joint_entropy: Joint Entropy

In netropy: Statistical Entropy Analysis of Network Data

Description

Computes the joint entropies between all pairs of (discrete) variables in a multivariate data set.

Usage

joint_entropy(dat, dec = 3)

Arguments

dat	dataframe with rows as observations and columns as variables. Variables must all be observed or transformed categorical with finite range spaces.
dec	the precision given in number of decimals for which the frequency distribution of unique entropy values is created. Default is 3.

Details

The joint entropy J(X,Y) of discrete variables X and Y is a measure of dependence or association between them, defined as

J(X,Y) = H(X) + H(Y) - H(X,Y).

Two variables are independent if their joint entropy, i.e. their mutual information, is equal to zero. The frequency distributions can be used to decide upon convenient thresholds for constructing association graphs.

Value

List with

matrix	an upper triangular joint entropy matrix (univariate entropies in the diagonal).
freq	a dataframe giving the frequency distributions of unique joint entropy values.

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.

Nowicki, K., Shafie, T., & Frank, O. (Forthcoming 2022). Statistical Entropy Analysis of Network Data.

See Also

assoc_graph, entropy_bivar

Examples

# use internal data set
data(lawdata)
df.att <- lawdata[[4]]

# three steps of data editing:
# 1. categorize variables 'years' and 'age' based on
# approximately three equally size groups (values based on cdf)
# 2. make sure all outcomes start from the value 0 (optional)
# 3. remove variable 'senior' as it consists of only unique values (thus redundant)
df.att.ed <- data.frame(
   status   = df.att$status,
   gender   = df.att$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)

# calculate joint entropies
J <- joint_entropy(df.att.ed)
# joint entropy matrix
J$matrix
# frequency distribution of joint entropy values
J$freq

netropy documentation built on Feb. 2, 2022, 9:07 a.m.