How do you incorporate latent variables and measurement errors in your SEM model?

1 What are latent variables?

Latent variables are unobserved constructs that cannot be measured directly, but are inferred from a set of observed indicators. For example, customer satisfaction, intelligence, or depression are latent variables that are measured by surveys, tests, or scales. Latent variables are often the key concepts of interest in SEM, as they represent the underlying factors that explain the variation and covariation among the observed variables.

3 How to model latent variables?

One way to model latent variables in SEM is to use reflective indicators, which are assumed to be caused by the latent variable. In other words, the latent variable reflects its indicators, and the indicators share a common cause. For example, if customer satisfaction is a latent variable, its indicators could be ratings of different aspects of the service or product. To model reflective indicators, you can use a factor analysis approach, where the latent variable is estimated by the weighted average of its indicators, and the measurement errors are represented by the residuals.

4 How to model measurement errors?

Another way to model latent variables in SEM is to use formative indicators, which are assumed to cause the latent variable. In other words, the latent variable is formed by its indicators, and the indicators have independent effects. For example, if income is a latent variable, its indicators could be education, occupation, and assets. To model formative indicators, you can use a composite analysis approach, where the latent variable is estimated by the sum of its indicators, and the measurement errors are represented by the disturbances.

5 How to choose between reflective and formative indicators?

The choice between reflective and formative indicators depends on the nature and purpose of the latent variable. Reflective indicators are appropriate when the latent variable is a well-defined construct that can be measured by multiple interchangeable indicators that share a common meaning. Formative indicators are appropriate when the latent variable is a composite construct that is determined by multiple distinct indicators that have different meanings. The choice also has implications for the identification, estimation, and interpretation of the SEM model.

6 How to test and improve your SEM model?

Once you have specified your SEM model with latent variables and measurement errors, you need to test and improve its fit and validity. You can use various criteria and indices to evaluate the overall fit of your model to the data, such as chi-square, RMSEA, CFI, or SRMR. You can also use modification indices, standardized residuals, or factor loadings to identify and modify potential sources of misfit or error. Finally, you can use cross-validation, bootstrapping, or sensitivity analysis to assess the robustness and generalizability of your model.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?