OptimalBinningWoE (version 1.0.8)

ob_categorical_mob: Optimal Binning for Categorical Variables using Monotonic Optimal Binning (MOB)

Description

This function performs optimal binning for categorical variables using the Monotonic Optimal Binning (MOB) algorithm. It creates bins that maintain monotonic Weight of Evidence (WoE) trends while maximizing Information Value.

Usage

ob_categorical_mob(
  feature,
  target,
  min_bins = 3L,
  max_bins = 5L,
  bin_cutoff = 0.05,
  max_n_prebins = 20L,
  bin_separator = "%;%",
  convergence_threshold = 1e-06,
  max_iterations = 1000L
)

Value

A list containing the results of the optimal binning procedure:

id

Numeric vector of bin identifiers (1 to n_bins)

bin

Character vector of bin labels, which are combinations of original categories separated by bin_separator

woe

Numeric vector of Weight of Evidence values for each bin

iv

Numeric vector of Information Values for each bin

count

Integer vector of total observations in each bin

count_pos

Integer vector of positive outcomes in each bin

count_neg

Integer vector of negative outcomes in each bin

total_iv

Numeric scalar. Total Information Value across all bins

converged

Logical. Whether the algorithm converged within the specified tolerance

iterations

Integer. Number of iterations performed

Arguments

feature

A character vector or factor representing the categorical predictor variable. Missing values (NA) will be converted to the string "NA" and treated as a separate category.

target

An integer vector containing binary outcome values (0 or 1). Must be the same length as feature. Cannot contain missing values.

min_bins

Integer. Minimum number of bins to create. Must be at least 1. Default is 3.

max_bins

Integer. Maximum number of bins to create. Must be greater than or equal to min_bins. Default is 5.

bin_cutoff

Numeric. Minimum relative frequency threshold for individual categories. Categories with frequency below this proportion will be merged with others. Value must be between 0 and 1. Default is 0.05 (5%).

max_n_prebins

Integer. Maximum number of initial bins before optimization. Used to control computational complexity when dealing with high-cardinality categorical variables. Default is 20.

bin_separator

Character string used to separate category names when multiple categories are merged into a single bin. Default is "%;%".

convergence_threshold

Numeric. Threshold for determining algorithm convergence based on changes in total Information Value. Must be positive. Default is 1e-6.

max_iterations

Integer. Maximum number of iterations for the optimization process. Must be positive. Default is 1000.

Details

The MOB algorithm follows these steps:

1. Initial sorting: Categories are ordered by their individual WoE values

2. Rare category handling: Categories below bin_cutoff frequency are merged with similar ones

3. Pre-binning limitation: Reduces initial bins to max_n_prebins using similarity-based merging

4. Monotonicity enforcement: Ensures WoE is either consistently increasing or decreasing across bins

5. Bin count optimization: Adjusts to meet min_bins/max_bins constraints

Key features include:

• Automatic sorting of categories by WoE for initial structure

• Bayesian smoothing to stabilize WoE estimates for sparse categories

• Guaranteed monotonic WoE trend across final bins

• Configurable minimum and maximum bin counts

• Similarity-based merging for optimal bin combinations

Mathematical definitions: $$WoE_i = \ln\left(\frac{p_i^{(1)}}{p_i^{(0)}}\right)$$ where \(p_i^{(1)}\) and \(p_i^{(0)}\) are the proportions of positive and negative cases in bin \(i\), respectively, adjusted using Bayesian smoothing.

$$IV = \sum_{i=1}^{n} (p_i^{(1)} - p_i^{(0)}) \times WoE_i$$

Examples

# Generate sample data
set.seed(123)
n <- 1000
feature <- sample(letters[1:8], n, replace = TRUE)
target <- rbinom(n, 1, prob = ifelse(feature %in% c("a", "b"), 0.7, 0.3))

# Perform optimal binning
result <- ob_categorical_mob(feature, target)
print(result[c("bin", "woe", "iv", "count")])

# With custom parameters
result2 <- ob_categorical_mob(
  feature = feature,
  target = target,
  min_bins = 2,
  max_bins = 4,
  bin_cutoff = 0.03
)

# Handling missing values
feature_with_na <- feature
feature_with_na[sample(length(feature_with_na), 50)] <- NA
result3 <- ob_categorical_mob(feature_with_na, target)