Nonparametric Bootstrap Confidence Intervals for Variance Components Applied to Interlaboratory Comparisons

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4 Citations (Scopus)

Abstract

Exact confidence intervals for variance components in linear mixed models rely heavily on normal distribution assumptions. If the random effects in the model are not normally distributed, then the true coverage probabilities of these conventional intervals may be erratic. In this paper we examine the performance of nonparametric bootstrap confidence intervals based on restricted maximum likelihood (REML) estimators. Asymptotic theory suggests that these intervals will achieve the nominal coverage value as the sample size increases. Incorporating a small-sample adjustment term in the bootstrap confidence interval construction process improves the performance of these intervals for small to intermediate sample sizes. Simulation studies suggest that the bootstrap standard method (with a transformation) and the bootstrap bias-corrected and accelerated (BC a) method produce confidence intervals that have good coverage probabilities under a variety of distribution assumptions. For an interlaboratory comparison of mercury concentration in oyster tissue, a balanced one-way random effects model is used to quantify the proportion of the variation in mercury concentration that can be attributed to the laboratories. In this application the exact confidence interval using normal distribution theory produces misleading results and inferences based on nonparametric bootstrap procedures are more appropriate.

Original languageEnglish (US)
Pages (from-to)228-245
Number of pages18
JournalJournal of Agricultural, Biological, and Environmental Statistics
Volume17
Issue number2
DOIs
StatePublished - Jun 2012

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Nonparametric Bootstrap
interlaboratory comparison
Bootstrap Confidence Intervals
Variance Components
Exact Confidence Interval
confidence interval
Mercury
Coverage Probability
Normal distribution
Confidence Intervals
Bootstrap
Interval
Gaussian distribution
Sample Size
Restricted Maximum Likelihood Estimator
Normal Distribution
Linear Mixed Model
Distribution Theory
mercury
Random Effects Model

Keywords

  • Bootstrap BC method
  • Bootstrap standard method
  • One-way random effects model
  • Small-sample adjustment

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

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title = "Nonparametric Bootstrap Confidence Intervals for Variance Components Applied to Interlaboratory Comparisons",
abstract = "Exact confidence intervals for variance components in linear mixed models rely heavily on normal distribution assumptions. If the random effects in the model are not normally distributed, then the true coverage probabilities of these conventional intervals may be erratic. In this paper we examine the performance of nonparametric bootstrap confidence intervals based on restricted maximum likelihood (REML) estimators. Asymptotic theory suggests that these intervals will achieve the nominal coverage value as the sample size increases. Incorporating a small-sample adjustment term in the bootstrap confidence interval construction process improves the performance of these intervals for small to intermediate sample sizes. Simulation studies suggest that the bootstrap standard method (with a transformation) and the bootstrap bias-corrected and accelerated (BC a) method produce confidence intervals that have good coverage probabilities under a variety of distribution assumptions. For an interlaboratory comparison of mercury concentration in oyster tissue, a balanced one-way random effects model is used to quantify the proportion of the variation in mercury concentration that can be attributed to the laboratories. In this application the exact confidence interval using normal distribution theory produces misleading results and inferences based on nonparametric bootstrap procedures are more appropriate.",
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AB - Exact confidence intervals for variance components in linear mixed models rely heavily on normal distribution assumptions. If the random effects in the model are not normally distributed, then the true coverage probabilities of these conventional intervals may be erratic. In this paper we examine the performance of nonparametric bootstrap confidence intervals based on restricted maximum likelihood (REML) estimators. Asymptotic theory suggests that these intervals will achieve the nominal coverage value as the sample size increases. Incorporating a small-sample adjustment term in the bootstrap confidence interval construction process improves the performance of these intervals for small to intermediate sample sizes. Simulation studies suggest that the bootstrap standard method (with a transformation) and the bootstrap bias-corrected and accelerated (BC a) method produce confidence intervals that have good coverage probabilities under a variety of distribution assumptions. For an interlaboratory comparison of mercury concentration in oyster tissue, a balanced one-way random effects model is used to quantify the proportion of the variation in mercury concentration that can be attributed to the laboratories. In this application the exact confidence interval using normal distribution theory produces misleading results and inferences based on nonparametric bootstrap procedures are more appropriate.

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