Work

Linear Models with Nested Random Effects

Year: 2025

Type: article

Abstract: Symmetry is a crucial concept in various fields of mathematics, offering a systematic approach to understanding structural properties and simplifying complex problems. This study focuses on linear mixed models, emphasizing the role of symmetry in the design of experiments and the structure of variance–covariance matrices. Building on foundational works, this paper introduces the concept of nested models and employs Wishart matrices for variance component estimation, enhancing the efficiency of complex model analysis. The methodology is particularly applicable when variance–covariance matrices conform to a commutative Jordan algebra (CJA). The practical significance of this modeling approach is demonstrated through numerical applications using both simulated and real-world data.

Source: Symmetry

DOI: 10.3390/sym17030374

Author: Dário Ferreira

Institution: University of Beira Interior

Language: English

Topic: Optimal Experimental Design Methods

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Fundação para a Ciência e a Tecnologia