Visualising pairwise scores using bullseye.

Visualising associations

The usual starting point is the visualisation of a correlation of numeric variables:

plot(pair_cor(peng))

If you wish to also include factor variables, use an alternative to pair_cor which accepts numeric and factor variables, eg pair_cancor. To see the available methods which handle all variable types use

filter(pair_methods,nn&ff&fn)
#> # A tibble: 3 × 7
#>   name        nn    ff    fn    from                range ordinal
#>   <chr>       <lgl> <lgl> <lgl> <chr>               <chr> <lgl>  
#> 1 pair_ace    TRUE  TRUE  TRUE  acepack::ace        [0,1] FALSE  
#> 2 pair_cancor TRUE  TRUE  TRUE  cancor              [0,1] FALSE  
#> 3 pair_nmi    TRUE  TRUE  TRUE  linkspotter::maxNMI [0,1] FALSE

Alternatively, if you wish to show different association measures for correlation for numeric variables and cancor for non numeric, plot the result of pairwise_scores:

plot(pairwise_scores(peng), interactive=TRUE)

Adding interactive=TRUE means tooltips are available.

By default variables in this plot are re-ordered to emphasize pairs with maximum absolute scores. This re-ordering uses hierarchical clustering to place high score pairs adjacently, and also to push high score pairs to the top-left of the display.

Visualising multiple scores

The pairwise structure has multiple association scores when each (x,y) pair appears multiple times in the pairwise structure.

scores <- pairwise_scores(peng, by="species")
plot(scores, interactive=TRUE) 

The bullseye plot shown here has a pie wedge representing the conditional correlations. The overall or ungrouped correlation is shown in the pie center. As there are multiple scores for each (x,y) pair the ordering algorithm is based on the maximum of these scores.

An alternative ordering algorithm gives emphasis to pairs with the largest difference in the scores:

plot(scores, var_order="seriate_max_diff", interactive=TRUE) 

Pairs of numeric variables exhibit Simpsons paradox if the ungrouped correlation is negative and the grouped corelations are positive (or vice-versa). This is present for the pairs (body_mass_mm, bill_depth_mm) and (bill_depth_mm, bill_length_mm).

The island variable is also associated with the penguin dimension variables. However, this is mostly because two of the species (Gentoo and Chinstrap) are located on one island only. For these species, the score values for island and the other variables is NA, shown in grey.

Multiple pairwise scores also occur when pairwise data structures are combined:

mscores <- 
bind_rows(
  pair_cor(peng),
  pair_cor(peng, method="spearman"),
  pair_dcor(peng),
  pair_ace(peng)
) |> filter(pair_type=="nn") |>
  mutate(value=abs(value)) # convert all scores to 0-1

plot(mscores, interactive=TRUE) 

In this case the various measures of association are fairly consistent. For the bill_depth variable the ace correlations are higher than the others, indicating the presence of a non-linear association.

Visualising multiple scagnostic scores

sc <- pair_scagnostics(peng)
plot(sc, interactive=TRUE)

With many scores for example with scagnostics, an alternative display is perhaps easier to read.

So we offer an alternative plot of the pairwise structure:

plot(sc, type="linear")

The default ordering arranges the variable pairs in order of their maximum score. Here all the high-scoring pairs involve year, which is not surprising as year takes just three distinct values.

sc |> filter(y != "year")|>
plot(type="linear", geom="point", add_lines=TRUE)

According to the scagnostic measures, all pairwise scatterplots exhibit skewness, and body_mass:flipper_length scores highly on the outlier measure.

Linear display for filtered pairwise objects

We use the American Community Survey (2012) from the R package openintro which contains results from the US Census American Community Survey in 2012.

acs12 <- openintro::acs12

scores <- pairwise_multi(acs12)

The scores contains various pairwise measures for the 78 variable pairs. Many of the scores will be low, so we pick out the pairs with a score of .25 or above to display:

mutate(scores, valmax = max(abs(value)), .by=c(x,y))|>
  filter(valmax > .25) |>
  plot(type="linear",geom="point", interactive=TRUE)

employment:income has the highest score, measured using ace, suggesting a higher association for transformed income.

The ave_cor function calls acepack::ace (handling factors and missing) and shows that ace picks a transformation that compresses high income values.

a <- ace_cor(acs12$income, acs12$employment)
plot(a$x, a$tx)

Similarly age:income has a high ace score, and a plot of these two variables shows income goes up with age until about age 40 and then drops off.

Next, we calculate scores by race and filter those x,y pairs with high values and high differences:

group_scores <- pairwise_scores(acs12, by = "race")

# filtering variable pairs with a range of 0.25 or greater
rng <- function(vals){
  if (all(is.na(vals))) 0 else max(vals, na.rm=TRUE)- min(vals,na.rm=TRUE)
}

mutate(group_scores, valrange = rng(value),valmax = max(abs(value)), .by=c(x,y))|>
  filter(valrange > .25 | valmax > .4) |>
  plot(type="linear", geom="point", pair_order = "seriate_max_diff")+ 
   theme(legend.text = element_text(size = rel(.5)), legend.title = element_text(size = rel(.5))
  )

Asians have much higher association than other groups for many of the variables. Employed Asians report much higher hours worked:

ggplot(data=acs12, aes(x=employment, y=hrs_work))+
  geom_boxplot()+
  facet_grid(cols=vars(race)) +scale_x_discrete(na.translate = FALSE)

For Asians, there is a big difference in travel time to work for genders compared to other races.

ggplot(data=acs12, aes(x=gender, y=time_to_work))+
  geom_boxplot()+
  facet_grid(cols=vars(race)) 

For Asians, there is a big difference in income across genders compared to other races.

ggplot(data=acs12, aes(x=gender, y=income))+
  geom_boxplot()+
  facet_grid(cols=vars(race))

So Asians work more than other groups, but Asian women commute less and earn less.