Advanced multilevel modeling for a science of groups: A short primer on multilevel structural equation modeling.

A science of groups needs to take different levels of analysis into account since only multilevel perspectives provide a full and realistic picture of processes within and between social groups. A multilevel perspective, however, requires appropriate statistical models. Conventional multilevel regression models suffer from a number of limitations. Amongst these are the restriction to include only manifest variables and only one level 1 outcome variable. Moreover, it is not possible to test complex models (i.e., with multiple mediators and outcomes in a single step). In this paper, we introduce multilevel structural equation modeling (MSEM) as a new and promising development within psychological methods that helps overcome the limitations inherent in conventional MLM. MSEM combines SEM with MLM and offers the best of both worlds. Because MSEM allows using latent instead of manifest variables, measurement error can be taken into account. Moreover, the measurement model can be tested on both the within and between-levels of analysis. MSEM enables researchers to specify level 2 outcome variables and allows the researcher to test complex multilevel models (i.e., simultaneous tests of multiple direct and indirect effects). We illustrate the potential of MSEM using three examples from our own research, provide the corresponding software code as online supplementary material, and discuss important practical issues