Background/Context: In meta-analysis examining educational intervention, characterizing heterogeneity and exploring the sources of variation in synthesized effects have become increasingly prominent areas of interest. When combining results from a collection of studies, statistical dependency among their effects size estimates will arise when a…

Small sample sizes pose a severe threat to convergence and accuracy of between-group level parameter estimates in multilevel structural equation modeling (SEM). However, in certain situations, such as pilot studies or when populations are inherently small, increasing samples sizes is not feasible. As a remedy, we propose a two-stage regularized…

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…

In this article, we present a two-stage estimation approach applied to multilevel latent class analysis (LCA) with covariates. We separate the estimation of the measurement and structural model. This makes the extension of the structural model computationally efficient. We investigate the robustness against misspecifications of the proposed…

When planning a cluster randomized trial, evaluators often have access to an enumerated cohort representing the target population of clusters. Practicalities of conducting the trial, such as the need to oversample clusters with certain characteristics in order to improve trial economy or support inferences about subgroups of clusters, may preclude…

The cross-classified data structure is ubiquitous in education, psychology, and health outcome sciences. In these areas, assessment instruments that are made up of multiple items are frequently used to measure latent constructs. The presence of both the cross-classified structure and multivariate categorical outcomes leads to the so-called…

In Bayesian statistics, the most widely used criteria of Bayesian model assessment and comparison are Deviance Information Criterion (DIC) and Watanabe-Akaike Information Criterion (WAIC). A multilevel mediation model is used as an illustrative example to compare different types of DIC and WAIC. More specifically, the study compares the…

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…

Developmental researchers commonly utilize multilevel models (MLMs) to describe and predict individual differences in change over time. In such growth model applications, researchers have been widely encouraged to supplement reporting of statistical significance with measures of effect size, such as R-squareds ("R[superscript 2]") that…

This study examined the impact of omitting covariates interaction effect on parameter estimates in multilevel multiple-indicator multiple-cause models as well as the sensitivity of fit indices to model misspecification when the between-level, within-level, or cross-level interaction effect was left out in the models. The parameter estimates…

Deciding which random effects to retain is a central decision in mixed effect models. Recent recommendations advise a maximal structure whereby all theoretically relevant random effects are retained. Nonetheless, including many random effects often leads to nonpositive definiteness. A typical remedy is to simplify the random effect structure by…

Researchers face many choices when conducting large-scale multisite individually randomized control trials. One of the most common quantities of interest in multisite RCTs is the overall average effect. Even this quantity is non-trivial to define and estimate. The researcher can target the average effect across individuals or sites. Furthermore,…

We consider two-level models where a continuous response R and continuous covariates C are assumed missing at random. Inferences based on maximum likelihood or Bayes are routinely made by estimating their joint normal distribution from observed data R[subscript obs] and C[subscript obs]. However, if the model for R given C includes random…

Background: Standard methods for analysing data from large-scale assessments (LSA) cannot merely be adopted if hierarchical (or multilevel) regression modelling should be applied. Currently various approaches exist; they all follow generally a design-based model of estimation using the pseudo maximum likelihood method and adjusted weights for the…