esa-2scm 0.2.4

ESA-2SCM Python Package for Causal Discovery

ESA-2SCM: Elastic Segment Allocation-based 2SLS Structural Causal Model for Causal Discovery

ESA-2SCM is a new method for detecting causality based on Elastic Segment Allocation-based synthetic instrumental variables with 2SLS application for estimating structural causal models.

For details of the model design, please refer to my Original Article:

• Lee, Sanghoon (2024). ESA-2SCM for Causal Discovery: Causal Modeling with Elastic Segmentation-based Synthetic Instrumental Variable, SnB Political and Economic Research Institute, 1, 21. <snbperi.org/article/230>

Model Overview

Suppose that you are interested in discovering the causal relationship between $x_1$ and $x_2$ (e.g., determining the true causal direction: $x_1$ -> $x_2$ vs. $x_2$ -> $x_1$, measuring the magnitude of causal impact):

Estimation of the above equation under standard OLS is structurally biased and inconsistent due to endogeneity:

where

thus,

The estimators are also asymptotically inconsistent, as:

ESA-2SCM provides a countermeasure to such problem, enabling the determination of true causal direction and estimation of the true causal coefficient through the following procedures.

1. Vector definition:

2. Sorting:

3. Set initial number of segments (M):

4. Segment size allocation:

5. Elastic adjustment algorithm for adjusting the number of segments:

6. Grouping based on the adjusted sizes and number of segments:

7. Segment value assignment:

8. Apply 2SLS using the generated Synthetic IV vectors (Z):
   

   • Get $z_1$ and $z_2$ via applying the process (1) to (7) for $x_1$ and $x_2$, then perform 2SLS to estimate for:

Compare fits to determine the true causal direction, and estimate the true causal coefficient from the correctly identified model.

Requirements

• Python3

• numpy

• pandas

• scipy

Installation

To install the ESA-2SCM package, use pip as follows:

pip install esa-2scm

Example Usage

import numpy as np
import pandas as pd
from esa_2scm import Esa2Scm

# For causal discovery and determination of the true causal direction, input x_1 and x_2 as follows to initialize the ESA-2SCM model:
model = Esa2Scm(x1, x2)

# Fit the model, using Synthetic IV generation method(syniv_method, default: 'ESA') to estimate causality
# Adjust the parameter M(default=2) to manually manage the degree of correlation between the Synthetic IVs (2SLS-converted) and the respective endogenous variables
model.fit(syniv_method="esa", M=2)

# To confirm the estimated causal direction:
print(model.causal_direction)

# To confirm the causal impact coefficient for the detected causal direction:
print(model.causal_coef)

# To confirm the true goodness of fit of the ESA-2SCM for determination of the causal direction:
print(model.esa2scm_score)

# With causal direction determined via ESA-2SCM, to confirm the posthoc goodness of fit of the Regression Model using original variables:
print(model.posthoc_score)

# To check the degree of correlation between the generated Synthetic IVs and the endogenous variables (x1 and x2, respectively):
print(model.corr_x1_to_slsiv)
print(model.corr_x2_to_slsiv)

# For model summary:
model.summary()

Documentation

Original Article of the ESA-2SCM:

• Lee, Sanghoon (2024). ESA-2SCM for Causal Discovery: Causal Modeling with Elastic Segmentation-based Synthetic Instrumental Variable, SnB Political and Economic Research Institute, 1, 21. <snbperi.org/article/230> [ARTICLE LINK]

Examples

Examples of running ESA-2SCM in Jupyter Notebook are included in esa_2scm/examples

License

My package is licensed under the terms of the MIT license

References

ESA-2SCM Package

Should you use my package to perform ESA-2SCM for causal discovery, please kindly cite my Original Article:

• Lee, Sanghoon (2024). ESA-2SCM for Causal Discovery: Causal Modeling with Elastic Segmentation-based Synthetic Instrumental Variable, SnB Political and Economic Research Institute, 1, 21. <snbperi.org/article/230> [ARTICLE LINK]