Nonparametric Bootstrap Confidence Intervals for Variance Components in One-Way Random Effects Models

• Activity Number: 253
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Brent Burch*+
• Companies: Northern Arizona University
• Keywords: Bootstrap BC_a method ; Bootstrap standard method ; 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 intervals may be erratic. In this study 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 improves the performance of these bootstrap confidence 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 method produce confidence intervals that have good coverage probabilities under a variety of distribution assumptions. In an interlaboratory comparison application, the exact confidence interval using normal distribution theory produces misleading results and inferences based on nonparametric bootstrap procedures are more appropriate.