Date: Thursday, 17 July 2025, at 12:55 pm
Venue: Seminar Room Bruguier Pacini, DEM
Speaker and Title:
Zhi Yang Tho (Australian National University)
A Proportional Random Effect Block Bootstrap for Highly Unbalanced Clustered Data
Abstract:
Clustered data arise naturally in a wide range of scientific and applied research settings where units are grouped within cluster, and are commonly analyzed using linear mixed model to account for within-cluster correlations. This article focuses on the scenario in which cluster sizes might be highly unbalanced, and proposes a proportional random effect block bootstrap that is applicable in such case and is robust to misspecification of the stochastic assumptions of the linear mixed model. The proposed method is a generalization of the random effect block bootstrap, originally designed for the balanced case, and can be used to perform inferences on parameters of the linear mixed model or functions thereof. We establish asymptotic consistency of the proposed bootstrap under general cluster sizes scenario, showing that the original random effect block bootstrap is only consistent when cluster sizes are balanced. A modified random effect block bootstrap is also proposed which enjoys similar asymptotic consistency properties as the proportional random effect block bootstrap. Simulation study demonstrates the strong finite sample inferential performance of the proposed bootstraps, particularly compared with the random effect block bootstrap and several existing bootstrap methods for clustered data. We apply the proposed bootstraps to the Oman rainfall enhancement trial dataset with cluster sizes ranging from 1 to 58. Results show that the bootstrap confidence intervals based on our proposed bootstraps are more adequate than those of random effect block bootstrap and that the employed ionization technology has a statistically significant effect in increasing the amount of rainfall.