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Structural equation modeling

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Structural Equation Modeling (SEM) is a statistical technique for building and testing models, which are often causal in nature. It is a hybrid technique that encompasses aspects of confirmatory factor analysis, path analysis and regression. Indeed all of these can be seen as special cases of SEM.

Among its strengths is the ability to model constructs as latent variables which are not measured directly, but are estimated in the model from a number of manifest variables assumed to 'tap into' the construct. This allows the modeller to explicitly capture unreliability of measurement in the model, in theory allowing the structural relations between latent variables to be accurately modelled.

SEM encourages a confirmatory, as opposed to exploratory, approach to modelling. In other words it is normal to start with a hypothesis, specify a model that reflects this and then set about operationalising the constructs of interest with a measurement instrument and test the model. Often the initial hypothesis requires adjustment in light of model evidence, but it is rare to see SEM used in a purely exploratory mode.

With an accepted theory or otherwise confirmed model, one can also use SEM in an inductive mode by specifying a model and using data to estimate the values of free parameters.

TETRAD and Partial Least Squares offer alternatives to SEM for exploratory modeling.

Part 1: Introduction to SEM

  • What is Structural Equation Modeling (SEM)?

SEM is an extension of the General Linear Model (GLM) that simultaneously estimates relationships between multiple independent and dependent variables, in the case of a structural model and/or multiple observed and latent variables, in the case of confirmatory factor analysis. SEM is best applied to theory testing, as opposed to the more exploratory areas of theory development.

  • Why SEM?

SEM has several important advantages over ordinary least squares (OLS) regression. These include: -SEM allows for multiple dependent variable, whereas OLS regressions allows only a single dependent variable. -SEM accounts for measurement error, whereas OLS regression assumes perfect measurement. -SEM has more flexible assumptions that does OLS regression, although the assumption of multivariate normality must be met for SEM. -SEM allows simultaneous tests of multiple groups.

  • Types of SEM techniques
  • How is SEM same and different from other statistical techniques?

- SEM is similar to path analysis. In fact, path analysis can be thought of as a special case of SEM in which each latent construct has only a single indicator. This analysis is said to be conducted at the "scale level", whereas SEM is conducted at the "item level".

Part 2: Basic Concepts

  • Basic Steps in Performing SEM analysis
  • Data Preparation
  • Common Mistakes in SEM?

Part 3: Advanced Uses of SEM

  • Invariance
  • Modeling Growth
  • Relations to other types of advanced models (multilevel models; IRT models)
  • Alternative estimation and testing techniques
  • Interface with survey estimation

See also

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