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 language | English (US) |
|---|---|
| Pages (from-to) | 470-484 |
| Number of pages | 15 |
| Journal | Journal of Agricultural, Biological, and Environmental Statistics |
| Volume | 12 |
| Issue number | 4 |
| DOIs | |
| State | Published - Dec 2007 |
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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
Comparing pivotal and REML-based confidence intervals for heritability. / Burch, Brent D.
In: Journal of Agricultural, Biological, and Environmental Statistics, Vol. 12, No. 4, 12.2007, p. 470-484.Research output: Contribution to journal › Article
}
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
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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 -