# What is alluvial diagram?

Alluvial diagram is a variant of a Parallel Coordinates Plot (PCP) but for categorical variables. Variables are assigned to vertical axes that are parallel. Values are represented with blocks on each axis. Observations are represented with alluvia (sing. “alluvium”) spanning across all the axes.

You create alluvial diagrams with function alluvial(). This is one example using Titanic dataset. Let’s convert it to a data frame

tit <- as.data.frame(Titanic, stringsAsFactors = FALSE)
head(tit)
##   Class    Sex   Age Survived Freq
## 1   1st   Male Child       No    0
## 2   2nd   Male Child       No    0
## 3   3rd   Male Child       No   35
## 4  Crew   Male Child       No    0
## 5   1st Female Child       No    0
## 6   2nd Female Child       No    0

and create the alluvial diagram.

alluvial(tit[,1:4], freq=tit$Freq, col = ifelse(tit$Survived == "Yes", "orange", "grey"),
border = ifelse(tit$Survived == "Yes", "orange", "grey"), hide = tit$Freq == 0,
cex = 0.7
)

We have four variables:

• Class on the ship the passanger occupied
• Sex of the passenger
• Age of the passenger
• Whether the passenger Survived.

Vertical sizes of the blocks are proportional to the frequency, and so are the widths of the alluvia. Alluvia represent all combinations of values of the variables in the dataset. By default the vertical order of the alluvia is determined by alphabetical ordering of the values on each variable lexicographically (last variable changes first) drawn from bottom to top. In this example, the color is determined by passengers’ survival status, i.e. passenger who survived are represented with orange alluvia.

Alluvial diagrams are very useful in reading various conditional and uncoditional distributions in a multivariate dataset. For example, we can see that:

• Most of the Crew did not survived – majority of the height of the Crew category is covered by grey alluvia.
• Majortity of the Crew where adult men.
• Almost all women from the 1st Class did survive.
• The women who did not survive come mostly from 3rd class.

# Simple use

Minimal use requires supplying data frame(s) as first argument, and a vector of frequencies as the freq argument. By default all alluvia are drawn using gray, mildly transparent colors.

Two variables Class and Survived:

# Survival status and Class
tit %>% group_by(Class, Survived) %>%
summarise(n = sum(Freq)) -> tit2d

alluvial(tit2d[,1:2], freq=tit2d$n) Three variables Sex, Class, and Survived: # Survival status, Sex, and Class tit %>% group_by(Sex, Class, Survived) %>% summarise(n = sum(Freq)) -> tit3d alluvial(tit3d[,1:3], freq=tit3d$n)

# Customizing

There are several ways to customize alluvial diagrams with alluvial() the following sections illustrate probably most common usecases.

## Customizing colors

Colors of the alluvia can be customized with col, border and alpha arguments. For example:

alluvial(
tit3d[,1:3],
freq=tit3d$n, col = ifelse( tit3d$Sex == "Female", "pink", "lightskyblue"),
border = "grey",
alpha = 0.7,
blocks=FALSE
)

## Hiding and reordering alluvia

### Hiding

With alluvial sometimes it is desirable to hide omit plotting some of the alluvia. This is most frequently the case with larger datasets in which there are a lot of combinations of values of the variables associated with very small frequencies, or even 0s. Alluvia can be hidden with argument hide expecting a logical vector of length equal to the number of rows in the data. Alluvia for which hide is FALSE are not plotted. For example, to hide alluvia with frequency less than 150:

alluvial(tit2d[,1:2], freq=tit2d$n, hide=tit2d$n < 150)

This skips drawing the alluvia corresponding to the following rows in tit data frame:

tit2d %>% select(Class, Survived, n) %>%
filter(n < 150)
## Source: local data frame [2 x 3]
## Groups: Class [2]
##
##   Class Survived     n
##   <chr>    <chr> <dbl>
## 1   1st       No   122
## 2   2nd      Yes   118

You can see the gaps e.g. on the “Yes” and “No” category blocks on the Survived axis.

If you would rather omit these rows from the plot alltogether (i.e. no gaps), you need to filter your data before it is used by alluvial().

### Changing “layers”

By default alluvia are plotted in the same order in which the rows are ordered in the dataset.

Consider simple data:

d <- data.frame(
x = c(1, 2, 3),
y = c(3 ,2, 1),
freq=c(1,1,1)
)
d
##   x y freq
## 1 1 3    1
## 2 2 2    1
## 3 3 1    1

As there are three rows, we will have three alluvia:

alluvial(d[,1:2], freq=d$freq, col=1:3, alpha=1) # Reversing the order alluvial(d[ 3:1, 1:2 ], freq=d$freq, col=3:1, alpha=1)

Note that to keep colors matched in the same way to the alluvia we had to reverse the col argument too. Instead of reordering the data and keeping track of the other arguments plotting order can be adjusted with layer argument:

alluvial(d[,1:2], freq=d$freq, col=1:3, alpha=1, layer=3:1) The value of layer is passed to order so it is possible to use logical vectors e.g. if you only want to put some of the flows on top. For example, for Titanic data to put all alluvia for all survivors on top we can: alluvial(tit3d[,1:3], freq=tit3d$n,
col = ifelse( tit3d$Survived == "Yes", "orange", "grey" ), alpha = 0.8, layer = tit3d$Survived == "No"
)

First layer is the one on top, second layer below the first and so on. Consequently, in the example above, Survived == "No" is ordered after Survived == "Yes" so the former is below the latter.

