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DataScedasticity: Gnostic Homoscedasticity and Heteroscedasticity Test (Machine Gnostics)

The DataScedasticity class provides a gnostic approach to testing for homoscedasticity and heteroscedasticity in data using local gnostic distribution functions (ELDF, QLDF). Unlike classical statistical tests that check residuals, this method analyzes the variability of the gnostic scale parameter.

Overview

This class determines whether a dataset is homoscedastic (constant scale) or heteroscedastic (varying scale) using a fitted Gnostic (Local) Distribution Function (GDF).

The Gnostic Approach: If the estimated Scale parameter (S) is variable across the domain (varS=True), the data is considered heteroscedastic. If the Scale parameter is constant, the data is homoscedastic.

Key differences vs. standard tests: - Uses GDF's scale parameter (S_var) instead of residual-based heuristics. - Works with local/global gnostic scale (S_local, S_opt) for inference. - Integrates directly with Machine Gnostics models (ELDF, QLDF).

Key Features

  • Direct GDF Integration: Works seamlessly with ELDF and QLDF.
  • Scale-Based Inference: Uses the fundamental gnostic scale parameter.
  • Robust Classification: Simple decision boundary based on scale variability.
  • Detailed Diagnostics: Provides access to local and global scale parameters.

Parameters

Parameter Type Default Description
gdf Union[ELDF, QLDF] ELDF Fitted GDF instance (must be ELDF or QLDF) configured with varS=True.
catch bool True Whether to store analysis results in params.
verbose bool False Enables debug-level logging when True.

Attributes

  • gdf: Union[ELDF, QLDF] The underlying GDF instance.
  • params: dict Results container populated after fit().
  • fitted: bool Boolean indicating whether scedasticity classification has been run.

Methods

fit()

Classify scedasticity based on the variability of the GDF's scale parameter.

Returns: bool — True if data is homoscedastic (constant scale), False if heteroscedastic.

results()

Return a dictionary summarizing the scedasticity analysis.

Returns: dict — Contains keys:

  • 'scedasticity': 'homoscedastic' or 'heteroscedastic'
  • 'scale_parameter': The S_var array from the GDF
  • 'S_local': Local gnostic scale values
  • 'S_global': Global/optimal gnostic scale (S_opt)

Example Usage

import numpy as np
from machinegnostics.magcal import ELDF, DataScedasticity

# Example data (stack-loss data)
y = np.array([ 7,  8,  8,  8,  9, 11, 12, 13, 14, 14, 15, 15, 15, 18, 18, 19, 20, 28, 37, 37, 42])

# Step 1: Fit ELDF with variable scale (essential for scedasticity check)
eldf = ELDF(varS=True, verbose=False)
eldf.fit(data=y, plot=True)

# Step 2: Run scedasticity test
sc = DataScedasticity(gdf=eldf, verbose=True)
is_homo = sc.fit()

# Step 3: Check results
print(f"Is data homoscedastic? {is_homo}")
info = sc.results()

Scedasticity Analysis

Notes

  • The supplied gdf must be an instance of ELDF or QLDF, fitted with varS=True.
  • Validation is performed during initialization to ensure the GDF is compatible.
  • fit() sets the internal state; call results() afterwards to obtain a structured dictionary of outputs.

Author: Nirmal Parmar
Date: 2025-10-10