Confidence intervals for variance components in unbalanced one-way random effects model using non-normal distributions

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Abstract

In scenarios where the variance of a response variable can be attributed to two sources of variation, a confidence interval for a ratio of variance components gives information about the relative importance of the two sources. For example, if measurements taken from different laboratories are nine times more variable than the measurements taken from within the laboratories, then 90% of the variance in the responses is due to the variability amongst the laboratories and 10% of the variance in the responses is due to the variability within the laboratories. Assuming normally distributed sources of variation, confidence intervals for variance components are readily available. In this paper, however, simulation studies are conducted to evaluate the performance of confidence intervals under non-normal distribution assumptions. Confidence intervals based on the pivotal quantity method, fiducial inference, and the large-sample properties of the restricted maximum likelihood (REML) estimator are considered. Simulation results and an empirical example suggest that the REML-based confidence interval is favored over the other two procedures in unbalanced one-way random effects model.

Original languageEnglish (US)
Pages (from-to)3793-3807
Number of pages15
JournalJournal of Statistical Planning and Inference
Volume141
Issue number12
DOIs
StatePublished - Dec 2011

Fingerprint

Non-normal Distribution
Variance Components
Random Effects Model
Confidence interval
Maximum likelihood
Restricted Maximum Likelihood Estimator
Pivotal Quantity
Restricted Maximum Likelihood
Components of Variance
Variance components
Random effects model
Simulation Study
Scenarios
Evaluate
Simulation

Keywords

  • Fiducial inference
  • Pivotal quantity
  • Restricted maximum likelihood estimation

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Statistics and Probability

Cite this

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title = "Confidence intervals for variance components in unbalanced one-way random effects model using non-normal distributions",
abstract = "In scenarios where the variance of a response variable can be attributed to two sources of variation, a confidence interval for a ratio of variance components gives information about the relative importance of the two sources. For example, if measurements taken from different laboratories are nine times more variable than the measurements taken from within the laboratories, then 90{\%} of the variance in the responses is due to the variability amongst the laboratories and 10{\%} of the variance in the responses is due to the variability within the laboratories. Assuming normally distributed sources of variation, confidence intervals for variance components are readily available. In this paper, however, simulation studies are conducted to evaluate the performance of confidence intervals under non-normal distribution assumptions. Confidence intervals based on the pivotal quantity method, fiducial inference, and the large-sample properties of the restricted maximum likelihood (REML) estimator are considered. Simulation results and an empirical example suggest that the REML-based confidence interval is favored over the other two procedures in unbalanced one-way random effects model.",
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