What Is Structural Equation Modeling (SEM)? Concepts, Fit, and Procedure

What Is Structural Equation Modeling?

SEM estimates the causal paths among latent variables — measured through observed indicators — within one model. It consists of a measurement model (do the items measure the latent variable well?) and a structural model (how are the latent variables related?).

When Do You Use SEM Instead of Regression?

Use SEM when you need to control for measurement error, when there are several latent variables with a complex path structure, or when mediation and moderation must be tested within one model. For a straightforward effect estimate, regression analysis is enough.

How Do You Run SEM?

Use the two-step approach: validate the measurement model first, then estimate the structural model.

Step 1: Validate the Measurement Model

Use confirmatory factor analysis (CFA) to confirm that each latent variable is well measured by its items, checking convergent and discriminant validity.

Step 2: Estimate the Structural Model

Once the measurement model fits, estimate the path coefficients among latent variables and test your hypotheses.

Step 3: Evaluate Model Fit

Judge how well the model corresponds to the data using fit indices.

How Do You Read Fit Indices?

Read several indices together. Conventionally CFI and TLI at 0.9 or above, RMSEA at 0.08 or below, and SRMR at 0.08 or below indicate acceptable fit. Chi-square becomes significant easily with large samples, so avoid judging on it alone.

How Large a Sample Do You Need?

A sample of 200 or more is generally recommended, and a rule of thumb of 10 to 20 cases per estimated parameter is also used. The more complex the model, the larger the sample required.

Summary

SEM proceeds as measurement model (CFA), structural model, model fit, testing causal relationships among latent variables while accounting for measurement error. For the structure of a measurement instrument see factor analysis, and for simple effect estimation see regression analysis.