netropy (version 0.2.0)

joint_entropy: Joint Entropy

Description

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

Usage

joint_entropy(dat, dec = 3)

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.

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.

Author

Termeh Shafie

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.

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

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