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Explore poverty with statistical modeling: The bivariate polynomial binary logit regression (BPBLR).

Vita Ratnasari¹, Purhadi¹, Marisa Rifada¹

¹Sepuluh Nopember Institute of Technology, Airlangga University, Mulawarman University, Indonesia.

|January 15, 2025

Summary

This summary is machine-generated.

We introduce the Bivariate Polynomial Binary Logit Regression (BPBLR) for analyzing two related binary outcomes. This statistical method enhances logit regression for complex categorical data analysis, aiding in poverty assessment.

Keywords:

Binary responses Bivariate Logit regression Polynomial Poverty The Bivariate Polynomial Logit Regression Models

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Area of Science:

Statistics
Econometrics
Social Sciences

Background:

Logit regression is a standard statistical method for analyzing categorical data, particularly binary responses.
Existing models often struggle to capture the correlation between multiple binary outcome variables effectively.

Purpose of the Study:

To introduce the Bivariate Polynomial Binary Logit Regression (BPBLR) model.
To extend logit regression for modeling two correlated binary response variables using a polynomial pattern.
To apply the BPBLR model to real-world poverty data for Sustainable Development Goals (SDGs) 1.

Main Methods:

The Bivariate Polynomial Binary Logit Regression (BPBLR) model is proposed, incorporating a polynomial pattern to describe the association between correlated binary responses and predictor variables.
Parameter estimation is performed using the Maximum Likelihood Estimation (MLE) method.
Statistical testing of the model is conducted using the Maximum Likelihood Ratio Test (MLRT), with test statistics asymptotically following a Chi-square distribution.
Model selection and optimal polynomial degree determination are based on minimizing the Deviance value.

Main Results:

The BPBLR model provides a novel approach to statistical modeling for categorical data with two correlated binary response variables.
The MLRT method is utilized for robust statistical testing of the proposed model.
The application to poverty datasets demonstrates the model's utility in analyzing the depth and severity of poverty, contributing to SDG 1 objectives.

Conclusions:

The BPBLR model offers a significant statistical modeling innovation for handling correlated binary outcomes.
The developed methodology, including MLE and MLRT, provides a comprehensive framework for analysis and testing.
The successful application to poverty data highlights the model's practical relevance in addressing complex social issues and supporting global development goals.