Alluvial Diagrams in ggplot2

Alluvia (wide) format

The wide format reflects the visual arrangement of an alluvial diagram, but “untwisted”: Each row corresponds to a cohort of observations that take a specific value at each variable, and each variable has its own column. An additional column contains the weight of each row, e.g. the number of observational units in the cohort, which may be used to control the heights of the strata.² Basically, the wide format consists of one row per alluvium. This is the format into which the base function as.data.frame() transforms a frequency table, for instance the 3-dimensional UCBAdmissions dataset:

head(as.data.frame(UCBAdmissions), n = 12)

##       Admit Gender Dept Freq
## 1  Admitted   Male    A  512
## 2  Rejected   Male    A  313
## 3  Admitted Female    A   89
## 4  Rejected Female    A   19
## 5  Admitted   Male    B  353
## 6  Rejected   Male    B  207
## 7  Admitted Female    B   17
## 8  Rejected Female    B    8
## 9  Admitted   Male    C  120
## 10 Rejected   Male    C  205
## 11 Admitted Female    C  202
## 12 Rejected Female    C  391

is_alluvia_form(as.data.frame(UCBAdmissions), axes = 1:3, silent = TRUE)

## [1] TRUE

This format is inherited from the first version of ggalluvial, which modeled it after usage in alluvial: The user declares any number of axis variables, which stat_alluvium() and stat_stratum() recognize and process in a consistent way:

ggplot(as.data.frame(UCBAdmissions),
       aes(y = Freq, axis1 = Gender, axis2 = Dept)) +
  geom_alluvium(aes(fill = Admit), width = 1/12) +
  geom_stratum(width = 1/12, fill = "black", color = "grey") +
  geom_label(stat = "stratum", label.strata = TRUE) +
  scale_x_discrete(limits = c("Gender", "Dept"), expand = c(.05, .05)) +
  scale_fill_brewer(type = "qual", palette = "Set1") +
  ggtitle("UC Berkeley admissions and rejections, by sex and department")

An important feature of these diagrams is the meaningfulness of the vertical axis: No gaps are inserted between the strata, so the total height of the diagram reflects the cumulative weight of the observations. The diagrams produced by ggalluvial conform (somewhat; keep reading) to the “grammar of graphics” principles of ggplot2, and this prevents users from producing “free-floating” diagrams like the Sankey diagrams showcased here.³ ggalluvial parameters and existing ggplot2 functionality can also produce parallel sets plots, illustrated here using the Titanic dataset:⁴

ggplot(as.data.frame(Titanic),
       aes(y = Freq,
           axis1 = Survived, axis2 = Sex, axis3 = Class)) +
  geom_alluvium(aes(fill = Class),
                width = 0, knot.pos = 0, reverse = FALSE) +
  guides(fill = FALSE) +
  geom_stratum(width = 1/8, reverse = FALSE) +
  geom_text(stat = "stratum", label.strata = TRUE, reverse = FALSE) +
  scale_x_continuous(breaks = 1:3, labels = c("Survived", "Sex", "Class")) +
  coord_flip() +
  ggtitle("Titanic survival by class and sex")

This format and functionality are useful for many applications and will be retained in future versions. They also involve some conspicuous deviations from ggplot2 norms:

• The axis[0-9]* position aesthetics are non-standard: they are not an explicit set of parameters but a family based on a regular expression pattern; and at least one, but no specific one, is required.
• stat_alluvium() ignores any argument to the group aesthetic; instead, StatAlluvium$compute_panel() uses group to link the rows of the internally-transformed dataset that correspond to the same alluvium.
• The label.strata parameter instructs stat_stratum() (called by geom_text()) to take the values of the axis variables as labels.
• The horizontal axis must be manually corrected (using scale_x_discrete() or scale_x_continuous()) to reflect the implicit categorical variable identifying the axis.

Furthermore, format aesthetics like fill are necessarily fixed for each alluvium; they cannot, for example, change from axis to axis according to the value taken at each. This means that, although they can reproduce the branching-tree structure of parallel sets, this format and functionality cannot produce alluvial diagrams with the color schemes featured here (“Alluvial diagram”) and here (“Controlling colors”), which are “reset” at each axis.

