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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

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.

Part 2: Basic Concepts

  • Basic Steps in Performing SEM analysis

1. Model Specification--Since SEM is a confirmatory technique, it is imperative that the model is specified correctly based on the type of analysis that the modeller is attempting to confirm. There are two main types of models: the structural model and the measurement model. Specifying the model delineates relationships between variables that are thought to be related (and therefore want to be 'free' to vary) and those relationships between variables that already have an estimated relationship, which can be gathered from previous studies (these relationships are 'fixed' in the model). 2. Estimation of Free Parameters--appropriating the best fitting model in SEM is an iterative process. Therefore, an estimation is made comparing the actual variance/covariance matrices representing the relationships between variables and the estimated variance/covariance matrices of the best fitting model. This is best accomplished by using an SEM analysis program, such as LISREL or AMOS. 3. Assessment of Fit--Using an SEM analysis program, the iterations compare the estimated matrices representing the relationships between variables in the model to the actual matrices. Individual factors within the model are also examined within the estimated model in order to see how well the proposed model fits the driving theory. 4. Model Modification--The model may need to be modified in order to maximize the fit, thereby estimating the most likely relationships between variables. 5. Interpretation and Communication--The model is then interpreted and claims about the constructs are made based on the best fitting model. Because SEM is limited to correlational data, caution should always be taken when making claims of causality unless further experimentation or time-ordered studies have been done. 6. Replication and Revalidation--All model modifications should be replicated and revalidated before interpreting and communicating the results.

  • 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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