eulerr (version 4.1.0)

euler: Area-proportional Euler diagrams

Description

Fit Euler diagrams (a generalization of Venn diagrams) using numerical optimization to find exact or approximate solutions to a specification of set relationships. The shape of the diagram may be a circle or an ellipse.

Usage

euler(combinations, ...)
# S3 method for default
euler(combinations, input = c("disjoint", "union"),
  shape = c("circle", "ellipse"), control = list(), ...)
# S3 method for data.frame
euler(combinations, weights = NULL, by = NULL, ...)
# S3 method for matrix
euler(combinations, ...)
# S3 method for table
euler(combinations, ...)
# S3 method for list
euler(combinations, ...)

Arguments

combinations

set relationships as a named numeric vector, matrix, or data.frame (see methods (by class))

...

arguments passed down to other methods

input

type of input: disjoint identities ('disjoint') or unions ('union').

shape

geometric shape used in the diagram

control

a list of control parameters.

• extraopt: should the more thorough optimizer (currently GenSA::GenSA()) kick in (provided extraopt_threshold is exceeded)? The default is TRUE for ellipses and three sets and FALSE otherwise.

• extraopt_threshold: threshold, in terms of diagError, for when the extra optimizer kicks in. This will almost always slow down the process considerably. A value of 0 means that the extra optimizer will kick in if there is any error. A value of 1 means that it will never kick in. The default is 0.001.

• extraopt_control: a list of control parameters to pass to the extra optimizer, such as max.call. See GenSA::GenSA().

weights

a numeric vector of weights of the same length as the number of rows in combinations.

by

a factor or character matrix to be used in base::by() to split the data.frame or matrix of set combinations

Value

A list object of class 'euler' with the following parameters.

coefficients

a matrix of h and k (x and y-coordinates for the centers of the shapes), semiaxes a and b, and rotation angle phi

original.values

set relationships in the input

fitted.values

set relationships in the solution

residuals

residuals

regionError

the difference in percentage points between each disjoint subset in the input and the respective area in the output

diagError

the largest regionError

stress

normalized residual sums of squares

Methods (by class)

• default: a named numeric vector, with combinations separated by an ampersand, for instance A&B = 10. Missing combinations are treated as being 0.

• data.frame: a data.frame of logicals, two-level factors (see examples).

• matrix: a matrix that can be converted to a data.frame of logicals (as in the description above) via base::as.data.frame.matrix().

• table: A table with max(dim(x)) < 3.

• list: a list of vectors, each vector giving the contents of that set (with no duplicates). Vectors in the list do not need to be named.

Details

If the input is a matrix or data frame and argument by is specified, the function returns a list of euler diagrams.

The function minimizes the stress statistic from venneuler,

$$ \frac{ \sum_{i=1}^{n} (y_i - \hat{y}_i) ^ 2}{\sum_{i=1}^{n} y_i ^ 2}, $$

where \(\hat{y}\) are ordinary least squares estimates from the regression of the fitted areas on the original areas that are currently being explored. The stress statistic can also be used as a goodness of fit measure.

euler() also returns diagError and regionError from eulerAPE. regionError is computed as

$$ \left| \frac{y_i}{\sum y_i} - \frac{\hat{y}_i}{\sum \hat{y}_i}\right|. $$

diagError is simply the maximum of regionError.

References

Wilkinson L. Exact and Approximate Area-Proportional Circular Venn and Euler Diagrams. IEEE Transactions on Visualization and Computer Graphics (Internet). 2012 Feb (cited 2016 Apr 9);18(2):321-31. Available from: http://doi.org/10.1109/TVCG.2011.56

Micallef L, Rodgers P. eulerAPE: Drawing Area-Proportional 3-Venn Diagrams Using Ellipses. PLOS ONE (Internet). 2014 Jul (cited 2016 Dec 10);9(7):e101717. Available from: http://dx.doi.org/10.1371/journal.pone.0101717

See Also

plot.euler(), print.euler()

Examples

# NOT RUN {
# Fit a diagram with circles
combo <- c(A = 2, B = 2, C = 2, "A&B" = 1, "A&C" = 1, "B&C" = 1)
fit1 <- euler(combo)

# Investigate the fit
fit1

# Refit using ellipses instead
fit2 <- euler(combo, shape = "ellipse")

# Investigate the fit again (which is now exact)
fit2

# Plot it
plot(fit2)

# A set with no perfect solution
euler(c("a" = 3491, "b" = 3409, "c" = 3503,
        "a&b" = 120, "a&c" = 114, "b&c" = 132,
        "a&b&c" = 50))

# Using grouping via the 'by' argument through the data.frame method
dat <- data.frame(
  A = sample(c(TRUE, FALSE), size = 100, replace = TRUE),
  B = sample(c(TRUE, TRUE, FALSE), size = 100, replace = TRUE),
  gender = sample(c("Men", "Women"), size = 100, replace = TRUE),
  nation = sample(c("Sweden", "Denmark"), size = 100, replace = TRUE)
)

euler(dat, by = list(gender, nation))


dat2 <- data.frame(A = c(TRUE, FALSE, TRUE, TRUE),
                   B = c(FALSE, TRUE, TRUE, FALSE))
euler(dat2, weights = c(3, 2, 1, 1))

# Using the matrix method
mat <- cbind(A = sample(c(TRUE, TRUE, FALSE), size = 50, replace = TRUE),
             B = sample(c(TRUE, FALSE), size = 50, replace = TRUE))
euler(mat)
# The table method
plot(euler(as.table(apply(Titanic, 2:4, sum))))
# A euler diagram from a list of sample spaces (the list method)
euler(list(A = c("a", "ab", "ac", "abc"),
           B = c("b", "ab", "bc", "abc"),
           C = c("c", "ac", "bc", "abc")))
# }