Multiple comparison of several linear regression models

Wei Liu, Mortaza Jamshidian, Ying Zhang

Research output: Contribution to journalArticle

53 Citations (Scopus)

Abstract

Research on multiple comparison during the past 50 years or so has focused mainly on the comparison of several population means. Several years ago, Spurrier considered the multiple comparison of several simple linear regression lines. He constructed simultaneous confidence bands for all of the contrasts of the simple linear regression lines over the entire range (-∞, ∞) when the models have the same design matrices. This article extends Spurrier's work in several directions. First, multiple linear regression models are considered and the design matrices are allowed to be different. Second, the predictor variables are either unconstrained or constrained to finite intervals. Third, the types of comparison allowed can be very flexible, including pairwise, many-one, and successive. Two simulation methods are proposed for the calculation of critical constants. The methodologies are illustrated with examples.

Original languageEnglish (US)
Pages (from-to)395-403
Number of pages9
JournalJournal of the American Statistical Association
Volume99
Issue number466
DOIs
StatePublished - Jun 1 2004

Fingerprint

Regression line
Simple Linear Regression
Multiple Comparisons
Linear Regression Model
Simultaneous Confidence Bands
Multiple Linear Regression
Simulation Methods
Pairwise
Predictors
Entire
Interval
Methodology
Range of data
Design
Linear regression
Linear regression model
Multiple comparisons
Model
Multiple linear regression
Simulation methods

Keywords

  • Drug stability testing
  • Linear regression
  • Multiple comparisons
  • Simultaneous inference
  • Statistical simulation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Multiple comparison of several linear regression models. / Liu, Wei; Jamshidian, Mortaza; Zhang, Ying.

In: Journal of the American Statistical Association, Vol. 99, No. 466, 01.06.2004, p. 395-403.

Research output: Contribution to journalArticle

Liu, Wei ; Jamshidian, Mortaza ; Zhang, Ying. / Multiple comparison of several linear regression models. In: Journal of the American Statistical Association. 2004 ; Vol. 99, No. 466. pp. 395-403.
@article{a020ecd075a349bf833a4df5e3113a25,
title = "Multiple comparison of several linear regression models",
abstract = "Research on multiple comparison during the past 50 years or so has focused mainly on the comparison of several population means. Several years ago, Spurrier considered the multiple comparison of several simple linear regression lines. He constructed simultaneous confidence bands for all of the contrasts of the simple linear regression lines over the entire range (-∞, ∞) when the models have the same design matrices. This article extends Spurrier's work in several directions. First, multiple linear regression models are considered and the design matrices are allowed to be different. Second, the predictor variables are either unconstrained or constrained to finite intervals. Third, the types of comparison allowed can be very flexible, including pairwise, many-one, and successive. Two simulation methods are proposed for the calculation of critical constants. The methodologies are illustrated with examples.",
keywords = "Drug stability testing, Linear regression, Multiple comparisons, Simultaneous inference, Statistical simulation",
author = "Wei Liu and Mortaza Jamshidian and Ying Zhang",
year = "2004",
month = "6",
day = "1",
doi = "10.1198/016214504000000395",
language = "English (US)",
volume = "99",
pages = "395--403",
journal = "Journal of the American Statistical Association",
issn = "0162-1459",
publisher = "Taylor and Francis Ltd.",
number = "466",

}

TY - JOUR

T1 - Multiple comparison of several linear regression models

AU - Liu, Wei

AU - Jamshidian, Mortaza

AU - Zhang, Ying

PY - 2004/6/1

Y1 - 2004/6/1

N2 - Research on multiple comparison during the past 50 years or so has focused mainly on the comparison of several population means. Several years ago, Spurrier considered the multiple comparison of several simple linear regression lines. He constructed simultaneous confidence bands for all of the contrasts of the simple linear regression lines over the entire range (-∞, ∞) when the models have the same design matrices. This article extends Spurrier's work in several directions. First, multiple linear regression models are considered and the design matrices are allowed to be different. Second, the predictor variables are either unconstrained or constrained to finite intervals. Third, the types of comparison allowed can be very flexible, including pairwise, many-one, and successive. Two simulation methods are proposed for the calculation of critical constants. The methodologies are illustrated with examples.

AB - Research on multiple comparison during the past 50 years or so has focused mainly on the comparison of several population means. Several years ago, Spurrier considered the multiple comparison of several simple linear regression lines. He constructed simultaneous confidence bands for all of the contrasts of the simple linear regression lines over the entire range (-∞, ∞) when the models have the same design matrices. This article extends Spurrier's work in several directions. First, multiple linear regression models are considered and the design matrices are allowed to be different. Second, the predictor variables are either unconstrained or constrained to finite intervals. Third, the types of comparison allowed can be very flexible, including pairwise, many-one, and successive. Two simulation methods are proposed for the calculation of critical constants. The methodologies are illustrated with examples.

KW - Drug stability testing

KW - Linear regression

KW - Multiple comparisons

KW - Simultaneous inference

KW - Statistical simulation

UR - http://www.scopus.com/inward/record.url?scp=2942568478&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2942568478&partnerID=8YFLogxK

U2 - 10.1198/016214504000000395

DO - 10.1198/016214504000000395

M3 - Article

AN - SCOPUS:2942568478

VL - 99

SP - 395

EP - 403

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 466

ER -