We consider Bayesian estimation of a hierarchical linear model (HLM) from partially observed data, assumed to be missing at random, and small sample sizes. A vector of continuous covariates C includes cluster-level partially observed covariates with interaction effects. Due to small sample sizes from 37 patient-physician encounters repeatedly…

A growing body of literature has focused on missing data methods that factorize the joint distribution into a part representing the analysis model of interest and a part representing the distributions of the incomplete predictors. Relatively little is known about the utility of this method for multilevel models with interactive effects. This study…

We consider Bayesian estimation of a hierarchical linear model (HLM) from small sample sizes. The continuous response Y and covariates C are partially observed and assumed missing at random. With C having linear effects, the HLM may be efficiently estimated by available methods. When C includes cluster-level covariates having interactive or other…

Meta-analysis allows researchers to combine evidence from multiple studies, making it a powerful tool for synthesizing information on the safety profiles of new medical interventions. There is a critical need to identify subgroups at high risk of experiencing treatment-related toxicities. However, this remains quite challenging from a statistical…

Specialized imputation routines for multilevel data are widely available in software packages, but these methods are generally not equipped to handle a wide range of complexities that are typical of behavioral science data. In particular, existing imputation schemes differ in their ability to handle random slopes, categorical variables,…

Modeling the distribution of site level effects is an important problem, but it is also an incredibly difficult one. Current methods rely on distributional assumptions in multilevel models for estimation. There it is hoped that the partial pooling of site level estimates with overall estimates, designed to take into account individual variation as…

The multilevel latent class model (MLCM) is a multilevel extension of a latent class model (LCM) that is used to analyze nested structure data structure. The nonparametric version of an MLCM assumes a discrete latent variable at a higher-level nesting structure to account for the dependency among observations nested within a higher-level unit. In…

A challenge associated with traditional mixture regression models (MRMs), which rest on the assumption of normally distributed errors, is determining the number of unobserved groups. Specifically, even slight deviations from normality can lead to the detection of spurious classes. The current work aims to (a) examine how sensitive the commonly…

We propose a hierarchical Bayesian model for analyzing multi-site experimental fMRI studies. Our method takes the hierarchical structure of the data (subjects are nested within sites, and there are multiple observations per subject) into account and allows for modeling between-site variation. Using posterior predictive model checking and model…

Increasing college participation rates, and diversity in student population, is posing a challenge to colleges in their attempts to facilitate learners achieve their full academic potential. Learning analytics is an evolving discipline with capability for educational data analysis that could enable better understanding of learning process, and…