Multiple regression design for a full factorial base model associated with a commutative Jordan algebra

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

If for each treatment of a base model we consider a multiple linear regression on the same variables (dependent and independent) a multiple regression design (MRD) is obtained. If the number of observations per regression is equal, the MRD is balanced, otherwise it is unbalanced. The purpose of this work is to show that is possible to extend the study of the full factorial design of fixed effects and the MRD associated to these designs to the unbalanced cases, combining the linear model associated with a commutative Jordan algebra (CJA) and the L-Model theory. The structure of the factorial design used in this work is based on linear spaces on Galois fields as well as on the relationship between a linear model and a CJA.

Original languageEnglish
Title of host publication2018 International Conference on Mathematics and Statistics, ICoMS 2018
PublisherAssociation for Computing Machinery
Pages41-45
Number of pages5
ISBN (Electronic)9781450365383
DOIs
Publication statusPublished - 15 Jul 2018
Event2018 International Conference on Mathematics and Statistics, ICoMS 2018 - Porto, Portugal
Duration: 15 Jul 201817 Jul 2018

Conference

Conference2018 International Conference on Mathematics and Statistics, ICoMS 2018
CountryPortugal
CityPorto
Period15/07/1817/07/18

Fingerprint

Algebra
Linear regression

Keywords

  • Design of experiments
  • Linear models
  • Multiple linear regression
  • Unbalanced designs

Cite this

Oliveira, S., Moreira, E., Fonseca, M., & Mexia, J. T. (2018). Multiple regression design for a full factorial base model associated with a commutative Jordan algebra. In 2018 International Conference on Mathematics and Statistics, ICoMS 2018 (pp. 41-45). Association for Computing Machinery. https://doi.org/10.1145/3274250.3274255
Oliveira, Sandra ; Moreira, Elsa ; Fonseca, Miguel ; Mexia, João T. / Multiple regression design for a full factorial base model associated with a commutative Jordan algebra. 2018 International Conference on Mathematics and Statistics, ICoMS 2018. Association for Computing Machinery, 2018. pp. 41-45
@inproceedings{d40cd508dea34e6bba53f71b3e9aea9c,
title = "Multiple regression design for a full factorial base model associated with a commutative Jordan algebra",
abstract = "If for each treatment of a base model we consider a multiple linear regression on the same variables (dependent and independent) a multiple regression design (MRD) is obtained. If the number of observations per regression is equal, the MRD is balanced, otherwise it is unbalanced. The purpose of this work is to show that is possible to extend the study of the full factorial design of fixed effects and the MRD associated to these designs to the unbalanced cases, combining the linear model associated with a commutative Jordan algebra (CJA) and the L-Model theory. The structure of the factorial design used in this work is based on linear spaces on Galois fields as well as on the relationship between a linear model and a CJA.",
keywords = "Design of experiments, Linear models, Multiple linear regression, Unbalanced designs",
author = "Sandra Oliveira and Elsa Moreira and Miguel Fonseca and Mexia, {Jo{\~a}o T.}",
year = "2018",
month = "7",
day = "15",
doi = "10.1145/3274250.3274255",
language = "English",
pages = "41--45",
booktitle = "2018 International Conference on Mathematics and Statistics, ICoMS 2018",
publisher = "Association for Computing Machinery",

}

Oliveira, S, Moreira, E, Fonseca, M & Mexia, JT 2018, Multiple regression design for a full factorial base model associated with a commutative Jordan algebra. in 2018 International Conference on Mathematics and Statistics, ICoMS 2018. Association for Computing Machinery, pp. 41-45, 2018 International Conference on Mathematics and Statistics, ICoMS 2018, Porto, Portugal, 15/07/18. https://doi.org/10.1145/3274250.3274255

Multiple regression design for a full factorial base model associated with a commutative Jordan algebra. / Oliveira, Sandra; Moreira, Elsa; Fonseca, Miguel; Mexia, João T.

2018 International Conference on Mathematics and Statistics, ICoMS 2018. Association for Computing Machinery, 2018. p. 41-45.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - Multiple regression design for a full factorial base model associated with a commutative Jordan algebra

AU - Oliveira, Sandra

AU - Moreira, Elsa

AU - Fonseca, Miguel

AU - Mexia, João T.

PY - 2018/7/15

Y1 - 2018/7/15

N2 - If for each treatment of a base model we consider a multiple linear regression on the same variables (dependent and independent) a multiple regression design (MRD) is obtained. If the number of observations per regression is equal, the MRD is balanced, otherwise it is unbalanced. The purpose of this work is to show that is possible to extend the study of the full factorial design of fixed effects and the MRD associated to these designs to the unbalanced cases, combining the linear model associated with a commutative Jordan algebra (CJA) and the L-Model theory. The structure of the factorial design used in this work is based on linear spaces on Galois fields as well as on the relationship between a linear model and a CJA.

AB - If for each treatment of a base model we consider a multiple linear regression on the same variables (dependent and independent) a multiple regression design (MRD) is obtained. If the number of observations per regression is equal, the MRD is balanced, otherwise it is unbalanced. The purpose of this work is to show that is possible to extend the study of the full factorial design of fixed effects and the MRD associated to these designs to the unbalanced cases, combining the linear model associated with a commutative Jordan algebra (CJA) and the L-Model theory. The structure of the factorial design used in this work is based on linear spaces on Galois fields as well as on the relationship between a linear model and a CJA.

KW - Design of experiments

KW - Linear models

KW - Multiple linear regression

KW - Unbalanced designs

UR - http://www.scopus.com/inward/record.url?scp=85058144356&partnerID=8YFLogxK

U2 - 10.1145/3274250.3274255

DO - 10.1145/3274250.3274255

M3 - Conference contribution

SP - 41

EP - 45

BT - 2018 International Conference on Mathematics and Statistics, ICoMS 2018

PB - Association for Computing Machinery

ER -

Oliveira S, Moreira E, Fonseca M, Mexia JT. Multiple regression design for a full factorial base model associated with a commutative Jordan algebra. In 2018 International Conference on Mathematics and Statistics, ICoMS 2018. Association for Computing Machinery. 2018. p. 41-45 https://doi.org/10.1145/3274250.3274255