Calculating the scagnostics

The usage is illustrated with the package’s example data, datasauRus dozen. This data is also available in the datasauRus package. There are several pairs of variables that have with the same mean, variance and correlation but strikingly different visual features. We will use a handful of these pairwise plots to show the best way to utilise the cassowaryr package. Here is a plot of the selected datasauRus dozen plots:

library(cassowaryr)
library(ggplot2)
#> Warning: package 'ggplot2' was built under R version 4.3.1
library(dplyr)
#> Warning: package 'dplyr' was built under R version 4.3.1
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union

# pick examples
exampledata <- datasaurus_dozen %>%
  filter(dataset %in% c("slant_up", "circle", "dots", "away"))


#plot them
exampledata %>%
  ggplot(aes(x=x,y=y, colour=dataset))+
  geom_point() +
  facet_wrap("dataset") +
  theme_minimal() +
  theme(legend.position = "none", aspect.ratio=1)

From a data frame, there are several ways to calculate scagnostics. If we simply have two variables we wish to calculate several scagnostics on, we use the calc_scags function and pass through the two variables as vectors.

calc_scags(exampledata$x, exampledata$y, scags=c("clumpy2", "convex", "striated2")) %>%
  knitr::kable(digits=4, align="c")

If instead we have a data frame with two variables and a grouping variable (a long form of a data set) then we can use the calc_scags function to get the scagnostics for each group.

longscags <- exampledata %>%
  group_by(dataset) %>%
  summarise(calc_scags(x, y, scags=c("clumpy2", "convex", "striated2", "dcor")))
longscags %>%
  knitr::kable(digits=4, align="c")

Finally, if we have a wide data set consisting of only numerical variables, we can use the calc_scags_wide to find the scagnostics on every pairwise combination of variables.

exampledata_wide <- datasaurus_dozen_wide[,c(1:2,5:6,9:10,17:18)]
widescags<- calc_scags_wide(exampledata_wide, scags=c("clumpy2", "convex", "striated2", "dcor"))
head(widescags, 4) %>%
  knitr::kable(digits=4, align="c")

Using the scagnostics

If the resulting scagnostic data set is small enough, we can find interesting scatter plots by simply looking at the table, however this is often not the case. If we want to find pairwise plots that are different to the others, we can find outliers on combinations of the scagnostics using an interactive scatter plot matrix (SPLOM). The code (but not the output) on how to do this is shown below:

library(GGally)
library(plotly)

splom_data <- widescags %>%
  mutate(lab = paste0(Var1, " , ", Var2)) %>%
  select(-c(Var1, Var2))

p <- ggpairs(splom_data, columns=c(1:4), aes(label=lab)) +
  theme_minimal()
ggplotly(p) 

There are several functions that can summarise the scagnostics results. Using top_pairs allows us to find the top scagnostic for each pair of variables, while top_scags finds the top pair of variables for each scagnostic. Their usage is similar and looks like:

top_scags(widescags) %>%
  knitr::kable(digits=4, align="c")

Drawing functions

Occasionally we will get unexpected results for a scagnostic. To diagnose a scagnostic result, the package has several draw functions that will plot the graph based objects that are used to construct the measures: draw_alphahull(), draw_convexhull() and draw_mst(). Below shows the MST drawn for the dots pair of variables in the datasaurus_dozen, and it can be seen to have some difficulty, as would be expected, defining the MST when all points are equidistant.

drawexample <- exampledata %>%
  filter(dataset== "dots")

draw_mst(drawexample$x, drawexample$y, alpha=0.2) + theme_minimal()