Estimation and Hypothesis Testing of Fixed Effects Models-Based Uncertainty for Factor Designs

2026-03-17

AI Summary

This study addresses the lack of effective modeling and inference methods for fixed effects in factorial designs under data uncertainty. It introduces uncertainty measures into one-way and two-way fixed-effects models—with and without interaction—for both balanced and unbalanced designs. Building upon uncertainty theory, the authors develop a unified framework for parameter estimation and hypothesis testing, thereby extending the applicability of classical analysis of variance to settings involving uncertain data. The proposed approach is validated through three real-world case studies, demonstrating consistent effectiveness and practical utility across diverse experimental structures. This work establishes a novel paradigm for analyzing experimental data characterized by inherent uncertainty.

Technology Category

• Reasoning under Uncertainty: Uncertainty Representations
• Machine Learning: Calibration & Uncertainty Quantification
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

To analyze the uncertain data frequently encountered in practice, this paper proposes novel fixed-effects models that incorporate an uncertain measure to investigate variables of interest and nuisance variables in factor designs. First, an uncertain fixed-effects (UFE) model of a single-factor design is established, and uncertain estimation and hypothesis testing are conducted. We then extend the UFE model to two-factor designs with and without interactions and classify them as balanced or unbalanced based on the equality of replicates within each combination. In the above UFE models, the effectiveness and practicality of estimation and hypothesis methods are demonstrated through three real-world cases, including both balanced and unbalanced designs. These examples highlight the models' ability to handle uncertain experimental data.

Problem

• uncertain data
• fixed-effects models
• factor designs
• hypothesis testing
• estimation

Innovation

• uncertain fixed-effects model
• factorial design
• uncertainty measure
• hypothesis testing
• balanced and unbalanced designs