Date of Award




Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Epidemiology and Biostatistics



Content Description

1 online resource (v, 58 pages)

Dissertation/Thesis Chair

Recai M. Yucel

Committee Members

Trang Q. Nguyen, Edward L. Valachovic


marginalized multilevel model, missing data, multilevel data, random effects, sequential hierarchical regression imputation, Multiple imputation (Statistics), Multilevel models (Statistics), Markov processes, Monte Carlo method, Markov Chains, Monte Carlo Method

Subject Categories



This dissertation study extends sequential hierarchical regression imputation (SHRIMP) methods to multilevel datasets with three levels of nesting and proposes a marginal method based on marginalized multilevel model (MMM) framework. Specifically, the proposed model consists of two levels such that the first level relates the marginal mean of responses with covariates through a generalized regression model and the second level includes subject specific random effects within the same generalized regression model. To draw the inference on the population-averaged or subject-specified coefficients, the hierarchical regression and/or MMM is applied as the imputation and estimation models. We employ Markov Chain Monte Carlo (MCMC) and/or numerical integration are applied to approximate the conditional posterior predictive distributions. Multiply imputed datasets as drawn from the posterior predictive distribution are analyzed and inferences are then combined using standard multiple imputation (MI) inference (Rubin, 1987). This is essentially a Monte Carlo version of averaging the statistical results over the predictive distribution of the missing data. As we adopt variable-by-variable imputation routines under MMM, the MI estimation can overcome the problem of item nonresponse with skip patterns, bounds, and diverse measurement. The validity of both models is assessed through a Monte Carlo simulation study under various scenarios, and results indicate that our methods and computational algorithms lead to well-calibrated inferences. Finally, we also evaluated the performance of our proposed methods under extreme random-effects distributions through simulation experiment.

Included in

Biostatistics Commons