Hierarchical data is often observed in education data. Analyzing such data with Multilevel Modeling becomes crucial to understanding the relationship at the individual and group levels. However, one of the most significant problems with this kind of data is small sample sizes and very low Intraclass Correlations. The multivariate Latent Covariate…

The Q-matrix played a key role in implementations of diagnostic classification models (DCMs) or cognitive diagnostic models (CDMs) -- a family of psychometric models that are gaining attention in providing diagnostic information on students' mastery of cognitive attributes or skills. Using two Monte Carlo simulation studies, this dissertation…

In randomized control trials (RCT), the recent focus has shifted to how an intervention yields positive results on its intended outcome. This aligns with the recent push of implementation science in healthcare (Bauer et al., 2015) but goes beyond this. RCTs have moved to evaluating the theoretical framing of the intervention as well as differing…

This dissertation informed researchers about the performance of different level-specific and target-specific model fit indices in Multilevel Latent Growth Model (MLGM) using unbalanced design and different trajectories. As the use of MLGMs is a relatively new field, this study helped further the field by informing researchers interested in using…

Multilevel experiments have been widely used in education and social sciences to evaluate causal effects of interventions. Two key considerations in designing experimental studies are statistical power and the minimal use of resources. Optimal design framework simultaneously addresses both considerations. This dissertation extends previous optimal…

Propensity score analysis has been used to minimize the selection bias in observational studies to identify causal relationships. A propensity score is an estimate of an individual's probability of being placed in a treatment group given a set of covariates. Propensity score analysis aims to use the estimate to create balanced groups, akin to a…

When studying differential item functioning (DIF) with students with disabilities (SWD) focal groups typically suffer from small sample size, whereas the reference group population is usually large. This makes it possible for a researcher to select a sample from the reference population to be similar to the focal group on the ability scale. Doing…

The current study evaluated the performance of traditional versus modern MDTs in the estimation of fixed-effects and variance components for data missing at the second level of an hierarchical linear model (HLM) model across 24 different study conditions. Variables manipulated in the analysis included, (a) number of Level-2 variables with missing…

This dissertation proposes two modified cognitive diagnostic models (CDMs), the deterministic, inputs, noisy, "and" gate with hierarchy (DINA-H) model and the deterministic, inputs, noisy, "or" gate with hierarchy (DINO-H) model. Both models incorporate the hierarchical structures of the cognitive skills in the model estimation…