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

TL;DR

This paper introduces novel fixed-effects models that incorporate uncertainty measures to improve analysis and hypothesis testing in factor designs, effectively handling real-world uncertain data.

Contribution

It develops a new uncertain fixed-effects (UFE) model for single and multi-factor designs, including balanced and unbalanced cases, with demonstrated practical effectiveness.

Findings

Effective estimation and hypothesis testing in uncertain data scenarios

Models successfully applied to real-world balanced and unbalanced designs

Enhanced analysis of factor designs with uncertain measurements

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.