Introduction to Structural Equation Modelling

Structural Equation Modelling (SEM) is a powerful tool to analyse latent variable models that are 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 its corresponding manifest indicators in the measurement models. Additionally, SEM 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 to theory and practice of SEM on a general level. The course starts using the software AMOS but introduces into lavaan (R) and Mplus as well.

Basic modelling techniques of SEM are explained and applied by exercises using free access social science data. Additionally, participants have got the possibility and are encouraged to use their own data for analyses. Exercises allow the application and transfer of SEM methodology to own research interests.

The first part (week 1) of the course introduces to principles of Structural Equation Modelling. It is shown 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. The first week includes the following topics:

• On first day, a general introduction to advantages, possibilities, and applications of SEM and its relations to Principal Component Analysis (PCA), regression analysis and path analysis are shown and discussed. Basic concepts like manifest and latent variables, measurement model and structural model, formative and reflective indicators, and relation of modelling and theory are introduced.
• Day 2 introduces to basic principles of SEM (e.g. causality and theory testing, notation, assumptions, formalisation, estimation procedures, model specification, model identification). It is shown how a Confirmatory Factor Analysis (CFA) can be estimated to operationalise latent constructs specifying measurement models with manifest indicators (multiple-indicator models). Data and modelling ideas of participants for their own projects will be discussed.
• Day 3 deals with the question of how to identify “good” CFA models, i.e. the interpretation of fit indices. It is shown 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. The specification of higher order constructs to measure multidimensional latent constructs is demonstrated. Further, it is shown how to deal with systematic measurement errors (e.g. error correlations and specification of method factors) and how to estimate one-indicator measurement models. Further, validity and reliability estimates in CFA are introduced.
• Multiple group analysis is a very important and powerful tool for comparative social science. On day 4, it is shown 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).
• On day 5, multiple group models are extended to the specification of a CFA with meanstructure, i.e. with latent means and intercepts. This allows the estimation and comparison of latent means between different groups and countries. Possible problems of models with meanstructure will be discussed.

In the second part of the course (week 2), full SEM is introduced to specify and estimate causal relations between latent constructs and thus to test theoretical hypotheses. Additionally, advanced techniques of SEM and special problems will be illustrated and discussed.

• Day 6 deals with the specification of full causal structural equation models. Alternative modelling strategies and equivalent causal models will be shown and discussed. Further, it is illustrated how to specify, estimate and interpret MIMIC models (“Multiple Indicators and Multiple Causes”).
• On day 7, decomposition of causal effects, model modification and interpretation of parameters will be introduced. It will be shown how to estimate direct, indirect and total effects and how to estimate their standard errors and significance (models with intervening latent variables). Thus, it is demonstrated how to test for mediation effects. Further, it is illustrated how to specify and estimate non-recursive models (models with feedback loops) and how to handle special problems of these models.
• Full SEM is extended to multiple group comparison to test for moderator effects (and combined moderator-mediator models) on day 8. Additionally, full SEM will be extended to full SEM with meanstructure, i.e. with latent means and intercepts. Further, issues of standardisation and sample size in SEM are discussed.
• On day 9, special topics of SEM will be discussed. This includes the logic and specification of SEM with categorical indicators and non-normal data (e.g. bootstrapping), strategies how to deal with missing values and how to specify non-linear effects. Interaction models are introduced as an alternative to multiple group analysis. Further, it is shown how to specify formative measurement models.
• On the last day, open questions will be discussed and participants present their own models. Further, advanced models will be introduced, e.g. panel models like cross-lagged autoregressive models or latent growth curve models. Additionally, best practice of how to report SEM results will be given. A final discussion deals with problems and possible traps of SEM.

Participants should understand basic principles of regression analysis and the meaning of regression results. A basic understanding of principal component analysis (explorative factor analysis) would be helpful. Participants should be familiar with software to manage data (e.g. SPSS, STATA, R).