Multi-Level 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 etc. 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 would be desirable for the purposes of this class.  If you don’t have this, consider taking our Mplus refresher course in the pre-session.  If you are not very strong in either multilevel modeling or structural equation modeling, you could 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 spend some time getting to know each other and reviewing the most important components of multilevel modeling and structural equation modeling.  We will go into notation to define our multilevel structural equation models.  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.

This course is taught at the upper intermediate to advanced level and therefore assumes a working knowledge of both multilevel modeling (MLM) and structural equation modeling (SEM).  You should understand what path models, confirmatory factor models and the combination of these two models are.  Additionally, you need to have an understanding of random intercept and slope models.  I expect that the main target audience for this class will be people who regularly use one of these techniques but not the other.  If you are one of these people, while there will be a quick review of both of these techniques on day 1, I would still strongly urge you to first take, at least, the first week of the other class where your knowledge is lacking.  Alternatively, you may do independent preparation and get ready for this class.  For people who need to review structural equation modeling, I recommend you read Kline’s SEM book (any edition).  If you need multilevel modeling, I recommend Luke’s little green (SAGE) book.  As you are independently reviewing the content and realize you cannot follow these texts I recommend that instead of the MLSEM course, start with the SEM or MLM courses.  If you have basic knowledge and usage experience with both MLM and SEM, you are ready for this course.  Basic knowledge of Mplus is assumed.  If you don’t have this, I suggest you start with the pre-session software course on Mplus.