entropy_tetravar: Tetravariate Entropy

In netropy: Statistical Entropy Analysis of Network Data

Tetravariate Entropy

Description

Computes tetravariate entropies, expected conditional entropies, and expected conditional joint entropies for all quadruples of variables in a multivariate discrete data set.

Usage

entropy_tetravar(dat, dec = 2)

Arguments

dat	dataframe with rows as observations and columns as variables. Variables must be categorical with finite range spaces.
dec	number of decimals used for rounding the entropy values. Default is 2.

Details

For four variables X, Y, Z, and U, the tetravariate entropy is denoted H(X,Y,Z,U). The expected conditional entropies are computed as

EH(U|X,Y,Z) = H(X,Y,Z,U) - H(X,Y,Z)

and

EH(Z|X,Y,U) = H(X,Y,Z,U) - H(X,Y,U).

The expected conditional joint entropy is computed as

EJ(X,Y|Z,U) = H(X,Z,U) + H(Y,Z,U) - H(Z,U) - H(X,Y,Z,U).

This quantity measures deviation from conditional independence of the form X \perp Y \,\vert\, Z, U. Smaller values indicate weaker conditional dependence.

Value

A dataframe with one row for each ordered decomposition of four variables into predictors and conditioning variables. The columns are:

X	first variable in the pair of interest.
Y	second variable in the pair of interest.
Z	first conditioning variable.
U	second conditioning variable.
H_XYZU	tetravariate entropy H(X,Y,Z,U).
EH_U_XYZ	expected conditional entropy EH(U|X,Y,Z).
EH_Z_XYU	expected conditional entropy EH(Z|X,Y,U).
EJ_XY_ZU	expected conditional joint entropy EJ(X,Y|Z,U).

Author(s)

Termeh Shafie

References

Frank, O., & Shafie, T. (2016). Multivariate entropy analysis of network data. Bulletin of Sociological Methodology/Bulletin de Méthodologie Sociologique, 129(1), 45-63.

See Also

entropy_trivar, entropy_bivar, prediction_power

Examples

# use internal data set
data(lawdata)

# extract node attributes
df_att <- lawdata[[4]]

# data editing:
# 1. discretize 'years' and 'age' into three approximately balanced groups
# 2. recode selected variables so categories start at 0
att_var <- data.frame(
  status    = df_att$status - 1,
  gender    = df_att$gender,
  office    = df_att$office - 1,
  years     = ifelse(df_att$years <= 3, 0,
                ifelse(df_att$years <= 13, 1, 2)),
  age       = ifelse(df_att$age <= 35, 0,
                ifelse(df_att$age <= 45, 1, 2)),
  practice  = df_att$practice,
  lawschool = df_att$lawschool - 1
)

# compute tetravariate entropy quantities for five selected variables
entropy_tetravar(
  dat = att_var[, c("gender", "years", "age", "office", "practice")]
)

netropy documentation built on April 24, 2026, 9:06 a.m.