Multi-treatment regression analysis: the unbalanced case

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

2 Citations (Scopus)

Abstract

Under multi-treatment regression analysis, instead of a sample for each treatment of a linear model, there is a linear regression in the same variables. Then, instead of the action of the treatments on the sample mean values, the action on regression coefficients is studied. When data is unbalanced, the regression matrices differs between regressions. This problem is solved through the use of a block-wise diagonal covariance matrix in the ANOVA procedures. The methodology was then applied to data obtained from experiments of electrodialtic removal of 3 heavy metals from contaminated wood. First, polynomial regressions of the 4th and 3rd were fitted to each metal concentration in the electrolytes through time. Then the unbalanced case of multi-treatment regression analysis was applied aiming to choose the best treatment in jointly removing the 3 metals. Results pointed to the choice of treatment 1 as the most efficient.

Original languageEnglish
Title of host publicationRecent Researches in Applied Mathematics, Simulation and Modelling - Proceedings of the 5th International Conference on Applied Mathematics, Simulation, Modelling, ASM'11
Pages69-74
Number of pages6
Publication statusPublished - 29 Nov 2011
Event5th International Conference on Applied Mathematics, Simulation, Modelling, ASM'11 - Corfu Island, Greece
Duration: 14 Jul 201116 Jul 2011

Conference

Conference5th International Conference on Applied Mathematics, Simulation, Modelling, ASM'11
CountryGreece
CityCorfu Island
Period14/07/1116/07/11

Fingerprint

Regression Analysis
Regression analysis
Analysis of variance (ANOVA)
Covariance matrix
Metals
Linear regression
Heavy metals
Wood
Electrolytes
Polynomials
Regression
Heavy Metals
Polynomial Regression
Experiments
Sample mean
Diagonal matrix
Electrolyte
Regression Coefficient
Mean Value
Linear Model

Keywords

  • ANOVA
  • F tests
  • Multiple comparison
  • Multiple regression
  • Scheffé
  • Unbalanced data

Cite this

Moreira, E. E., & Mexia, J. T. (2011). Multi-treatment regression analysis: the unbalanced case. In Recent Researches in Applied Mathematics, Simulation and Modelling - Proceedings of the 5th International Conference on Applied Mathematics, Simulation, Modelling, ASM'11 (pp. 69-74)
Moreira, Elsa Estevão ; Mexia, João Tiago. / Multi-treatment regression analysis: the unbalanced case. Recent Researches in Applied Mathematics, Simulation and Modelling - Proceedings of the 5th International Conference on Applied Mathematics, Simulation, Modelling, ASM'11. 2011. pp. 69-74
@inproceedings{b7e3877c195b40438ee53d76e1673273,
title = "Multi-treatment regression analysis: the unbalanced case",
abstract = "Under multi-treatment regression analysis, instead of a sample for each treatment of a linear model, there is a linear regression in the same variables. Then, instead of the action of the treatments on the sample mean values, the action on regression coefficients is studied. When data is unbalanced, the regression matrices differs between regressions. This problem is solved through the use of a block-wise diagonal covariance matrix in the ANOVA procedures. The methodology was then applied to data obtained from experiments of electrodialtic removal of 3 heavy metals from contaminated wood. First, polynomial regressions of the 4th and 3rd were fitted to each metal concentration in the electrolytes through time. Then the unbalanced case of multi-treatment regression analysis was applied aiming to choose the best treatment in jointly removing the 3 metals. Results pointed to the choice of treatment 1 as the most efficient.",
keywords = "ANOVA, F tests, Multiple comparison, Multiple regression, Scheff{\'e}, Unbalanced data",
author = "Moreira, {Elsa Estev{\~a}o} and Mexia, {Jo{\~a}o Tiago}",
year = "2011",
month = "11",
day = "29",
language = "English",
isbn = "9781618040169",
pages = "69--74",
booktitle = "Recent Researches in Applied Mathematics, Simulation and Modelling - Proceedings of the 5th International Conference on Applied Mathematics, Simulation, Modelling, ASM'11",

}

Moreira, EE & Mexia, JT 2011, Multi-treatment regression analysis: the unbalanced case. in Recent Researches in Applied Mathematics, Simulation and Modelling - Proceedings of the 5th International Conference on Applied Mathematics, Simulation, Modelling, ASM'11. pp. 69-74, 5th International Conference on Applied Mathematics, Simulation, Modelling, ASM'11, Corfu Island, Greece, 14/07/11.

Multi-treatment regression analysis: the unbalanced case. / Moreira, Elsa Estevão; Mexia, João Tiago.

Recent Researches in Applied Mathematics, Simulation and Modelling - Proceedings of the 5th International Conference on Applied Mathematics, Simulation, Modelling, ASM'11. 2011. p. 69-74.

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

TY - GEN

T1 - Multi-treatment regression analysis: the unbalanced case

AU - Moreira, Elsa Estevão

AU - Mexia, João Tiago

PY - 2011/11/29

Y1 - 2011/11/29

N2 - Under multi-treatment regression analysis, instead of a sample for each treatment of a linear model, there is a linear regression in the same variables. Then, instead of the action of the treatments on the sample mean values, the action on regression coefficients is studied. When data is unbalanced, the regression matrices differs between regressions. This problem is solved through the use of a block-wise diagonal covariance matrix in the ANOVA procedures. The methodology was then applied to data obtained from experiments of electrodialtic removal of 3 heavy metals from contaminated wood. First, polynomial regressions of the 4th and 3rd were fitted to each metal concentration in the electrolytes through time. Then the unbalanced case of multi-treatment regression analysis was applied aiming to choose the best treatment in jointly removing the 3 metals. Results pointed to the choice of treatment 1 as the most efficient.

AB - Under multi-treatment regression analysis, instead of a sample for each treatment of a linear model, there is a linear regression in the same variables. Then, instead of the action of the treatments on the sample mean values, the action on regression coefficients is studied. When data is unbalanced, the regression matrices differs between regressions. This problem is solved through the use of a block-wise diagonal covariance matrix in the ANOVA procedures. The methodology was then applied to data obtained from experiments of electrodialtic removal of 3 heavy metals from contaminated wood. First, polynomial regressions of the 4th and 3rd were fitted to each metal concentration in the electrolytes through time. Then the unbalanced case of multi-treatment regression analysis was applied aiming to choose the best treatment in jointly removing the 3 metals. Results pointed to the choice of treatment 1 as the most efficient.

KW - ANOVA

KW - F tests

KW - Multiple comparison

KW - Multiple regression

KW - Scheffé

KW - Unbalanced data

UR - http://www.scopus.com/inward/record.url?scp=82055200211&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781618040169

SP - 69

EP - 74

BT - Recent Researches in Applied Mathematics, Simulation and Modelling - Proceedings of the 5th International Conference on Applied Mathematics, Simulation, Modelling, ASM'11

ER -

Moreira EE, Mexia JT. Multi-treatment regression analysis: the unbalanced case. In Recent Researches in Applied Mathematics, Simulation and Modelling - Proceedings of the 5th International Conference on Applied Mathematics, Simulation, Modelling, ASM'11. 2011. p. 69-74