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## ABCs of Structural Equations Models (2020-US-45MP-590)

Level: Intermediate

Laura Castro-Schilo, JMP Research Statistician Developer, SAS Institute, JMP Division
James Koepfler, Research Statistician Tester, SAS Institute, JMP Division

This presentation provides a detailed introduction to Structural Equation Modeling (SEM) by covering key foundational concepts that enable analysts, from all backgrounds, to use this statistical technique. We start with comparisons to regression analysis to facilitate understanding of the SEM framework. We show how to leverage observed variables to estimate latent variables, account for measurement error, improve future measurement and improve estimates of linear models. Moreover, we emphasize key questions analysts’ can tackle with SEM and show how to answer those questions with examples using real data. Attendees will learn how to perform path analysis and confirmatory factor analysis, assess model fit, compare alternative models and interpret all the results provided in the SEM platform of JMP Pro.

### PRESENTATION MATERIALS

The slides and supplemental materials from this presentation are available for download here.

Check out the list of resources at the end of this blog post to learn more about SEM.

The article and data used for the examples of this presentation are available in this link.

Auto-generated transcript...

Hi,

This webinar is super pertinent and complete. But, I still have a question about how to create a factor regrouping variables (questions)? Like Dr. Laura Castro-Schilo did with her to factors.

Nataly

Glad to know you enjoyed the webinar!

The first step for creating a measurement scale, after you've collected your data, is to do an exploratory factor analysis. You can do this in JMP by going to Analysis > Multivariate Methods > Factor Analysis, selecting all your measured variables and launching the platform. The platform allows you to explore the adequate number of factors (i.e., latent variables) to extract --once you've found a good factor solution (e.g., you've accounted for a good amount of variance in the data, you have factors with a combination of strong and weak standardized factor loadings --known as simple structure,-- acceptable fit, etc), you should use an independent dataset to fit a confirmatory factor analysis in SEM that helps you validate the factorial structure (the pattern of standardized factor loadings). You can find more info on exploratory factor analysis in our documentation:

In sum, the standardized factor loadings of an exploratory factor analysis help you identify which variables group to define the latent variable in SEM. Theory and domain expertise should also guide this process, as you probably have an expectation of which variables are hypothesized to be caused by the same unobserved (latent) variable.

HTH,

~Laura

Thank you Dr Castro-Schilo,

But, I still have a question on how to create a factor (variable) grouping the elements of one dimension (questions) into one column and then test the effect of the dimension on the others. It's like when you go to see the fit measurements -> Composite reliability / construct.

For example, I have 3 dimensions:

- Cognitive: 2 sub-dimensions (13 items)

- Affective: 1 sub-dimension (6 items)

- Behavior: 3 sub-dimension (14 items)

How do I create a new variable comprising the 2 cognitive sub-dimensions, another with the 6 of the affective dimension and the 14 that make up the behavior dimension? In your tutorial, you mention having done it and I see the variable with a « star » after its names. If you watch your video at 34 minutes 40 seconds, you will find what I means. I hope I am clear ...

Thank you very much for your collaboration!

Nataly

Dear Dr. Castro-Schilo,

I forgot to mentioned that I have already done my exploratory factor analysis which allowed me to reduce from 100 questions to 33. Now, I want to do confirmatory factor analysis and SEM including patch analysis, convergent, discriminant and nomological validity.

So, how do we create a model like this in the SEM of JMP Pro? See the photo attached (Sorry for the quality of my drawing).

Thank you so much for your help.

Nataly

Hi

That's a great diagram! =)

Composite variables, as those I show in the video at minute 34 with 40 seconds, are just averages across the variables that load onto a latent variable. JMP makes it easy to create these averages by selecting the columns in the data table, right-clicking and finding the New Formula Column > Combine > Average option:

Once you have the composite variables, you can use those to create latent variables as described in the video in minute 22 with 19 seconds. However, you might want to use your original variables and specify a "higher order confirmatory factor model" by first using the original questions to create your sub-dimensions and then selecting those latent variables to create an overall latent variable that represents your higher-order construct:

Moreover, the statistics from "Assess Measurement Model" can be computed from the current JMP 15.2 output (the option will be available in the upcoming JMP Pro v16.0). Here's a brief description to help you obtain a few of those statistics:

Indicator Reliability: these are squared standardized loadings. You can obtain the values by selecting "Standardized Parameter Estimates" from the RTM. Then, hover over the stdz loadings, right-click on the table, and select "Make into Data Table." In the new data table, right-click over "Estimate" and select New Formula Column > Transform > Square. The new column has the indicator reliabilities, which you can take to  graph builder to make an Estimate^2 by Loading barplot.

Construct Validity Matrix: has standardized covariances (correlations) among latent variables in the lower triangular, which will be displayed when you get the table of standardized estimates. The upper triangular has squared correlations among latent variables, so simply square the correlation values. Lastly, the diagonal has the average variance extracted by each latent variable; you can obtain these values by averaging the squared stdz loadings for each latent variable. In the data table that has the Estimate^2, select the "Loadings" column, right-click on it, and go to New Formula Column > Character > First Word. Then go to the Tables menu and select Summary. Place "First[Loadings]" under "Group" and get "Mean(Estimate^2)" under "Statistics." After clicking OK, you'll see a new data table with the average variance extracted by each latent variable.

Exploring reliability and validity takes a bit longer in version 15.2, but I certainly hope you upgrade to v16 this March so you can take advantage of these and other great new features!

Best,

~Laura

Thank you very much: it's clear and answering all my questions.

Best regards!

Nataly :)

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