This note is concerned with the study of temporal development in several indices reflecting clustering effects in multilevel designs that are frequently utilized in educational and behavioral research. A latent variable method-based approach is outlined, which can be used to point and interval estimate the growth or decline in important functions…

Several variants of the autoregressive structural equation model were suggested over the past years, including, for example, the random intercept autoregressive panel model, the latent curve model with structured residuals, and the STARTS model. The present work shows how to place these models into a mixed-effects model framework and how to…

Multilevel factor mixture modeling (FMM) is a hybrid of multilevel confirmatory factor analysis (CFA) and multilevel latent class analysis (LCA). It allows researchers to examine population heterogeneity at the within level, between level, or both levels. This tutorial focuses on explicating the model specification of multilevel FMM that considers…

Clustered data structures are common in many areas of educational and psychological research (e.g., students clustered in schools, patients clustered by clinician). In the course of conducting research, questions are often administered to obtain scores reflecting latent constructs. Multilevel measurement models (MLMMs) allow for modeling…

We present a bias-adjusted three-step estimation approach for multilevel latent class models (LC) with covariates. The proposed approach involves (1) fitting a single-level measurement model while ignoring the multilevel structure, (2) assigning units to latent classes, and (3) fitting the multilevel model with the covariates while controlling for…

We note two possibilities for how our science might capitalize on advances in computing that harness and weave "big data" into the rich tapestry of how human development unfolds. First, we propose that the classic theoretical models that have guided developmental research since the 1970s and the hierarchical analytical models used to…

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…

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…

Mixture modeling is a latent variable (i.e., a variable that cannot be measured directly) approach to quantitatively represent unobserved subpopulations within an overall population. It includes a range of cross-sectional (such as latent class [LCA] or latent profile analysis) and longitudinal (such as latent transition analysis) analyses and is…

The challenge and pleasures of studying child and adolescent peer experiences come from the complexity and the significance of these relationships for development in childhood and adolescence. In spite of the recognized strengths of the current literature on the effects of experiences with peers, research on peer experiences is often limited by an…

Typical longitudinal growth models assume constant functional growth over time. However, there are often conditions where trajectories may not be constant over time. For example, trajectories of psychological behaviors may vary based on a participant's age, or conversely, participants may experience an intervention that causes trajectories to…

Multilevel modelling (MLM) is the most frequently used approach for evaluating interventions with clustered data. MLM, however, has some limitations that are associated with numerous obstacles to model estimation and valid inferences. Longitudinal multiple-group (LMG) modelling is a longstanding approach for testing intervention effects using…

Module Overview: In this digital ITEMS module, Dr. Jodi M. Casabianca provides a primer on the "hierarchical rater model" (HRM) framework and the recent expansions to the model for analyzing raters and ratings of constructed responses. In the first part of the module, she establishes an understanding of the nature of constructed…

We discuss possible uses of multilevel mixed methods (M[superscript 3]) research in educational psychology. To begin, we describe M[superscript 3] research and how such research can enable researchers to investigate potential variation at the group level and at the subgroup/individual level. We discuss why M[superscript 3] research designs are…