and Daniel Lüdecke and Mattan S. Ben-Shachar and Brenton M. Wiernik},
@@ -167,7 +175,7 @@ @Manual{R-genridge
   title = {genridge: Generalized Ridge Trace Plots for Ridge Regression},
   author = {Michael Friendly},
   year = {2024},
-  note = {R package version 0.7.1},
+  note = {R package version 0.8.0},
   url = {https://github.com/friendly/genridge},
 }
 
@@ -199,7 +207,7 @@ @Manual{R-ggbiplot
   title = {ggbiplot: A Grammar of Graphics Implementation of Biplots},
   author = {Vincent Q. Vu and Michael Friendly},
   year = {2024},
-  note = {R package version 0.6.2},
+  note = {R package version 0.6.3},
   url = {https://github.com/friendly/ggbiplot},
 }
 
@@ -273,7 +281,7 @@ @Manual{R-heplots
   title = {heplots: Visualizing Hypothesis Tests in Multivariate Linear Models},
   author = {Michael Friendly and John Fox and Georges Monette},
   year = {2024},
-  note = {R package version 1.7.1},
+  note = {R package version 1.7.3},
   url = {http://friendly.github.io/heplots/},
 }
 
@@ -309,6 +317,14 @@ @Manual{R-knitr
   url = {https://yihui.org/knitr/},
 }
 
+@Manual{R-langevitour,
+  title = {langevitour: Langevin Tour},
+  author = {Paul Harrison},
+  year = {2024},
+  note = {R package version 0.7},
+  url = {https://logarithmic.net/langevitour/},
+}
+
 @Manual{R-lattice,
   title = {lattice: Trellis Graphics for R},
   author = {Deepayan Sarkar},
@@ -317,6 +333,14 @@ @Manual{R-lattice
   url = {https://lattice.r-forge.r-project.org/},
 }
 
+@Manual{R-liminal,
+  title = {liminal: Multivariate Data Visualization with Tours and Embeddings},
+  author = {Stuart Lee},
+  year = {2021},
+  note = {R package version 0.1.2},
+  url = {https://github.com/sa-lee/liminal/},
+}
+
 @Manual{R-lubridate,
   title = {lubridate: Make Dealing with Dates a Little Easier},
   author = {Vitalie Spinu and Garrett Grolemund and Hadley Wickham},
@@ -344,9 +368,9 @@ @Manual{R-marginaleffects
 
 @Manual{R-MASS,
   title = {MASS: Support Functions and Datasets for Venables and Ripley's MASS},
-  author = {Brian Ripley},
+  author = {Brian Ripley and Bill Venables},
   year = {2024},
-  note = {R package version 7.3-60.0.1},
+  note = {R package version 7.3-61},
   url = {http://www.stats.ox.ac.uk/pub/MASS4/},
 }
 
@@ -462,7 +486,7 @@ @Manual{R-rgl
   title = {rgl: 3D Visualization Using OpenGL},
   author = {Daniel Adler and Duncan Murdoch},
   year = {2024},
-  note = {R package version 1.3.12},
+  note = {R package version 1.3.14},
   url = {https://github.com/dmurdoch/rgl},
 }
 
@@ -623,7 +647,7 @@ @Book{car2019
   year = {2019},
   publisher = {Sage},
   address = {Thousand Oaks {CA}},
-  url = {https://socialsciences.mcmaster.ca/jfox/Books/Companion/},
+  url = {https://www.john-fox.ca/Companion/},
 }
 
 @Misc{correlationPackage,
@@ -850,6 +874,17 @@ @InCollection{knitr2014
   note = {ISBN 978-1466561595},
 }
 
+@Article{langevitour2023,
+  title = {langevitour: Smooth Interactive Touring of High Dimensions, Demonstrated with scRNA-Seq Data},
+  author = {Paul Harrison},
+  journal = {The R Journal},
+  year = {2023},
+  volume = {15},
+  number = {2},
+  pages = {206-219},
+  doi = {10.32614/RJ-2023-046},
+}
+
 @Book{lattice2008,
   title = {Lattice: Multivariate Data Visualization with R},
   author = {Deepayan Sarkar},