Post-Conference Workshop

Post-Conference Workshop: May 21, 9:00-5:00 pm

Multilevel Structural Equation Modeling Using xxM

Dr. Paras Mehta

Contact person and lecturer:

Paras Mehta:


Paras D. Mehtais an associate professor of clinical and industrial/organizational psychology at the Texas Institute for Measurement, Evaluation and Statistics at the University of Houston. His research interests are in multi-level structural equation modeling, growth-curve modeling, and the application of these techniques to educational and organizational research. He is a current member of the Society for Multivariate Experimental Psychology (SMEP).

Workshop abstract:

N-level structural equation modeling is a superset of linear mixed-effects (LME) and structural equation models (SEM).  The framework accommodates conventional multilevel models (e.g., HLM, MLM) with random slopes as well as LISREL-like structural equation models for any number of levels. A level is defined as any factor with multiple exchangeable units with observed and/or latent variable. With this definition of a level, a SEM model is defined within each level.  Observed and latent variables at any level may influence variables at a lower level. A complete NL-SEM model is therefore a directed graph or network of SEM sub-models. The notion of a network of SEM models with influence across sub-models makes the task of specifying complex dependencies with complicated data-structures (e.g., multivariate and longitudinal outcomes with complex cross-classification at multiple levels) rather easy. An R-package called xxM provides an implementation of the NL-SEM framework.  xxM ( is very easy to learn and use.

xxM can handle large datasets with complex structures including:

  •  Hierarchically nested data (e.g., students << classrooms << schools << districts).
  •  Cross-classified data (e.g., students crossed within schools and neighborhoods).
  •  Partial nesting (e.g., only at-risk students in a classroom receive additional instruction by a tutor).
  •  Longitudinal data (long or wide).
  •  Longitudinal data with switching classification (e.g., students changing classrooms/teachers over time).
  •   Round-robin design (e.g., each person rates every other person in a small group).
  •   360 performance evaluation data.
  •   A combination of above structures for different level pairs.

xxM can be used for estimating latent variable models with any number of levels including:

  •   Multilevel models (MLM) with random effects of observed variables.
  •   Multilevel structural equation models (ML-SEM) with observed and latent variables at all levels.
  •   Linear Mixed-Effects Models (LME) with constraints on both G and R side of the model. Linear Growth  Curve Models.
  •   David Kenny’s Social Relations Model for reciprocal dyadic ratings.

The workshop will provide a practical and hands-on introduction to using xxM for estimating NL-SEM models. xxM uses a LEGO-like approach to building models. In other words, once the user learns how to specify a SEM model for a two-level data-structure, they should be able to specify a model with any number of levels with complex dependency across multiple levels. NL-SEM models have an intuitive graphical representation that is easy to understand.  There is a one-to-one correspondence between the graphical model and the xxM script.  There are only five simple xxM commands that the user needs to master. The workshop will walk the participants through concrete examples to help them learn the syntax of xxM. More importantly, the examples are designed to help the user to understand how to conceptualize n-Level SEM models with complex data-structures. The datasets, annotated R-script for estimating each model, and annotated output will be made available. The workshop assumes only a basic understanding of multilevel and structural equation models.

basic understanding of multilevel and structural equation models.

The first part of the workshop will be focus on understanding the structure of core multilevel SEM models and the corresponding syntax in xxM.

1.       Conventional single Level Structural Equation Modeling

2.       Conventional two and three level/cross-classified multilevel models

3.       Latent Growth Curve Models with nested data

The second part of the workshop will focus on the application of xxM for estimating models with complex dependencies.

5.       Longitudinal data with changing classification

In educational settings, students are nested within a classroom/teacher within a given grade. Across-grades students switch to different teachers and classrooms.  A teacher may teach multiple classrooms within the same year/grade and are likely to repeat across years.  Students are also nested within schools and districts. A student may also move from one school to another.  Multilevel model specification of such data are complicated and difficult to understand and specify.  More importantly, conventional specification make untested simplifying assumptions. NL-SEM models for such data have a clear and easy to understand graphical representation and allows direct specification of hypothesis such as the ‘persistent teacher effects’.

6.       Social Relations Model: Reciprocal ratings obtained in round-robin design

Reciprocal ratings are becoming increasing common in the age of social networks.  Such data involve complex dependencies that are difficult to conceptualize using conventional multilevel modeling approaches.  NL-SEM allows specification of multivariate, latent variable Social Relations Model for such data that is as easy to understand and specify.