UC Davis

Intensive longitudinal studies gather at least 20 repeated measurements spaced closely in time from multiple individuals. The spacing of the repeated measurements is close enough in time to provide a granular look at the dynamic process taking place. Multilevel location scale models (MLSMs) are ideally suited to describe the dynamic processes captured by the collection of intensive longitudinal data. They include a sub-model for the person-specific variance of the residuals about each individual longitudinal trajectory, facilitating the study of observed and unobserved individual differences in the average within-individual variance. They can also include a sub-model for the variance of each random effect that describes an aspect of the individual-level trajectories (e.g., intercepts and slopes), facilitating the study of heterogeneity of the random-effect variances due to observed occasion- and individual-level covariates. When incomplete level 2 covariates are included in multilevel models, it is common for individuals who are missing level 2 covariate data to be excluded from the analysis. This reduction in sample size can result in decreased statistical power and increased risk of biased inference. The purpose of this dissertation is to explore methods for augmenting incomplete level 2 covariates so that important characteristics of MLSM-generated data are preserved. Chapter 1 reviews the literature on missing data and missing data handling methods in the context of estimating MLSMs. This includes the review of multilevel multiple imputation (MMI), a missing data handling method commonly applied in the context of estimating a multilevel model. MMI is used to fill in missing values to preserve important characteristics of multilevel data, provided that the imputation model is accurately specified. MMI as currently implemented in standard statistical software, however, fails to preserve important features of MLSM-generated data. Chapter 2 describes a simulation study explicating the conditions under which the application of MMI to data generated according to a MLSM results in biased inference. The results of this simulation study demonstrate a need to explore alternatives to MMI for MLSM-generated data. Chapter 3 presents a fully Bayesian approach to data augmentation that has been shown in the literature to perform well as a missing data handling method for complex data structures. This approach is applied to two empirical datasets that are assumed to follow a MLSM and one dataset simulated according to a MLSM. The results from each analysis are compared to the results from complete-case analyses. The results of Chapter 3 indicate the suitability of a fully Bayesian approach to handling MLSM-generated, incomplete level 2 covariate data.