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…

Simulations were conducted to establish best practice in hyperparameter optimization and accounting for clustering in Generalized Linear Mixed-Effects Model Trees (GLMM trees). Using data-driven best practices, the relationship between a 9th Grade On-Track to Graduate (9G-OTG) indicator and observed high school graduation within four years was…

Identifying items with differential item functioning (DIF) in an assessment is a crucial step for achieving equitable measurement. One critical issue that has not been fully addressed with existing studies is how DIF items can be detected when data are multilevel. In the present study, we introduced a Lord's Wald X[superscript 2] test-based…

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…

While hierarchical linear modeling is often used in social science research, the assumption of normally distributed residuals at the individual and cluster levels can be violated in empirical data. Previous studies have focused on the effects of nonnormality at either lower or higher level(s) separately. However, the violation of the normality…

While significant attention has been given to test equating to ensure score comparability, limited research has explored equating methods for rater-mediated assessments, where human raters inherently introduce error. If not properly addressed, these errors can undermine score interchangeability and test validity. This study proposes an equating…

A recent review found that 11% of published factor models are hierarchical models with second-order factors. However, dedicated recommendations for evaluating hierarchical model fit have yet to emerge. Traditional benchmarks like RMSEA <0.06 or CFI >0.95 are often consulted, but they were never intended to generalize to hierarchical models.…

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…

Multilevel structural equation models (MSEMs) are well suited for educational research because they accommodate complex systems involving latent variables in multilevel settings. Estimation using Croon's bias-corrected factor score (BCFS) path estimation has recently been extended to MSEMs and demonstrated promise with limited sample sizes. This…

Background: Multilevel randomized controlled trials (MRCTs) have been widely used to evaluate the causal effects of educational interventions. Traditionally, educational researchers and policymakers focused on the average treatment effects (ATE) of the intervention. Recently there has been an increasing interest in evaluating the heterogeneity of…

Developmental researchers commonly utilize longitudinal data to decompose reciprocal and dynamic associations between repeatedly measured constructs to better understand the temporal precedence between constructs. Although the cross-lagged panel model (CLPM) is commonly used in developmental research, it has been criticized for its potential to…

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…

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…