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

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
)

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.

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

Details

The MOB algorithm follows these steps:

Initial sorting: Categories are ordered by their individual WoE values
Rare category handling: Categories below bin_cutoff frequency are merged with similar ones
Pre-binning limitation: Reduces initial bins to max_n_prebins using similarity-based merging
Monotonicity enforcement: Ensures WoE is either consistently increasing or decreasing across bins
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.

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

Note

Target variable must contain both 0 and 1 values.
Empty strings in the feature vector are not allowed and will cause an error.
For datasets with very few observations in either class (<5), warnings will be issued as results may be unstable.
The algorithm guarantees monotonic WoE across bins.
When the number of unique categories is less than max_bins, each category will form its own bin.

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")])
#> $bin
#> [1] "c%;%f" "e%;%h" "d%;%g" "a%;%b"
#> 
#> $woe
#> [1] -0.6160508 -0.4979681 -0.2902418  1.2813219
#> 
#> $iv
#> [1] 0.08435798 0.05880863 0.02029562 0.41586980
#> 
#> $count
#> [1] 242 253 249 256
#> 

# 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)