Obtención de la matriz de varianzas y covarianzas a través de los productos Kronecker en modelos balanceados de dos y tres vías con aplicaciones en R

Abstract

Obtainment of the variance-covariance matrix through Kronecker products for balanced models of two and three ways withapplications in R. Objective. To present a methodology based on the concept of Kronecker products that facilitates the constructionof the variance and covariance matrix for designs with balanced data structure for 2 and 3 ways, and an application in R to facilitateits calculation and application in different areas. Materials and methods. We provide a starting point for people interested in using Rin the analysis of variance. Results. We use an application made in R for a methodology based on Kronecker products through whichwe build the covariance matrix for working with designs with balanced data structure developed by Moya (2003). We also present anapplication of the method with real data. Conclusions. With this methodology we can accelerate the development and solution of somepractical problems. The proposed methodology can be applied to mixed models with fixed or random effects with any number of factors.

Keywords

• Kronecker products
• variance and covariance matrix
• balanced designs
• linear models
• R Gui