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

Sandra Oliveira; Elsa Moreira; Miguel Fonseca; João T. Mexia

doi:10.1145/3274250.3274255

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

Sandra Oliveira, Elsa Moreira, Miguel Fonseca, João T. Mexia

CMA - Centro de Matemática e Aplicações

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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 language	English
Title of host publication	2018 International Conference on Mathematics and Statistics, ICoMS 2018
Publisher	Association for Computing Machinery
Pages	41-45
Number of pages	5
ISBN (Electronic)	9781450365383
DOIs	https://doi.org/10.1145/3274250.3274255
Publication status	Published - 15 Jul 2018
Event	2018 International Conference on Mathematics and Statistics, ICoMS 2018 - Porto, Portugal Duration: 15 Jul 2018 → 17 Jul 2018

Conference

Conference	2018 International Conference on Mathematics and Statistics, ICoMS 2018
Country/Territory	Portugal
City	Porto
Period	15/07/18 → 17/07/18

Keywords

Design of experiments
Linear models
Multiple linear regression
Unbalanced designs

Access to Document

10.1145/3274250.3274255

Cite this

@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 = jul,

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",

note = "2018 International Conference on Mathematics and Statistics, ICoMS 2018 ; Conference date: 15-07-2018 Through 17-07-2018",

}

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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

AN - SCOPUS:85058144356

SP - 41

EP - 45

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

PB - Association for Computing Machinery

T2 - 2018 International Conference on Mathematics and Statistics, ICoMS 2018

Y2 - 15 July 2018 through 17 July 2018

ER -

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

Abstract

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this