Compute Total Variation Similarity Between Weighted Categorical Distributions

`categorical_similarity()` measures distributional similarity between two weighted factor vectors using Total Variation (TV) distance across shared factor levels.

Usage

categorical_similarity(x, y, wx, wy)

Arguments

x

Factor vector. Categorical observations for the first group. Must share identical levels with y.

y

Factor vector. Categorical observations for the second group. Must share identical levels with x.

wx

Numeric vector. Sample weights for x.

wy

Numeric vector. Sample weights for y.

Value

A single numeric similarity score in \([0, 1]\), where 1 indicates identical weighted category proportions.

Details

Total Variation distance represents half the sum of absolute differences between category proportions: $$\text{TV} = \frac{1}{2} \sum_{k} |p_k - q_k|$$ The resulting similarity score is \(1 - \text{TV}\), bounded in \([0, 1]\). A value of 1 indicates identical category proportions, whereas 0 indicates completely disjoint distributions.

See also

scaleNumeric, numerical_similarity