Recruiting participants for studies of early-life longitudinal development is challenging, often resulting in practical upper bounds in sample size and missing data due to attrition. These factors pose risks for the statistical power of such studies depending on the intended analytic model. One mitigation strategy is to increase measurement…

We have entered an era in which scientific evidence increasingly informs research practice and policy. As there is an exponential increase in the use of single-case experimental designs (SCEDs) to evaluate intervention effectiveness, there is accumulating evidence available for quantitative synthesis. Consequently, there is a growing interest in…

Two- and three-level designs in educational and psychological research can involve entire populations of Level-3 and possibly Level-2 units, such as schools and educational districts nested within a given state, or neighborhoods and counties in a state. Such a design is of increasing relevance in empirical research owing to the growing popularity…

Cluster randomized trials (CRTs) are commonly used to evaluate the causal effects of educational interventions, where the entire clusters (e.g., schools) are randomly assigned to treatment or control conditions. This study introduces statistical methods for designing and analyzing two-level (e.g., students nested within schools) and three-level…

Background: Education scientists are increasingly interested in constructing interventions that are adaptive over time to suit the evolving needs of students, classrooms, or schools. Such "adaptive interventions" (also referred to as dynamic treatment regimens or dynamic instructional regimes) determine which treatment should be offered…

A latent variable modeling-based procedure is discussed that permits to readily point and interval estimate the design effect index in multilevel settings using widely circulated software. The method provides useful information about the relationship of important parameter standard errors when accounting for clustering effects relative to…

Comprehensive evaluation of treatment effects is aided by considerations for moderated effects. In educational research, the combination of natural hierarchical structures and prevalence of group-administered or shared facilitator treatments often produces three-level partially nested data structures. Literature details planning strategies for a…

Optimal sampling frameworks attempt to identify the most efficient sampling plans to achieve an adequate statistical power. Although such calculations are theoretical in nature, they are critical to the judicious and wise use of funding because they serve as important starting points that guide practical discussions around sampling tradeoffs and…

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…

Traditionally, cluster randomized controlled trials are analyzed with the average intervention effect of interest. However, in populations that contain higher degrees of heterogeneity or variation may differ across different values of a covariate, which may not be optimal. Within education and social science contexts, exploring the variation in…

Background: Regression Discontinuous Design (RDD) is widely used in educational studies. Through RDD, researchers can obtain unbiased results when Randomized Experimental Design (RED) is inaccessible. Compared to RED, the RDD only requires a cut score variable (continuous) and a cutoff value to assign students to the treatment or control groups.…

Cluster randomized control trials often incorporate a longitudinal component where, for example, students are followed over time and student outcomes are measured repeatedly. Besides examining how intervention effects induce changes in outcomes, researchers are sometimes also interested in exploring whether intervention effects on outcomes are…

Cluster randomized trials (CRTs) are commonly used to evaluate educational interventions, particularly their effectiveness. Recently there has been greater emphasis on using these trials to explore cost-effectiveness. However, methods for establishing the power of cluster randomized cost-effectiveness trials (CRCETs) are limited. This study…

Sample size determination in multilevel randomized trials (MRTs) and multilevel regression discontinuity designs (MRDDs) can be complicated due to multilevel structure, monetary restrictions, differing marginal costs per treatment and control units, and range restrictions in sample size at one or more levels. These issues have sparked a set of…

This study introduces a longitudinal diagnostic classification model, called the LTA+HDCM, which is a fusion of latent transition analysis (LTA; Collins & Flaherty, 2002; Collins & Wugalter, 1992) and the hierarchical diagnostic classification model (HDCM; Templin & Bradshaw, 2014). The primary goals in this study are (1) to evaluate…