Calculating pairwise scores using bullseye.

In bullseye: Visualising Multiple Pairwise Variable Correlations and Other Scores

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
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bullseye is an R package which calculates measures of correlation and other association scores for pairs of variables in a dataset and offers visualisations of these measures in different layouts. The package also calculates and visualises the pairwise scores for different levels of a grouping variable.

This vignette gives an overview of how these pairwise variable measures are calculated. Visualisations of these calculated measures are provided in the accompanying vignette.

# install.packages("palmerpenguins")

library(bullseye)
library(palmerpenguins)
library(dplyr)

Table 1 lists the different measures of association provided in the package with the variable types they can be used with, the package used for calculation, the information on whether the measure is symmetric, and the minimum and maximum value of the measure.

kableExtra::kbl(pair_methods,booktabs = T,caption = "List of the functions available in the package for calculating different association measures along with the packages used for calculation.") %>% kableExtra::kable_styling(latex_options = "scale_down")

Calculating correlation and other association measures

Each of the functions in the first column of Table 1 calculates pairwise scores for a dataset.

sc_dcor <- pair_dcor(penguins)
str(sc_dcor)

For example, we see that pair_dcor calculates the distance correlation for every pair of numeric variables in the penguins dataset. There are missing values in this dataset, all the pair_ functions use pairwise complete observations by default.

sc_dcor is a tibble of class pairwise, with the two variables in columns x and y (arranged in alphabetical order), calculated values in the column value, and the name of the score calculated in the column score. All of the variables are numeric, hence "nn" in the pair_type column.

Similarly, one can use pair_nmi to calculate normalised mutual information for numeric, factor and mixed pairs of variables.

sc_nmi <- pair_nmi(penguins)
sc_nmi

The main difference here is that factor variables are included. In the pair_type column, "ff" and "fn" indicate factor-factor and factor-numeric pairs.

If you want more control over the measure calculated, the function pairwise_scores calculates a different score depending on variable types.

pairwise_scores(penguins) |> distinct(score, pair_type)

As you can see, the default uses pearson's correlation for numeric pairs, and canonical correlation for factor-numeric or factor-factor pairs. In addition polychoric correlation is used for two ordered factors, but there are no ordered factors in this data. Alternative scores may be specified using the control argument to pairwise_scores. The default value for this control argument is given by

pair_control()

Calculating multiple measures

If you want for instance to compare distance correlation and mutual information measures in a display, two pairwise data structures can be combined:

bind_rows(sc_dcor, sc_nmi) |> arrange(x,y)

We provide another function pairwise_multi which calculates multiple association measures for every variable pair in a dataset. By default this function combines the results of pair_cor, pair_dcor,pair_mine,pair_ace, pair_cancor,pair_nmi,pair_uncertainty, pair_chi, but any subset of the pair_ functions may be supplied as an argument, as in the second example below.

pairwise_multi(penguins)
dcor_nmi <- pairwise_multi(penguins, c("pair_dcor", "pair_nmi"))

Calculating grouped measures

For each of the pairwise calculation functions, they can be wrapped using pairwise_by to build a score calculation for each level of a grouping variable. Of course, grouped scores could be calculated using dplyr machinery, but it is a bit more work.

pairwise_by(penguins, by="species", pair_cor)

Use argument ungrouped=FALSE to suppress calculation of the ungrouped scores.

pairwise_scores has a by argument, and provides pairwise scores for the levels of a grouping variable.

sc_sex <- pairwise_scores(penguins, by="species")

The column group now shows the levels of the grouping variable, along with "all" for ungrouped scores. Use ungrouped=FALSE to suppress calculation of the ungrouped scores.

sc_sex |> distinct(group)

If you want to calculate different scores to the default, specify this via the control argument:

pc <- pair_control(nn="pairwise_multi", nnargs= c("pair_dcor", "pair_ace"), fn=NULL, ff=NULL)
sc_sex <- pairwise_scores(penguins, by="species", control=pc, ungrouped=FALSE) 

Scagnostic measures

The package scagnostics provides pairwise variable scores based on graph-theoretic interestingness measures, for numeric variable pairs only.

pair_scagnostics(penguins[,1:5], scagnostic=c("Stringy", "Clumpy"))

Note that the first two variables of the penguins data are non-numeric and so are ignored in the above calculation.

For group-wise calculation:

pairwise_by(penguins[,1:5], by="species",function(x) pair_scagnostics(x, scagnostic=c("Stringy", "Clumpy")))

Converting symmetric matrices to pairwise and vice-versa.

The conventional way of representing pairwise scores or correlations is via a numeric symmetric matrix. The tidy pairwise structure we use in bullseye is more flexible, and is amenable to multiple measures of association and grouped measures.

It is straightforward to convert from a symmetric matrix to pairwise:

x <- cor(penguins[, c("bill_length_mm", "bill_depth_mm" ,"flipper_length_mm" ,"body_mass_g")], 
         use= "pairwise.complete.obs")
pairwise(x, score="pearson", pair_type = "nn")

And for the reverse, converting a pairwise to a symmetric matrix:

as.matrix(sc_dcor)

Converting structures from package correlation:

correlation package calculates different kinds of correlations, such as partial correlations, Bayesian correlations, multilevel correlations, polychoric correlations, biweight, percentage bend or Sheperd’s Pi correlations, distance correlation and more. The output data structure is a tidy dataframe with a correlation value and correlation tests for variable pairs for which the correlation method is defined.

correlation::correlation(penguins)

The default calculation uses Pearson correlation. Other options are available via the method argument.

As there is an as.matrix method provided for the results of correlation::correlation, it is straightforward to convert this to a pairwise tibble.

x <- correlation::correlation(penguins)
pairwise(as.matrix(x)) 

bullseye documentation built on Sept. 11, 2024, 9:24 p.m.