Maximum information preservable by supervised ordinal lumping

Calculates the lumping of an ordinal categorical covariate that preserves the maximum mutual information between the lumped covariate and a discrete outcome variable.

Usage

maximum_mutual_information_ordinal_supervised(joint_counts, threshold)

Arguments

joint_counts

Matrix with one row per level (in order) and one column per outcome category. Entry (k, y) is the number of observations with covariate level k and outcome y.

threshold

Minimum number of samples each lumped level must contain.

Value

A list containing information about the optimal lumping:

mutual_information

Double representing the mutual information between the lumped and unlumped variable.

loss

Double representing the amount of entropy lost in the lumping process.

lumping

Integer vector containing, sequentially, the points at which the lumped levels are separated. Lower bound inclusive and upper bound exclusive, so that if a_1,...,a_k is returned, the lumped levels correspond to the levels [a_1, a_2), ..., [a_(k-1), a_k).

Details

The runtime complexity is cubic in the number of levels.

See also

maximum_mutual_information_ordinal() for the unsupervised version.

maximum_mutual_information_ordinal_supervised_continuous() for a version that accepts a continuous outcome.

Author

Daan Koning

Examples

joint_counts <- matrix(c(10, 2, 5, 8, 1, 9, 3, 7, 4, 6), nrow = 5)
maximum_mutual_information_ordinal_supervised(joint_counts, threshold = 10)
#> $mutual_information
#> [1] 0.004307169
#> 
#> $loss
#> [1] 0.04793657
#> 
#> $lumping
#> [1] 1 2 4 6
#>