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Assessing the performance of normal-based and REML-based confidence intervals for the intraclass correlation coefficient

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  • Burch, Brent D.

Abstract

Using normal distribution assumptions, one can obtain confidence intervals for variance components in a variety of applications. A normal-based interval, which has exact coverage probability under normality, is usually constructed from a pivot so that the endpoints of the interval depend on the data as well as the distribution of the pivotal quantity. Alternatively, one can employ a point estimation technique to form a large-sample (or approximate) confidence interval. A commonly used approach to estimate variance components is the restricted maximum likelihood (REML) method. The endpoints of a REML-based confidence interval depend on the data and the asymptotic distribution of the REML estimator. In this paper, simulation studies are conducted to evaluate the performance of the normal-based and the REML-based intervals for the intraclass correlation coefficient under non-normal distribution assumptions. Simulated coverage probabilities and expected lengths provide guidance as to which interval procedure is favored for a particular scenario. Estimating the kurtosis of the underlying distribution plays a central role in implementing the REML-based procedure. An empirical example is given to illustrate the usefulness of the REML-based confidence intervals under non-normality.

Suggested Citation

  • Burch, Brent D., 2011. "Assessing the performance of normal-based and REML-based confidence intervals for the intraclass correlation coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1018-1028, February.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:2:p:1018-1028
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    References listed on IDEAS

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    1. S. Ahmed & A. Gupta & S. Khan & C. Nicol, 2001. "Simultaneous Estimation of Several Intraclass Correlation Coefficients," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 354-369, June.
    2. An, Lihua & Ahmed, S. Ejaz, 2008. "Improving the performance of kurtosis estimator," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2669-2681, January.
    3. Brent D. Burch & Ian R. Harris, 2001. "Closed-Form Approximations to the REML Estimator of a Variance Ratio (or Heritability) in a Mixed Linear Model," Biometrics, The International Biometric Society, vol. 57(4), pages 1148-1156, December.
    4. Bonett, Douglas G., 2006. "Approximate confidence interval for standard deviation of nonnormal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 775-782, February.
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    Cited by:

    1. Sofer Tamar, 2017. "Confidence intervals for heritability via Haseman-Elston regression," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 16(4), pages 259-273, September.

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