Analysis of uncertain fixed-effects model for Latin square designs

2026-06-18

AI Summary

This study addresses the challenge of frequency instability in Latin square designs arising from data uncertainty, which traditional fixed-effects models struggle to handle effectively. For the first time, uncertainty theory is integrated into Latin square design to formulate a fixed-effects model grounded in uncertain measures. The work proposes three estimation methods for treatment effects, constructs corresponding confidence intervals, and develops a hypothesis testing framework for assessing both homogeneity and the significance of treatment effects. Through numerical simulations, the methods are evaluated in terms of bias and mean squared error, and their practical utility is demonstrated using real-world educational data. Results show that the proposed approaches achieve high estimation accuracy and reliable inferential performance under uncertainty.

Abstract

Uncertain data without frequency stability often arises in experimental design. Classical fixed-effects models can only analyze precise experimental data. Based on an uncertain measure, this paper establishes uncertain fixed-effect models for Latin-square designs. First, we propose three methods with uncertainty to estimate the treatment and blocked effects and construct their confidence intervals. Then, uncertain homogeneity and common tests are conducted to assess the significance of treatment effects. In the numerical simulations, the three estimation methods are compared based on bias, mean squared error, mean absolute error, overall standard deviation, coverage probability, and average interval length. Several examples are given to illustrate the process of estimation and hypothesis. Finally, the uncertain fixed-effects model is applied to real education data, demonstrating its practical value.

Problem

• uncertain data
• fixed-effects model
• Latin square design
• experimental design
• uncertainty

Innovation

• uncertain fixed-effects model
• Latin square design
• uncertain measure
• confidence interval
• hypothesis testing