Optimal designs for mixed models in experiments based on ordered units

Dibyen Majumdar, John Stufken

Research output: Contribution to journalArticle

Abstract

We consider experiments for comparing treatments using units that are ordered linearly over time or space within blocks. In addition to the block effect, we assume that a trend effect influences the response. The latter is modeled as a smooth component plus a random term that captures departures from the smooth trend. The model is flexible enough to cover a variety of situations; for instance, most of the effects may be either random or fixed. The information matrix for a design will be a function of several variance parameters. While data will shed light on the values of these parameters, at the design stage, they are unlikely to be known, so we suggest a maximin approach, in which a minimal information matrix is maximized. We derive maximin universally optimal designs and study their robustness. These designs are based on semibalanced arrays. Special cases correspond to results available in the literature.

Original languageEnglish (US)
Pages (from-to)1090-1107
Number of pages18
JournalAnnals of Statistics
Volume36
Issue number3
DOIs
StatePublished - Jun 2008
Externally publishedYes

Fingerprint

Mixed Model
Maximin
Information Matrix
Unit
Experiment
Linearly
Cover
Robustness
Term
Design
Mixed model
Trends
Model

Keywords

  • Block designs
  • Orthogonal array of type II
  • Semibalanced arrays
  • Trend effects
  • Universal optimality
  • Variance components

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Optimal designs for mixed models in experiments based on ordered units. / Majumdar, Dibyen; Stufken, John.

In: Annals of Statistics, Vol. 36, No. 3, 06.2008, p. 1090-1107.

Research output: Contribution to journalArticle

Majumdar, Dibyen ; Stufken, John. / Optimal designs for mixed models in experiments based on ordered units. In: Annals of Statistics. 2008 ; Vol. 36, No. 3. pp. 1090-1107.
@article{74489dac0ea24e5b99fffb5a0757cd63,
title = "Optimal designs for mixed models in experiments based on ordered units",
abstract = "We consider experiments for comparing treatments using units that are ordered linearly over time or space within blocks. In addition to the block effect, we assume that a trend effect influences the response. The latter is modeled as a smooth component plus a random term that captures departures from the smooth trend. The model is flexible enough to cover a variety of situations; for instance, most of the effects may be either random or fixed. The information matrix for a design will be a function of several variance parameters. While data will shed light on the values of these parameters, at the design stage, they are unlikely to be known, so we suggest a maximin approach, in which a minimal information matrix is maximized. We derive maximin universally optimal designs and study their robustness. These designs are based on semibalanced arrays. Special cases correspond to results available in the literature.",
keywords = "Block designs, Orthogonal array of type II, Semibalanced arrays, Trend effects, Universal optimality, Variance components",
author = "Dibyen Majumdar and John Stufken",
year = "2008",
month = "6",
doi = "10.1214/07-AOS518",
language = "English (US)",
volume = "36",
pages = "1090--1107",
journal = "Annals of Statistics",
issn = "0090-5364",
publisher = "Institute of Mathematical Statistics",
number = "3",

}

TY - JOUR

T1 - Optimal designs for mixed models in experiments based on ordered units

AU - Majumdar, Dibyen

AU - Stufken, John

PY - 2008/6

Y1 - 2008/6

N2 - We consider experiments for comparing treatments using units that are ordered linearly over time or space within blocks. In addition to the block effect, we assume that a trend effect influences the response. The latter is modeled as a smooth component plus a random term that captures departures from the smooth trend. The model is flexible enough to cover a variety of situations; for instance, most of the effects may be either random or fixed. The information matrix for a design will be a function of several variance parameters. While data will shed light on the values of these parameters, at the design stage, they are unlikely to be known, so we suggest a maximin approach, in which a minimal information matrix is maximized. We derive maximin universally optimal designs and study their robustness. These designs are based on semibalanced arrays. Special cases correspond to results available in the literature.

AB - We consider experiments for comparing treatments using units that are ordered linearly over time or space within blocks. In addition to the block effect, we assume that a trend effect influences the response. The latter is modeled as a smooth component plus a random term that captures departures from the smooth trend. The model is flexible enough to cover a variety of situations; for instance, most of the effects may be either random or fixed. The information matrix for a design will be a function of several variance parameters. While data will shed light on the values of these parameters, at the design stage, they are unlikely to be known, so we suggest a maximin approach, in which a minimal information matrix is maximized. We derive maximin universally optimal designs and study their robustness. These designs are based on semibalanced arrays. Special cases correspond to results available in the literature.

KW - Block designs

KW - Orthogonal array of type II

KW - Semibalanced arrays

KW - Trend effects

KW - Universal optimality

KW - Variance components

UR - http://www.scopus.com/inward/record.url?scp=51049090787&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51049090787&partnerID=8YFLogxK

U2 - 10.1214/07-AOS518

DO - 10.1214/07-AOS518

M3 - Article

AN - SCOPUS:51049090787

VL - 36

SP - 1090

EP - 1107

JO - Annals of Statistics

JF - Annals of Statistics

SN - 0090-5364

IS - 3

ER -