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

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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.

Original languageEnglish (US)
Pages (from-to)1018-1028
Number of pages11
JournalComputational Statistics and Data Analysis
Volume55
Issue number2
DOIs
StatePublished - Feb 1 2011

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Intraclass Correlation Coefficient
Restricted Maximum Likelihood
Maximum likelihood
Confidence interval
Interval
Variance Components
Coverage Probability
Restricted Maximum Likelihood Estimator
Pivotal Quantity
Non-normal Distribution
Expected Length
Point Estimation
Non-normality
Pivot
Kurtosis
Maximum Likelihood Method
Normality
Asymptotic distribution
Guidance
Normal distribution

Keywords

  • Asymptotic distributions
  • Kurtosis
  • One-way random effects model
  • Pivotal quantity

ASJC Scopus subject areas

  • Computational Mathematics
  • Computational Theory and Mathematics
  • Statistics and Probability
  • Applied Mathematics

Cite this

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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.",
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