Structural Equation Modeling (SEM) is a popular method to test hypothetical relationships between constructs in the social sciences. These constructs may be unobserved (a.k.a., “latent”) or 
observed (a.k.a., “manifest”).
In this training, you will learn the different types of SEM: confirmatory factor analysis, path analysis for manifest and latent variables, and latent growth modeling (i.e., the application of SEM on longitudinal data).
We’ll discuss the different terminology, the commonly used symbols, and the different ways a model can be specified, as well as how to present results and evaluate the fit of the models.
This training will be at a very basic conceptual level; however, it is assumed that participants have an understanding of multiple regression, interpretation of statistical tests, and methods of data screening.
Note: This training is an exclusive benefit to members of the Statistically Speaking Membership Program and part of the Stat’s Amore Trainings Series. Each Stat’s Amore Training is approximately 90 minutes long.
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A multiple regression model could be conceptualized using Structural Equation Model path diagrams. That’s the simplest SEM you can create, but its real power lies in expanding on that regression model. Here I will discuss four types of structural equation models.
Path Analysis
More interesting research questions could be asked and answered using Path Analysis. Path Analysis is a type of structural equation modeling without latent variables. (more…)
Latent constructs, such as liberalism or conservatism, are theoretical and cannot be measured directly.
But we can represent the latent construct by combining a set of questions on a scale, called indicators. We do this via factor analysis.
Often prior research has determined which indicators represent the latent construct. Prudent researchers will run a confirmatory factor analysis (CFA) to ensure the same indicators work in their sample.
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Creating a quality scale for a latent construct (a variable that cannot be directly measured with one variable) takes many steps. Structural Equation Modeling is set up well for this task.
One important step in creating scales is making sure the scale measures the latent construct equally well and the same way for different groups of individuals.
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Whenever you use a multi-item scale to measure a construct, a key step is to create a score for each subject in the data set.
This score is an estimate of the value of the latent construct (factor) the scale is measuring for each subject. In fact, calculating this score is the final step of running a Confirmatory Factor Analysis.
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An extremely useful area of statistics is a set of models that use latent variables: variables whole values we can’t measure directly, but instead have to infer from others. These latent variables can be unknown groups, unknown numerical values, or unknown patterns in trajectories.
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