Comparing pivotal and REML-based confidence intervals for heritability

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Heritability quantifies the extent to which a physical characteristic is passed from one generation to the next. From a statistical perspective, heritability is the proportion of the phenotypic variance attributable to (additive) genetic effects and is equal to a function of variance components in linear mixed models. Relying on normal distribution assumptions, one can compute exact confidence intervals for heritability using a pivotal quantity procedure. Alternatively, large-sample properties of the restricted maximum likelihood (REML) estimator can be used to construct asymptotic confidence intervals for heritability. Exact and asymptotic intervals are compared to one another in a variety of situations, including a mixed model having correlated loineye muscle area measurements and balanced one-way random effects models having groups of correlated responses. In some cases the two interval methods yield vastly different results and the REML-based confidence interval does not maintain the nominal coverage value even for seemingly large sample sizes. For finite sample size applications, the validity of the REML-based procedure depends on the correlation structure of the data.

Original languageEnglish (US)
Pages (from-to)470-484
Number of pages15
JournalJournal of Agricultural, Biological, and Environmental Statistics
Volume12
Issue number4
DOIs
StatePublished - Dec 2007

Fingerprint

Heritability
Restricted Maximum Likelihood
heritability
confidence interval
Maximum likelihood
Confidence interval
Confidence Intervals
Sample Size
Normal Distribution
Restricted Maximum Likelihood Estimator
Normal distribution
Pivotal Quantity
Exact Confidence Interval
Components of Variance
Interval Methods
Linear Mixed Model
Muscle
correlated responses
Random Effects Model
Linear Models

Keywords

  • Exact and asymptotic results
  • Linear mixed models
  • Variance components

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Environmental Science(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics
  • Statistics, Probability and Uncertainty
  • Statistics and Probability

Cite this

@article{46af0b0bde644ffa9af94649bc26a16b,
title = "Comparing pivotal and REML-based confidence intervals for heritability",
abstract = "Heritability quantifies the extent to which a physical characteristic is passed from one generation to the next. From a statistical perspective, heritability is the proportion of the phenotypic variance attributable to (additive) genetic effects and is equal to a function of variance components in linear mixed models. Relying on normal distribution assumptions, one can compute exact confidence intervals for heritability using a pivotal quantity procedure. Alternatively, large-sample properties of the restricted maximum likelihood (REML) estimator can be used to construct asymptotic confidence intervals for heritability. Exact and asymptotic intervals are compared to one another in a variety of situations, including a mixed model having correlated loineye muscle area measurements and balanced one-way random effects models having groups of correlated responses. In some cases the two interval methods yield vastly different results and the REML-based confidence interval does not maintain the nominal coverage value even for seemingly large sample sizes. For finite sample size applications, the validity of the REML-based procedure depends on the correlation structure of the data.",
keywords = "Exact and asymptotic results, Linear mixed models, Variance components",
author = "Burch, {Brent D.}",
year = "2007",
month = "12",
doi = "10.1198/108571107X250526",
language = "English (US)",
volume = "12",
pages = "470--484",
journal = "Journal of Agricultural, Biological, and Environmental Statistics",
issn = "1085-7117",
publisher = "Springer New York",
number = "4",

}

TY - JOUR

T1 - Comparing pivotal and REML-based confidence intervals for heritability

AU - Burch, Brent D.

PY - 2007/12

Y1 - 2007/12

N2 - Heritability quantifies the extent to which a physical characteristic is passed from one generation to the next. From a statistical perspective, heritability is the proportion of the phenotypic variance attributable to (additive) genetic effects and is equal to a function of variance components in linear mixed models. Relying on normal distribution assumptions, one can compute exact confidence intervals for heritability using a pivotal quantity procedure. Alternatively, large-sample properties of the restricted maximum likelihood (REML) estimator can be used to construct asymptotic confidence intervals for heritability. Exact and asymptotic intervals are compared to one another in a variety of situations, including a mixed model having correlated loineye muscle area measurements and balanced one-way random effects models having groups of correlated responses. In some cases the two interval methods yield vastly different results and the REML-based confidence interval does not maintain the nominal coverage value even for seemingly large sample sizes. For finite sample size applications, the validity of the REML-based procedure depends on the correlation structure of the data.

AB - Heritability quantifies the extent to which a physical characteristic is passed from one generation to the next. From a statistical perspective, heritability is the proportion of the phenotypic variance attributable to (additive) genetic effects and is equal to a function of variance components in linear mixed models. Relying on normal distribution assumptions, one can compute exact confidence intervals for heritability using a pivotal quantity procedure. Alternatively, large-sample properties of the restricted maximum likelihood (REML) estimator can be used to construct asymptotic confidence intervals for heritability. Exact and asymptotic intervals are compared to one another in a variety of situations, including a mixed model having correlated loineye muscle area measurements and balanced one-way random effects models having groups of correlated responses. In some cases the two interval methods yield vastly different results and the REML-based confidence interval does not maintain the nominal coverage value even for seemingly large sample sizes. For finite sample size applications, the validity of the REML-based procedure depends on the correlation structure of the data.

KW - Exact and asymptotic results

KW - Linear mixed models

KW - Variance components

UR - http://www.scopus.com/inward/record.url?scp=56349164290&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=56349164290&partnerID=8YFLogxK

U2 - 10.1198/108571107X250526

DO - 10.1198/108571107X250526

M3 - Article

VL - 12

SP - 470

EP - 484

JO - Journal of Agricultural, Biological, and Environmental Statistics

JF - Journal of Agricultural, Biological, and Environmental Statistics

SN - 1085-7117

IS - 4

ER -