A Proportional Random Effect Block Bootstrap for General Clustered Data

Clustered data arise naturally in many scientific and applied research settings where units are grouped within clusters. Such data are commonly analyzed using linear mixed models to account for within-cluster correlations. This article proposes a proportional random effect block bootstrap applicable to general linear mixed model settings with imbalanced cluster sizes, both random intercepts and random slopes, and autocorrelation within clusters, while allowing for non-normal random effect and error distributions. It generalizes the original random effect block bootstrap, which was developed for more restrictive settings with balanced cluster sizes, random intercepts only, and constant within-cluster correlation. The proposed bootstrap is shown to be Fisher consistent under these more general settings. Simulations demonstrate strong finite sample inferential performance relative to the original random effect block bootstrap and several existing bootstrap methods for clustered data across a variety of scenarios. Application to the Mayo Clinic primary biliary cirrhosis dataset, which contains cluster sizes ranging from 1 to 16 and exhibits evidence of within-cluster autocorrelation and non-normality, further illustrates improved bootstrap confidence intervals using the proposed method.