### Abstract

A family of procedures is given to construct confidence intervals for the heritability coefficient in a mixed linear model. The procedures are applicable for constructing confidence intervals for a ratio of variance components in a mixed linear model having two sources of variation. If the random effects are correlated, the procedure is valid even when there are zero degrees of freedom for error. The resulting intervals are evaluated in terms of bias and expected length. A sufficient condition for local unbiasedness is given and a numerical procedure is discussed for computing expected lengths. The investigator may select the best confidence interval procedure from the family of procedures based on these criteria. Computer software for obtaining the best interval is available from the authors.

Original language | English (US) |
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Pages (from-to) | 1318-1333 |

Number of pages | 16 |

Journal | Biometrics |

Volume | 53 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1997 |

### Fingerprint

### Keywords

- Confidence intervals
- Expected length
- Mixed linear model
- Unbiasedness
- Variance components

### ASJC Scopus subject areas

- Agricultural and Biological Sciences(all)
- Public Health, Environmental and Occupational Health
- Agricultural and Biological Sciences (miscellaneous)
- Applied Mathematics
- Statistics and Probability

### Cite this

*Biometrics*,

*53*(4), 1318-1333. https://doi.org/10.2307/2533500

**Exact confidence intervals for a variance ratio (or heritability) in a mixed linear model.** / Burch, Brent D; Iyer, Hari K.

Research output: Contribution to journal › Article

*Biometrics*, vol. 53, no. 4, pp. 1318-1333. https://doi.org/10.2307/2533500

}

TY - JOUR

T1 - Exact confidence intervals for a variance ratio (or heritability) in a mixed linear model

AU - Burch, Brent D

AU - Iyer, Hari K.

PY - 1997/12

Y1 - 1997/12

N2 - A family of procedures is given to construct confidence intervals for the heritability coefficient in a mixed linear model. The procedures are applicable for constructing confidence intervals for a ratio of variance components in a mixed linear model having two sources of variation. If the random effects are correlated, the procedure is valid even when there are zero degrees of freedom for error. The resulting intervals are evaluated in terms of bias and expected length. A sufficient condition for local unbiasedness is given and a numerical procedure is discussed for computing expected lengths. The investigator may select the best confidence interval procedure from the family of procedures based on these criteria. Computer software for obtaining the best interval is available from the authors.

AB - A family of procedures is given to construct confidence intervals for the heritability coefficient in a mixed linear model. The procedures are applicable for constructing confidence intervals for a ratio of variance components in a mixed linear model having two sources of variation. If the random effects are correlated, the procedure is valid even when there are zero degrees of freedom for error. The resulting intervals are evaluated in terms of bias and expected length. A sufficient condition for local unbiasedness is given and a numerical procedure is discussed for computing expected lengths. The investigator may select the best confidence interval procedure from the family of procedures based on these criteria. Computer software for obtaining the best interval is available from the authors.

KW - Confidence intervals

KW - Expected length

KW - Mixed linear model

KW - Unbiasedness

KW - Variance components

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UR - http://www.scopus.com/inward/citedby.url?scp=0031455614&partnerID=8YFLogxK

U2 - 10.2307/2533500

DO - 10.2307/2533500

M3 - Article

VL - 53

SP - 1318

EP - 1333

JO - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 4

ER -