Concepts and Applications of Multivariate Multilevel (MVML) Analysis and Multilevel Structural Equation Modeling (MLSEM)

Multilevel or hierarchical models (MLM, HLM) are widely used in analyzing the nested data in educational research over the past decades. The current trend in the research includes systematical thinking of the relationships in education (e.g., ecosystem model of human development) and continuous measurement on individual’s performance (e.g., formative math assessment). These research focuses require that traditional analyses—structural equation modeling and multivariate analysis, work together with the MLM/HLM. This chapter will introduce two state-of-the-art techniques, which refer to multivariate multilevel (MVML) analysis and multilevel structural equation modeling (MLSEM). First, we will present the concepts of the MVML and MLSEM, emphasizing the ideas rather than algebra, to establish a theoretical and methodological foundation of the models. The MVML analysis allows for an analysis of multiple outcomes simultaneously, which can decompose the residual variances and covariances among outcome indicators into different levels. The MLSEM provides more appropriate estimates compared with SEM by considering the intra-class correlations. Then, we will discuss how the models can be applied to educational research. We expect both readers and researchers can find a more extended coverage of basic and advanced modeling techniques and get an enriched understanding of the value of MLM for future studies.