• Common method of understanding both simple and complex systems of behavior, emotion, decision making, etc. in the social and behavioral sciences.
• Draws on some now familar concepts such as factor analysis and regression. Similar to regression, SEM is used to understand how sets of variables are related.
• Also commonly referred to as "latent variable models."

There is rarely a single "right" approach to answering a research question. So when might you want to use SEM?

• Does my research question involve constructs that I cannot or did not directly measure?
• Do I have complex hypotheses that aim to descibe a whole system of constructs/variables?
• Do I want to compare two competing theories for how a set of variables relate to one another?
• Do I have a large enough sample for SEM?

• SEM could be thought of as a system of regressions and covariances between latent variables.
  
• Those latent variables are themselves constructed from observed variables (also called manifest variables) using factor analysis.

Thus, SEM can be broken down into two steps:

• define the latent constructs using CFA (in SEM, we call this part the measurement model- the model that describes how each latent variables is measured); and then
• define the regressions and covariances amongst the latent constructs.

• Continue with example from previous weeks and use SEM to test a theory of how these variables are related.
• I hypothesize that food insecurity negatively affects student mental health. I also predict that both food insecurity and mental health are predictive of academic success.

• We already determined that food insecurity (FI) can be thought of as having two subcomponents: lifetime food insecurity, and campus food insecurity.
• Similarly, the mental health scale measures both anxiety and depression.
• We will use SEM test hypotheses about the relations between these latent factors and academic performance.
• I will limit FI to only include the campus FI component.
• Academic Success (AS) is also a latent variable. The manifest variables for AS are cumulative GPA, major GPA, and median final exam score.

Latent variable models and SEM in particular are often translated into diagrams. Let's take a look at the hypothesized structural model for this example:

SEM Diagram

• The diagram helps understand the hypothesized theory, but remember that every piece of the model actually represents a mathematical relation. For this reason, there are specific standard for how these diagrams are drawn. Some of the features include:

• circles = latent variables
• squares = manifest (observed) variables
• single-headed arrows = regressions

• double-headed arrows = variances and covariances

Try on your own to break this model down into smaller components/hypotheses

• There are 4 measurement models; one for each latent variable
• Academic success is predicted by anxiety, depression, and campus food insecurity
• Anxiety and Depression covary

• Also notice that the arrows in the measurement models go from the latent variables to the manifest variables.
• This is the standard specification in SEM and represents the assumption that the underlying latent construct causes or leads to a participant's exhibited response.
• This also applies for factor analysis, as you may have noticed.

Structural models are very applicable to the complex theories we like to test in the social and behavioral sciences. They are also relatively intuitive, and even sometimes fun! There are some things to keep in mind while working in this framework, though.

• Sample Size and Power
• Causal language and Temporal Precedence
• Model Modification Indices