Lodes (long) format

The long format recognized by ggalluvial contains one row per lode, and can be understood as the result of “gathering” (in the dplyr sense) or “pivoting” (in the Microsoft Excel sense) the axis columns of a dataset in the alluvia format into a key-value pair of columns encoding the axis as the key and the stratum as the value. This format requires an additional indexing column that links the rows corresponding to a common cohort, i.e. the lodes of a single alluvium:

UCB_lodes <- to_lodes_form(as.data.frame(UCBAdmissions),
                           axes = 1:3,
                           id = "Cohort")
head(UCB_lodes, n = 12)

##    Freq Cohort     x  stratum
## 1   512      1 Admit Admitted
## 2   313      2 Admit Rejected
## 3    89      3 Admit Admitted
## 4    19      4 Admit Rejected
## 5   353      5 Admit Admitted
## 6   207      6 Admit Rejected
## 7    17      7 Admit Admitted
## 8     8      8 Admit Rejected
## 9   120      9 Admit Admitted
## 10  205     10 Admit Rejected
## 11  202     11 Admit Admitted
## 12  391     12 Admit Rejected

is_lodes_form(UCB_lodes, key = x, value = stratum, id = Cohort, silent = TRUE)

## [1] TRUE

The functions that convert data between wide (alluvia) and long (lodes) format include several parameters that help preserve ancillary information. See help("alluvial-data") for examples.

The same stat and geom can receive data in this format using a different set of positional aesthetics, also specific to ggalluvial:

• x, the “key” variable indicating the axis to which the row corresponds, which are to be arranged along the horizontal axis;
• stratum, the “value” taken by the axis variable indicated by x; and
• alluvium, the indexing scheme that links the rows of a single alluvium.

Heights can vary from axis to axis, allowing users to produce bump charts like those showcased here.⁵ In these cases, the strata contain no more information than the alluvia and often not plotted. For convenience, both stat_alluvium() and stat_flow() will accept arguments for x and alluvium even if none is given for stratum.⁶ As an example, we can group countries in the Refugees dataset by region, in order to compare refugee volumes at different scales:

data(Refugees, package = "alluvial")
country_regions <- c(
  Afghanistan = "Middle East",
  Burundi = "Central Africa",
  `Congo DRC` = "Central Africa",
  Iraq = "Middle East",
  Myanmar = "Southeast Asia",
  Palestine = "Middle East",
  Somalia = "Horn of Africa",
  Sudan = "Central Africa",
  Syria = "Middle East",
  Vietnam = "Southeast Asia"
)
Refugees$region <- country_regions[Refugees$country]
ggplot(data = Refugees,
       aes(x = year, y = refugees, alluvium = country)) +
  geom_alluvium(aes(fill = country, colour = country),
                alpha = .75, decreasing = FALSE) +
  scale_x_continuous(breaks = seq(2003, 2013, 2)) +
  theme_bw() +
  theme(axis.text.x = element_text(angle = -30, hjust = 0)) +
  scale_fill_brewer(type = "qual", palette = "Set3") +
  scale_color_brewer(type = "qual", palette = "Set3") +
  facet_wrap(~ region, scales = "fixed") +
  ggtitle("refugee volume by country and region of origin")

## Warning in f(...): Some differentiation aesthetics vary within alluvia, and will be diffused by their first value.
## Consider using `geom_flow()` instead.

The format allows us to assign aesthetics that change from axis to axis along the same alluvium, which is useful for repeated measures datasets. This requires generating a separate graphical object for each flow, as implemented in geom_flow(). The plot below uses a set of (changes to) students’ academic curricula over the course of several semesters. Since geom_flow() calls stat_flow() by default (see the next example), we override it with stat_alluvium() in order to track each student across all semesters:

data(majors)
majors$curriculum <- as.factor(majors$curriculum)
ggplot(majors,
       aes(x = semester, stratum = curriculum, alluvium = student,
           fill = curriculum, label = curriculum)) +
  scale_fill_brewer(type = "qual", palette = "Set2") +
  geom_flow(stat = "alluvium", lode.guidance = "frontback",
            color = "darkgray") +
  geom_stratum() +
  theme(legend.position = "bottom") +
  ggtitle("student curricula across several semesters")

The stratum heights y are unspecified, so each row is given unit height. This example demonstrates one way ggalluvial handles missing data. The alternative is to set the parameter na.rm to TRUE.⁷ Missing data handling (specifically, the order of the strata) also depends on whether the stratum variable is character or factor/numeric.

Finally, lode format gives us the option to aggregate the flows between adjacent axes, which may be appropriate when the transitions between adjacent axes are of primary importance. We can demonstrate this option on data from the influenza vaccination surveys conducted by the RAND American Life Panel:

data(vaccinations)
levels(vaccinations$response) <- rev(levels(vaccinations$response))
ggplot(vaccinations,
       aes(x = survey, stratum = response, alluvium = subject,
           y = freq,
           fill = response, label = response)) +
  scale_x_discrete(expand = c(.1, .1)) +
  geom_flow() +
  geom_stratum(alpha = .5) +
  geom_text(stat = "stratum", size = 3) +
  theme(legend.position = "none") +
  ggtitle("vaccination survey responses at three points in time")

This diagram ignores any continuity between the flows between axes. This “memoryless” plot produces a less cluttered diagram, in which at most one flow proceeds from each stratum at one axis to each stratum at the next, but at the cost of being able to track each cohort across the entire diagram.