Using Structural Equation Models to Uncover Relationships between Observed and Latent Variables

[#1]

Structural Equation Modeling is a multivariate technique to analyze structural relationships and test theories of relationships among observed (manifest) or unobserved (latent) variables.  SEM Combines Factor Analysis and Multiple Regression Analysis.  

New JMP SEM capabilities in JMP Pro 16 include:

• Ability to customize path diagrams using right-click menus
• Available prediction profiler for interacting with a model
• SEM platform now accepts summarized data, such as a correlation matrix
• Ability to build various models and compare them using a model comparison table
• Shortcuts for building commonly used model 

Use the attached video and journal with files and JMP Scripts to explore Path Analysis, Confirmatory Factor Analysis and Regression with Latent Variables.

Q&A from Jian Cao's live webinar April 22, 2021

Q: Does it include prediction equation with all the estimates for a given model?

A:  Yes, all the information for creating the prediction equations are available in the output but they’re presented in a table rather than a prediction equation format.

Q: Does JMP also provide modification indices

A: Yes, you find modification indices under the red triangle menu option.             

Q: Are training, verification and test sets used to build and evaluate the models?            

A: No, this is confirmatory analysis, not predictive.

Q: Can you analyze the residuals?

A: Yes, residuals can be explicitly modeled.

Q: Is there a way to get a rank order of variable importance?

A: There are standardized parameter estimates that can be used as an effect size. Those can be ranked in the output.  

Q: Can the JMP Pro SEM platform assist with Causal Analysis, as with SAS Proc Causalgraph (in particular, the concept of BackDoor Criterion?

A: The platform is comparable to PROC CALIS rather than PROC CAUSALGRAPH.

Q: On the diagram for the web example, what is the difference between Privacy latent (circle shape) vs. Privacy response variable (rectangular shape)?

A: The squares are the variables that we have in the data table.  They are the answers to several questions asked about the perceived privacy of a website. The Circle is an unobserved latent variable that we model by leveraging the information from the observed variables (the squares it points to).   

Q: Are indirect effects available?

A: Total and indirect effects with significance values will be available in 16.1, due to released 3Q.      

Resources

• ABCs of SEM Discovery Europe 2021 presentation and video by Laura Castro-Schilo, JMP and James R. Koepfler, JMP
• Structural Equation Modeling of Coupled Twin-Distillation Columns Discover Europe 2021 presentation and video by Markus Schafheutle, Consultant; Laura Castro-Schilo, JMP; and Christopher Gotwalt, JMP