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…

Multidimensionality and hierarchical data structure are common in assessment data. These design features, if not accounted for, can threaten the validity of the results and inferences generated from factor analysis, a method frequently employed to assess test dimensionality. In this article, we describe and demonstrate the application of the…

It is not always clear how to adjust for control data in causal inference, balancing the goals of reducing bias and variance. We show how, in a setting with repeated experiments, Bayesian hierarchical modeling yields an adaptive procedure that uses the data to determine how much adjustment to perform. The result is a novel analysis with increased…

This note is concerned with examining the relationship between within-group and between-group variances in two-level nested designs. A latent variable modeling approach is outlined that permits point and interval estimation of their ratio and allows their comparison in a multilevel study. The procedure can also be used to test various hypotheses…

This study examined waiting times for diagnostic assessment of Autism Spectrum Disorder in 11 adult services, prior to and following the implementation of a 12 month change program. Methods to support change are reported and a multi-level modelling approach determined the effect of the change program on overall wait times. Results were…

Since the 1990's, schools across the United States have been held accountable for increased student learning. Increased use of growth-based accountability models and a lack of clarity on what each model measures have resulted in a need for additional research focused on the real-world implications for teacher agency and school accountability. The…

An important concern when planning research studies is to obtain maximum precision of an estimate of a treatment effect given a budget constraint. When research designs have a "multilevel" or "hierarchical" structure changes in sample size at different levels of the design will impact precision differently. Furthermore, there…

Researchers are often interested in studying how the timing of a specific event affects concurrent and future development. When faced with such research questions there are multiple statistical models to consider and those models are the focus of this paper as well as their theoretical underpinnings and assumptions regarding the nature of the…

Designs that facilitate inferences concerning both the total and indirect effects of a treatment potentially offer a more holistic description of interventions because they can complement "what works" questions with the comprehensive study of the causal connections implied by substantive theories. Mapping the sensitivity of designs to…

Identity research largely emerged from clinical observations. Decades of empirical work advanced the field in refining existing approaches and adding new approaches. Furthermore, the existence of linkages of identity with psychopathology is now well established. Unfortunately, both the directionality of effects between identity aspects and…

Matching theories about growth, development, and change to appropriate statistical models can present a challenge, which can result in misuse, misinterpretation, and underutilization of different analytical approaches. We discuss the use of "derivatives": the change of a construct with respect to the change in another construct.…

Randomized experiments are generally considered to provide the strongest basis for causal inferences about cause and effect. Consequently randomized field trials have been increasingly used to evaluate the effects of education interventions, products, and services. Populations of interest in education are often hierarchically structured (such as…

Learning analysts often consider whether learning processes across time are related (1) to one another or (2) to learning outcomes at higher levels. For example, are a group's temporal sequences of talk (e.g., correct evaluation [right arrow] correct, new idea) during its problem solving related to its group solution? I show how to address these…

Modeling the distribution of site level effects is an important problem, but it is also an incredibly difficult one. Current methods rely on distributional assumptions in multilevel models for estimation. There it is hoped that the partial pooling of site level estimates with overall estimates, designed to take into account individual variation as…

Purpose: Singapore is a country with low teacher attrition rates and high performance on international assessments (TIMSS 2011/2015 and PISA 2012/2015). Consequently, its education system is often considered as a model for other nations. The purpose of this paper is to extend research on teacher job satisfaction in Singapore and provide…