**Introductory and Advanced Structural Equation Modelling using Mplus**

To book a place in the course, please use our booking form. Part one, introduction level will run from 7th July until 12:00 on 9th. Part two, advanced level will run from 13:00 9th July until 11th. The fees are as follows:

Part 1 **or** Part 2: Students/UoM staff: £400, Others: £600

Part 1 and Part 2: Students/UoM staff: £600, Others: £900

The fee for both parts includes 28 hours of face-to-face teaching over 5 days, and lunch on 4 days. The fee for just one part includes 14 hours face-to-face teaching. Once your booking has been processed please visit the e-store to pay by credit or debit card.

**Summary**

**Part 1: Introduction to Structural Equation Modelling**

Structural Equation Modelling (SEM) is a powerful statistical framework for modelling a wide range of social and psychological phenomena. The first, introductory part of this course shows students how to combine Regression, Mediation/ Path analysis and Confirmatory Factor Analysis to fit and evaluate SEMs using the flexible and powerful Mplus statistical package.

**Part 2: Advanced Structural Equation Modelling**

The SEM models covered in part 1 are based heavily on assumptions of normality, both for the observed and latent variables. These assumptions can be quite restrictive in applied social research. In the second, advanced, part of the course, students are shown how many of these restrictive assumptions of SEMs can be relaxed in Mplus by expanding the SEM framework to become Generalized Latent Variable Modelling (GLVM).

Students are shown how to use Item Response Theory Models to relax the assumption of multivariate normality for the observed variables. Finite Mixture modelling is used to relax the assumption of normally distributed latent factors. Latent Class Analysis is used to further relax assumptions about the distribution of the latent variables, as well as to relax fundamental assumptions of measurement invariance in different groups, i.e. the assumption the latent factors actually mean the same thing to different people

**About Generalized Latent Variable Modelling**

Before the emergence of GLVM, latent variable models were quite restrictive of the types of data that could be used to fit them and the assumptions about the latent variable distributions that had to be made in order to estimate the models. Such restrictions placed limitations on the substantive theories that could be evaluated with these models, Procrustean constraints that forced theory to accommodate the model rather than the other way round.

With GLVM modellers are freed from many of the somewhat arbitrary distinctions between earlier generations of Latent Variable models. For instance, Factor Analysis and Latent Class Analysis assume continuous and discrete latent variable distributions respectively, and are often still viewed as polar opposites suitable for very different applications. With GLVM aspects of these two models can be blended, producing hybrid models potentially far more suitable for many applications.

For example consider modelling clinical depression (a latent variable) in a general population. A large majority the population will show no symptoms of clinical depression at all, forming a discrete class of the ‘non-depressed’. A smaller group will show symptoms of depression to varying degrees, forming a continuous dimension of variation in severity of depression. This hybrid distribution, a mixture of latent classes and a latent dimensional ‘factor’, can be modelled effortlessly using a GLVM framework.

**The course will:**

- Introduce a suite of Structural Equation and Latent Variable models
- Show how to estimate these models using the Mplus statistical package.
- Show how to interpret the output of these models.
- Show how these models can be used to test substantive research questions.

- Part 1: Regression Analysis in Mplus; Path and Mediation Analysis; Confirmatory Factor Analysis
- Part 2: Item Response Theory, Finite Mixture Modelling; Latent Profile Analysis and Latent Class Analysis; Multiple Group modelling; Measurement and Factorial Invariance.

**Course Requirements**

Part 1 assumes that students are experienced users of linear regression models. No prior experience of using Mplus is required.

Part 2 assumes that students are experienced users of normal-theory SEMs, and are skilled in fitting and interpreting these models using Mplus.

**Booking**

Part 1 and Part 2 can be booked separately or together.

**Preliminary Reading**

Part 1:

Byrne, B. M. (2012). *Structural Equation Modeling with Mplus. Basic Concepts, Application, Programming*. New York, NY: Routledge.

Part 2:

Bartholomew, Knott & Moustaki (2011). *Latent Variable Models and Factor Analysis: A Unified Approach*(3rd Ed.). London: Wiley.

Muthen, B. O. (2002). Beyond SEM: General latent variable modelling. *Behaviormetrika*, 29, 81-117.