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 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 nomiral coverate 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.
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References
Burch, B. D., and Harris, I. R. (2001), “Closed-Form Approximations to the REML Estimator of a Variance Ratio (or Heritability) in a Mixed Linear Model,” Biometrics, 57, 1148–1156.
Burch, B. D., and Iyer, H. K. (1997), “Exact Confidence Intervals for a Variance Ratio (or Heritability) in a Mixed Linear Model,” Biometrics, 53, 1318–1333.
Burdick, R. K., Borror, C. M., and Montgomery, D. C. (2003), “A Review of Methods for Measurement Systems Capability Analysis,” Journal of Quality Technology, 35, 342–354.
Charif, H. A. (2003), “Confidence Intervals for the Variance Ratio in Mixed Linear Models,” Advances and Applications in Statistics, 3, 229–241.
Evans, J. L., Golden, B. L., Bailey, D. R. C., Gilbert, R. P., and Green, R. D., (1995), “Genetic Parameter Estimates of Ultrasound Measures of Backfat Thickness, Loineye Muscle Area, and Gray Shading Score in Red Angus Cattle,” Proceedings, Western Section, American Society of Animal Science, 46, 202–204.
Falconer, D. S., and Mackay, T. F. C. (1996), Introduction to Quantitative Genetics, Essex, England: Longman Scientific & Technical.
Gianola, D. (2000), “Statistics in Animal Breeding,” Journal of the American Statistical Association, 95, 296–299.
Harville, D. A., and Fenech, F. A. (1985), “Confidence Intervals for a Variance Ratio, or for Heritability, in an Unbalanced Mixed Linear Model,” Biometrics, 41, 137–152.
Henderson, C. R. (1976), “A Simple Method for Computing the Inverse of a Numerator Relationship Matrix used in Prediction of Breeding Values,” Biometrics, 32, 69–83.
Iyer, H. K., Wang, C. M. J., and Mathew, T. (2004), “Models and Confidence Intervals for True Values in Interlaboratory Trials,” Journal of the American Statistical Association, 99, 1060–1071.
Jiang, J. (1996), “REML Estimation: Asymptotic Behavior and Related Topics,” The Annals of Statistics, 24, 255–286.
Moran, P. A. P. (1971), “Maximum Likelihood Estimation in Non-standard Conditions,” Proceedings of the Cambridge Philosophical Society 70, 441–450.
Stern, S. E., and Welsh, A. H. (2000), “Likelihood Inference for Small Variance Components,” The Canadian Journal of Statistics, 28, 517–532.
Westfall, P. H. (1987), “A Comparison of Variance Component Estimates for Arbitrary Underlying Distributions,” Journal of the American Statistical Association, 82, 866–874.
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Burch, B.D. Comparing pivotal and REML-based confidence intervals for heritability. JABES 12, 470–484 (2007). https://doi.org/10.1198/108571107X250526
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DOI: https://doi.org/10.1198/108571107X250526