Introduction to Structural Equation Modelling

Structural Equation Modelling (SEM) is a powerful tool to analyse latent variable models common in social sciences, e.g. the analysis of personality factors, social and political attitudes, social values, and behavioural intentions.

SEM combines factor analysis and path analysis by simultaneously estimating causal relations between latent constructs and relations of latent constructs and their corresponding manifest indicators in the measurement models. SEM also allows the estimation and control for random and systematic measurement errors. Thus, SEM methodology allows an adequate modelling and empirical testing of measurement models and complex theoretical assumptions.

The course introduces the theory and practice of SEM on a general level. It does not stick to a specific computer software; rather, different software packages will be shown, used and compared, including R (package lavaan), Mplus and AMOS.

Basic modelling techniques of SEM are explained and applied by exercises using free access social science data. I encourage you to use your own data for analyses. Exercises allow the application and transfer of SEM methodology to your own research interests.

First week

I introduce principles of Structural Equation Modelling. I show how Confirmatory Factor Analysis (CFA) can be specified and estimated, i.e. how latent constructs (e.g. attitudes, values, behavioural intentions) can be operationalised by multiple manifest indicators and how these measurement models can be tested empirically.

Day 1
A general introduction to the advantages, possibilities, and applications of SEM and its relations to Principal Component Analysis (PCA). Regression analysis and path analysis are shown and discussed. I introduce basic concepts like manifest and latent variables, measurement model and structural model, formative and reflective indicators, and relation of modelling and theory.

Day 2
I introduce basic principles of SEM (e.g. causality and theory testing, notation, assumptions, formalisation, estimation procedures, model specification, model identification). I show how a Confirmatory Factor Analysis (CFA) can be estimated to operationalise latent constructs specifying measurement models with manifest indicators (multiple-indicator models). We discuss data and modelling ideas for participants’ own projects.

Day 3
How to identify ‘good’ CFA models, i.e. the interpretation of fit indices. I show how to specify, estimate, assess and re-specify a CFA model step-by-step (model modification). Preconditions like normality and outlier identification will be evaluated, and I demonstrate the specification of higher order constructs to measure multidimensional latent constructs. I show how to deal with systematic measurement errors (e.g. error correlations and specification of method factors) and how to estimate one-indicator measurement models. I introduce validity and reliability estimates in CFA.

Day 4
Multiple group analysis is a very important and powerful tool for comparative social science. I show how multiple group models can be specified, estimated and evaluated to test for measurement equivalence of different groups (e.g. within and between social groups, sub-populations, countries).

Day 5
Multiple group models are extended to the specification of a CFA with meanstructure, i.e. with latent means and intercepts. This lets us estimate and compare latent means between different groups and countries. We will discuss possible problems of models with meanstructure.

Second week

We introduce full SEM to specify and estimate causal relations between latent constructs and thus to test theoretical hypotheses. I will illustrate and discuss advanced techniques of SEM, and highlight special problems.

Day 6
This day deals with the specification of full causal structural equation models. We discuss alternative modelling strategies and equivalent causal models. I also show how to specify, estimate and interpret MIMIC (Multiple Indicators and Multiple Causes) models.

Day 7
I introduce decomposition of causal effects, model modification and interpretation of parameters. I show how to estimate direct, indirect and total effects and how to estimate their standard errors and significance (models with intervening latent variables). Thus, I demonstrate how to test for mediation effects. I show how to specify and estimate non-recursive models (models with feedback loops) and how to handle their particular problems.

Day 8
Full SEM is extended to multiple group comparison to test for moderator effects (and combined moderator-mediator models). We extend full SEM to full SEM with meanstructure, i.e. with latent means and intercepts. We discuss issues of standardisation and sample size in SEM.

Day 9
We discuss special topics of SEM, including its the logic and specification with categorical indicators and non-normal data (e.g. bootstrapping), strategies for dealing with missing values, and how to specify non-linear effects. I introduce interaction models as an alternative to multiple group analysis, and I show how to specify formative measurement models.

Day 10
Time for open questions and a chance for students to present their own models. I introduce advanced models e.g. panel models like cross-lagged autoregressive models and latent growth curve models, and advise on best practice when reporting SEM results. Our final discussion deals with problems and possible traps of SEM.

You should understand the basic principles of regression analysis and the meaning of regression results.

Basic understanding of principal component analysis (exploratory factor analysis) would be helpful.

You should be familiar with software to manage data, such as SPSS, STATA and R.