This is feature is experimental!

Usually the order of the variables (axes) is rather unimportant. However, having particular two variables next to each other facilitates analyzing dependency between those two variables. In alluvial diagrams the ordering of the variables determines the vertical plotting order of the alluvia. This vertical order, together with setting blocks to FALSE, can be used to turn category blocks into stacked barcharts.

Consider two versions of subsets of the Titanic data that differ only in the order of variables.

tit %>% group_by(Sex, Age, Survived) %>%
summarise( n= sum(Freq)) -> x

tit %>% group_by(Survived, Age, Sex) %>%
summarise( n= sum(Freq)) -> y

In x we have Sex-Age-Survived-n while in y we have Survived-Age-Sex-n.

If we color the alluvia according to the first axis, the category blocks of Age and Survived become barcharts showing relative frequencies of Men and Women within categories of Age and Survived.

alluvial(x[,1:3], freq=x$n, col = ifelse(x$Sex == "Male", "orange", "grey"),
alpha = 0.8,
blocks=FALSE
)

Now we can see for example that

• There were a little bit of more girls than boys (category Age == "Child")
• Among surviors there were roughly the same number of Men and Women.

Argument ordering can be used to fully customize the ordering of each alluvium on each axis without the need to reorder the axes themselves. This feature is experimental as you can easily break things. It expects a list of numeric vectors or NULLs one for each variable in the data:

• Value NULL does not change the default order on the corresponding axis.
• A numeric vector should have length equal to the number of rows in the data and is determines the vertical order of the alluvia on the corresponding axis.

For example:

alluvial(y[,1:3], freq=y$n, # col = RColorBrewer::brewer.pal(8, "Set1"), col = ifelse(y$Sex == "Male", "orange", "grey"),
alpha = 0.8,
blocks = FALSE,
ordering = list(
order(y$Survived, y$Sex == "Male"),
order(y$Age, y$Sex == "Male"),
NULL
)
)

The list passed to ordering has has three elements corresponding to Survived, Age, and Sex respectively (that’s the order of the variables in y). The elements of this list are

1. Call to order sorting the alluvia on the Survived axis. The alluvia need to be sorted according to Survived first (otherwise the categories “Yes” and “No” will be destroyed) and according to the Sex second.
2. Call to order sorting the alluvia on the Age axis. The alluvia need to be sorted according to Age first Sex second.
3. NULL leaves the default ordering on Sex axis.

In the example below alluvia are colored by sex (red=Female, blue=Male) and survival status (bright=survived, dark=did not survive). Each category block is a stacked barchart showing relative freuquencies of man/women who did/did not survive. The alluvia are reordered on the last axis (Age) so that Sex categories are next each other (red together and blue together):

pal <- c("red4", "lightskyblue4", "red", "lightskyblue")

tit %>%
mutate(
ss = paste(Survived, Sex),
k = pal[ match(ss, sort(unique(ss))) ]
) -> tit

alluvial(tit[,c(4,2,3)], freq=tit$Freq, hide = tit$Freq < 10,
col = tit$k, border = tit$k,
blocks=FALSE,
ordering = list(
NULL,
NULL,
order(tit$Age, tit$Sex )

)
)

# Appendix

sessionInfo()
## R version 3.3.1 (2016-06-21)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 16.04.1 LTS
##
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C
##  [3] LC_TIME=pl_PL.UTF-8        LC_COLLATE=C
##  [5] LC_MONETARY=pl_PL.UTF-8    LC_MESSAGES=en_US.UTF-8
##  [7] LC_PAPER=pl_PL.UTF-8       LC_NAME=C
## [11] LC_MEASUREMENT=pl_PL.UTF-8 LC_IDENTIFICATION=C
##
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base
##
## other attached packages:
## [1] dplyr_0.5.0    alluvial_0.1-2
##
## loaded via a namespace (and not attached):
##  [1] Rcpp_0.12.7     digest_0.6.10   assertthat_0.1  R6_2.1.3
##  [5] DBI_0.5         formatR_1.4     magrittr_1.5    evaluate_0.9
##  [9] stringi_1.1.1   lazyeval_0.2.0  rmarkdown_1.0   tools_3.3.1
## [13] stringr_1.1.0   yaml_2.1.13     htmltools_0.3.5 knitr_1.14
## [17] tibble_1.2