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Abstract:
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Longitudinal investigations play an increasingly prominent role in medicine, psychology and sociology in the last decades. This project is designed to address inference for a two-level mixed model for a longitudinal study where observational units are clustered at both levels. Bootstrap confidence intervals for model parameters are investigated under the issues of non-normality and limited sample size. A two stage case-resampling bootstrap will be established by sampling clusters with replacement at the higher level, and then within each selected cluster, sampling with replacement at the lower level. Monte Carlo simulations will be utilized to evaluate how well this bootstrap method for the mixed effects model performs in terms of confidence interval coverage for the fixed effects as well as for variance components of the random effects. The two-stage bootstrap will be compared to the residual bootstrap and to the bootstrap with case resampling at only the higher level. Furthermore, the effects of the number of clusters and cluster size will also be examined. The bootstrap methods will be applied to a longitudinal study of preschool children nested within classrooms.
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