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…

When well-implemented, mediation analyses play a critical role in probing theories of action because their results help lay the ground work for the critical development of a treatment and the iterative advancement of theories that are foundational to a discipline. Despite strong interest in designs that incorporate mediation, few studies have…

Large-scale education data are collected via complex sampling designs that incorporate clustering and unequal probability of selection. Multilevel models are often utilized to account for clustering effects. The probability weighted approach (PWA) has been frequently used to deal with the unequal probability of selection. In this study, we examine…

Traditional observed variable multilevel models for evaluating indirect effects are limited by their inability to quantify measurement and sampling error. They are further restricted by being unable to fully separate within- and between-level effects without bias. Doubly latent models reduce these biases by decomposing the observed within-level…

Small samples are common in growth models due to financial and logistical difficulties of following people longitudinally. For similar reasons, longitudinal studies often contain missing data. Though full information maximum likelihood (FIML) is popular to accommodate missing data, the limited number of studies in this area have found that FIML…

This article presents 3 standardized effect size measures to use when sharing results of an analysis of mediation of treatment effects for cluster-randomized trials. The authors discuss 3 examples of mediation analysis (upper-level mediation, cross-level mediation, and cross-level mediation with a contextual effect) with demonstration of the…

Educational researchers commonly use the rule of thumb of "design effect smaller than 2" as the justification of not accounting for the multilevel or clustered structure in their data. The rule, however, has not yet been systematically studied in previous research. In the present study, we generated data from three different models…

Many classroom climate studies suffer from 2 critical problems: They (a) treat climate as a student-level (L1) variable in single-level analyses instead of a classroom-level (L2) construct in multilevel analyses; and (b) rely on manifest-variable models rather than on latent-variable models that control measurement error at L1 and L2, and sampling…