Skip to contents

Optimal Binning for Numerical Variables using Enhanced ChiMerge Algorithm

Source: R/obn_cm.R
ob_numerical_cm.Rd

Performs supervised discretization of continuous numerical variables using the ChiMerge algorithm (Kerber, 1992) or the Chi2 algorithm (Liu & Setiono, 1995). This function merges adjacent bins based on Chi-square statistics to maximize the discrimination of the binary target variable while ensuring monotonicity and statistical robustness.

Usage

ob_numerical_cm(
  feature,
  target,
  min_bins = 3,
  max_bins = 5,
  bin_cutoff = 0.05,
  max_n_prebins = 20,
  convergence_threshold = 1e-06,
  max_iterations = 1000,
  init_method = "equal_frequency",
  chi_merge_threshold = 0.05,
  use_chi2_algorithm = FALSE
)

Arguments

feature

A numeric vector representing the continuous predictor variable. Missing values (NA) are not supported and should be handled before binning.

target

An integer vector of binary outcomes (0/1) corresponding to each observation in feature. Must have the same length as feature.

min_bins

Integer. The minimum number of bins to produce. Must be \(\ge\) 2. Defaults to 3.

max_bins

Integer. The maximum number of bins to produce. Must be \(\ge\) min_bins. Defaults to 5.

bin_cutoff

Numeric. The minimum fraction of total observations required for a bin to be considered valid. Bins with frequency < bin_cutoff will be merged. Value must be in (0, 1). Defaults to 0.05.

max_n_prebins

Integer. The number of initial bins created during the pre-binning phase before the merging process begins. Higher values provide more granular starting points. Must be \(\ge\) max_bins. Defaults to 20.

convergence_threshold

Numeric. The threshold for the change in total IV to determine convergence during the iterative merging process. Defaults to 1e-6.

max_iterations

Integer. Safety limit for the maximum number of merging iterations. Defaults to 1000.

init_method

Character string specifying the initialization method. Options are "equal_frequency" (quantile-based) or "equal_width". Defaults to "equal_frequency".

chi_merge_threshold

Numeric. The significance level (\(\alpha\)) for the Chi-square test. Pairs of bins with a p-value > chi_merge_threshold are candidates for merging. Defaults to 0.05.

use_chi2_algorithm

Logical. If TRUE, uses the Chi2 algorithm variant which performs multi-phase merging with decreasing significance levels (0.5, 0.1, 0.05, 0.01, ...). This is often more robust for noisy data. Defaults to FALSE.

Value

A list containing the binning results:

  • id: Integer vector of bin identifiers (1 to k).

  • bin: Character vector of bin labels in interval notation.

  • woe: Numeric vector of Weight of Evidence for each bin.

  • iv: Numeric vector of Information Value contribution per bin.

  • count: Integer vector of total observations per bin.

  • count_pos: Integer vector of positive cases (target=1).

  • count_neg: Integer vector of negative cases (target=0).

  • cutpoints: Numeric vector of upper boundaries (excluding Inf).

  • converged: Logical indicating if the algorithm converged.

  • iterations: Integer count of iterations performed.

  • total_iv: The total Information Value of the binned variable.

  • algorithm: String identifying the algorithm used ("ChiMerge" or "Chi2").

  • monotonic: Logical indicating if the final WoE trend is monotonic.

Details

The function implements two major discretization strategies:

  1. Standard ChiMerge:

    • Initializes bins using init_method.

    • Iteratively merges adjacent bins with the lowest \(\chi^2\) statistic.

    • Merging continues until all adjacent pairs have a p-value less than chi_merge_threshold or the number of bins reaches max_bins.

  2. Chi2 Algorithm:

    • Activated when use_chi2_algorithm = TRUE.

    • Performs multiple passes with decreasing significance levels (0.5 \(\to\) 0.001) to automatically select the optimal significance threshold.

    • Checks for inconsistency rates in the data during the process.

Both methods include post-processing steps to enforce:

  • Minimum Bin Size: Merging rare bins smaller than bin_cutoff.

  • Monotonicity: Ensuring WoE trend is strictly increasing or decreasing to improve model interpretability.

References

Kerber, R. (1992). ChiMerge: Discretization of numeric attributes. Proceedings of the Tenth National Conference on Artificial Intelligence, 123-128.

Liu, H., & Setiono, R. (1995). Chi2: Feature selection and discretization of numeric attributes. Tools with Artificial Intelligence, 388-391.

Examples

# Example 1: Standard ChiMerge
set.seed(123)
feature <- rnorm(1000)
# Create a target with a relationship to the feature
target <- rbinom(1000, 1, plogis(2 * feature))

res_cm <- ob_numerical_cm(feature, target,
  min_bins = 3,
  max_bins = 6,
  init_method = "equal_frequency"
)

print(res_cm$bin)
#> [1] "(-Inf;0.664416]"     "(0.665160;0.840540]" "(0.844904;1.253815]"
#> [4] "(1.263185;1.675697]" "(1.684436;+Inf]"    
print(res_cm$iv)
#> [1] 0.2381152 0.1010034 0.2925531 0.3484273 0.3484273

# Example 2: Using the Chi2 Algorithm variant
res_chi2 <- ob_numerical_cm(feature, target,
  min_bins = 3,
  max_bins = 6,
  use_chi2_algorithm = TRUE
)

cat("Total IV (ChiMerge):", res_cm$total_iv, "\n")
#> Total IV (ChiMerge): 1.328526 
cat("Total IV (Chi2):", res_chi2$total_iv, "\n")
#> Total IV (Chi2): 1.328526