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## An Introduction to Structural Equations Models in JMP(R) Pro 15 (2020-EU-45MP-423)

Level: Beginner

Laura Castro-Schilo, JMP Research Statistician Developer, SAS

Abstract:

Structural Equations Models (SEM) is a new platform in JMP Pro 15 that offers numerous modeling tools. Confirmatory factor analysis, path analysis, measurement error models and latent growth curve models are just some of the possibilities. In this presentation, we provide a general introduction to SEM by describing what it is, the unique features it offers to analysts and researchers, how it is implemented in JMP Pro 15 and how it is applied in a variety of fields, including market and consumer research, engineering, education, health and others. We use an empirical example – that everyone can relate to – to show how the SEM platform is used to explore relations across variables and test competing theories.

Summary:

The video below shows how to fit models consistent with each of the "Emotion Theories" in the presentation. Together with the attached slides, users can be guided on how to use the SEM platform. Here are the takeaway points:

1. We have 3 a-priori theories of how our variables relate to each other
2. We fit models in SEM that map onto each of the theories
3. We look for the most appropriate model by:
1. Examining individual model fit. In this example we used the chi-square, a measure of misfit --we want it to be small with respect to the degrees of freedom (df) and non-significant, but the CFI and RMSEA can be used too and are better with large sample sizes. We also used the normalized residuals heatmap; we want those residuals within +/- 2 units.
2. Comparing fit across models. The AICc weights help us with this task. When the models are nested (i.e., one is entirely contained within the other --in our example, the model for Theory #1 is nested within that for Theory #2), we can take the difference between the chi-squares and the df to obtain a delta-chi-square and delta-df that can be tested for significance with a chi-square distribution.

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