SD302 - Multilevel Structural Equation Modelling

Structural equation modeling (SEM) and multilevel modeling (MLM) are both very popular analytical methodologies in the social sciences today. Multilevel modeling allows us to assess data on multiple levels of analysis as long as the sample size, on both levels, is sufficient for large-n analysis. Most common applications are international surveys that are starting to approach these sample size requirements. But applications also include within person designs, regional analyses, students nested within schools, patients nested within hospitals, and so on. Structural equation models combine the power of factor analysis flushing out measurement error and path analysis which are, in essence, simultaneous regression models considering complex causal structures between our observed variables or factors.  Multilevel structural equation modeling (MLSEM) is marriage between the two methods in which structures of relationships can be assessed at multiple levels of analysis.

An ever increasing number of software packages are implementing multilevel approaches to structural equation models.  While computationally, analytically and structurally complex, these methods are effectively implemented in a user friendly way in at least one software: Mplus.  (Basic Mplus knowledge is expected for the purposes of this class.  If you don’t have this, take our Mplus refresher course in the Winter School.  If you are not very strong in either multilevel modeling or structural equation modeling, you should also take the first week of these courses to brush up on the basics.)  In this course we will go though the most common applications of multilevel structural equation models with examples in Mplus.  Mplus has several advantages (user friendly, flexible) but has clear disadvantages as well (expensive, closed). While we considered other software (xxM, OpenMX) but settled on the more user friendly option (though if you are good with matrix algebra, you certainly will have an easier time learning these software options after the conclusion of the class).  This said, all examples used in the class will run in the free demo version of Mplus.  Please bring your laptop with Mplus or Mplus Demo installed.  Mplus is compatible with Windows, Mac and Linux. Android and iOS are inadequate for the purposes of this class.

Monday, we will review the most important components of multilevel modeling and structural equation modeling.  We will go into notation to define our multilevel structural equation models. We will also brush up on Mplus syntax. Tuesday we start with multilevel path analysis.  Wednesday we cover multilevel confirmatory factor analysis.  Thursday we discuss full structural models in a multilevel framework.  Friday we discuss advanced topics and the various different conceptualizations for defining multilevel structural equation models.   If time permits, we will demo alternative software.

Mplus 7.3 (or higher). Mplus is a proprietary software, but all examples will be made so that they can be run on the (free) demo version of Mplus. All students are required to have at least the demo version of Mplus installed upon coming to the first class.

All students are required to bring their laptops to class.

Byrne, B. M. (2011). Structural Equation Modeling with Mplus: Basic Concepts, Applications, and Programming. London: Routledge. (Especially the last chapter).

Bosancianu, C. M., Littvay, L., and Castanho Silva, B. Multilevel Structural Equation Modeling. Unpublished manuscript (in progress).

Heck, R. H., & Thomas, S. L. (2015). An Introduction to Multilevel Modeling Techniques: MLM and SEM Approaches Using Mplus. New York: Routledge.

Hox, J. J. (2010). Multilevel Analysis: Techniques and Applications. Second edition. London: Routledge.

Rabe-Hesketh, S., Skrondal, A., and Zheng, X. 2012. Multilevel Structural Equation Modeling. In: Hoyle, R. H (ed). Handbook of Structural Equation Modeling, New York: Guilford Press, pp. 512-531.