Food security vulnerability

Food Security Under Scrutiny: How Robust Regression Can Help

Theo Raines in Tech & Innovation August 2025 • 4 min read.

"Uncover Food Security Vulnerabilities: A Deep Dive into Data Analysis and Regression Techniques to Safeguard Central Java's Food Supply"

Regression analysis is one of the most versatile tools in a statistician's arsenal. Whether dealing with linear or nonlinear relationships, it helps us model cause-and-effect dynamics across diverse fields—from science and sociology to industry and business. By studying how a dependent variable changes in relation to one or more independent variables, we can create predictive models for future events.

One core objective of regression analysis is estimating regression coefficients within a model. The regression model serves as a structured method for expressing the key elements of a statistical relationship. It captures how the average value of a dependent variable shifts with changes in independent variables, while also accounting for the scatter of points around the estimated model.

The method of least squares is commonly used to estimate regression coefficients. However, this method relies on certain assumptions about the data, such as linearity, normally distributed errors with a constant variance, and the absence of multicollinearity between predictors. When these assumptions are not met, the least squares estimator can become inefficient.

The Outlier Problem and the Need for Robust Methods

Outliers, data points that significantly deviate from the norm, pose a unique challenge. While detecting them can be done in various ways, simply discarding them isn't always wise. Outliers may contain valuable information. Their presence can distort regression coefficient estimates, leading to inaccurate models. This is where robust regression methods come into play. They are designed to be less sensitive to outliers, providing more reliable estimates.

Robust regression techniques offer a way to mitigate the impact of outliers, making them an invaluable tool for data analysis. These methods provide estimates that remain stable even when faced with anomalies. Instead of being drastically affected by outliers, a robust estimator remains relatively unchanged, ensuring the integrity of the analysis.

Some key robust regression methods include:

M-estimation: Renowned for its precision and wide applicability.
Least Trimmed Squares (LTS): Offers robustness by minimizing the sum of squared residuals for a subset of the data.
Least Median Squares (LMS): Focuses on minimizing the median of squared residuals.
S-estimation and MM-estimation: Advanced techniques to further refine robustness.

Among these, M-estimation stands out as a popular choice due to its balance of robustness and efficiency. It involves an iterative process known as Iteratively Reweighted Least Squares (IRLS), which assigns weights to data points based on their residuals. Common weighting functions used in IRLS include Huber's function and Tukey's Bisquare function. The selection of the weighting function is critical to the effectiveness of the robust regression.

Applying Robust Regression to Food Security

The original research paper delves into how M-estimation IRLS using Huber and Tukey Bisquare functions can be applied to food security data in Central Java. By comparing the goodness-of-fit of these methods, the study aims to identify the most reliable approach for estimating model parameters. The findings suggest that the Tukey Bisquare function may be more suitable than the Huber function in this context, as indicated by lower Mean Square Error and higher determination coefficient values. This underscores the importance of carefully selecting robust regression techniques to ensure accurate and insightful analysis of complex datasets.

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This article is based on research published under:

DOI-LINK: 10.14710/medstat.5.1.1-10, Alternate LINK

Title: Kajian Estimasi-M Irls Menggunakan Fungsi Pembobot Huber Dan Bisquare Tukey Pada Data Ketahanan Pangan Di Jawa Tengah

Subject: Anesthesiology and Pain Medicine

Journal: MEDIA STATISTIKA

Publisher: Institute of Research and Community Services Diponegoro University (LPPM UNDIP)

Authors: Elen Dwi Pradewi, Sudarno Sudarno

Published: 2012-06-30

Everything You Need To Know

What is regression analysis and how is it used in statistical modeling?

Regression analysis is a statistical method used to model the relationship between a dependent variable and one or more independent variables. It's versatile and applicable across various fields, helping to create predictive models by estimating how the dependent variable changes in relation to the independent variables. The core objective is to estimate regression coefficients, providing a structured way to express statistical relationships.

What are outliers and why are robust regression methods important when dealing with them?

Outliers are data points that deviate significantly from the norm. While their detection is important, simply discarding them isn't always the best approach because they may contain valuable information. The presence of outliers can distort regression coefficient estimates, leading to inaccurate models. Robust regression methods are designed to mitigate the impact of outliers, providing more reliable estimates even when anomalies are present.

What are robust regression techniques, and what are some key methods?

Robust regression techniques are methods designed to be less sensitive to outliers, providing more reliable estimates than ordinary least squares regression when anomalies are present in the data. Key robust regression methods include M-estimation, Least Trimmed Squares (LTS), Least Median Squares (LMS), S-estimation, and MM-estimation. These techniques aim to ensure the integrity of the analysis by remaining relatively unchanged by outliers.

What is M-estimation in robust regression, and how does it work?

M-estimation is a robust regression method known for its precision and wide applicability. It involves an iterative process called Iteratively Reweighted Least Squares (IRLS), which assigns weights to data points based on their residuals. Common weighting functions used in IRLS include Huber's function and Tukey's Bisquare function. The selection of the weighting function is critical to the effectiveness of the robust regression. Its popularity stems from its balance of robustness and efficiency.

How can robust regression methods be applied to food security data, and what are the implications for analysis?

In the context of food security data analysis in Central Java, M-estimation IRLS using Huber and Tukey Bisquare functions can be applied to estimate model parameters. Research suggests that the Tukey Bisquare function may be more suitable than the Huber function, as indicated by lower Mean Square Error and higher determination coefficient values. This highlights the importance of carefully selecting robust regression techniques to ensure accurate and insightful analysis of complex datasets related to food security.