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…

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…

Linking score scales across different tests is considered speculative and fraught, even at the aggregate level (Feuer et al., 1999; Thissen, 2007). We introduce and illustrate validation methods for aggregate linkages, using the challenge of linking U.S. school district average test scores across states as a motivating example. We show that…

Multilevel data are a reality for many disciplines. Currently, although multiple options exist for the treatment of multilevel data, most disciplines strictly adhere to one method for multilevel data regardless of the specific research design circumstances. The purpose of this Monte Carlo simulation study is to compare several methods for the…

In multilevel multiple-indicator multiple-cause (MIMIC) models, covariates can interact at the within level, at the between level, or across levels. This study examines the performance of multilevel MIMIC models in estimating and detecting the interaction effect of two covariates through a simulation and provides an empirical demonstration of…

The use of multilevel modeling (MLM) to analyze nested data has grown in popularity over the years in the study of school psychology. However, with the increase in use, several statistical misconceptions about the technique have also proliferated. We discuss some commonly cited myths and golden rules related to the use of MLM, explain their…

Multiple-baseline studies provide meta-analysts the opportunity to compute effect sizes based on either within-series comparisons of treatment phase to baseline phase observations, or time specific between-series comparisons of observations from those that have started treatment to observations of those that are still in baseline. The advantage of…

This study compared five common multilevel software packages via Monte Carlo simulation: HLM 7, M"plus" 7.4, R (lme4 V1.1-12), Stata 14.1, and SAS 9.4 to determine how the programs differ in estimation accuracy and speed, as well as convergence, when modeling multiple randomly varying slopes of different magnitudes. Simulated data…

The hierarchical network model (HNM) is a framework introduced by Sweet, Thomas, and Junker for modeling interventions and other covariate effects on ensembles of social networks, such as what would be found in randomized controlled trials in education research. In this article, we develop calculations for the power to detect an intervention…

Designs that facilitate inferences concerning both the total and indirect effects of a treatment potentially offer a more holistic description of interventions because they can complement "what works" questions with the comprehensive study of the causal connections implied by substantive theories. Mapping the sensitivity of designs to…

Multilevel modeling has grown in use over the years as a way to deal with the nonindependent nature of observations found in clustered data. However, other alternatives to multilevel modeling are available that can account for observations nested within clusters, including the use of Taylor series linearization for variance estimation, the design…

The design of research studies utilizing binary multilevel models must necessarily incorporate knowledge of multiple factors, including estimation method, variance component size, or number of predictors, in addition to sample sizes. This Monte Carlo study examined the performance of random effect binary outcome multilevel models under varying…

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…

Clustered data (e.g., students within schools) are often analyzed in educational research where data are naturally nested. As a consequence, multilevel modeling (MLM) has commonly been used to study the contextual or group-level (e.g., school) effects on individual outcomes. The current study investigates the use of an alternative procedure to…

Using a "naïve" specification, this paper estimates the relationship between 36 high school characteristics and 24 student outcomes controlling for students' pre-high school characteristics. The goal of this exploration is not to generate casual estimates, but rather to: (a) compare the size of the relationships to determine which inputs…