Categorical Variables and SEM

OmegaOkapi125

Hi,

I have 2 questions on using categorical variables with SEM. I am running an SEM analysis, where I would like to model 2 continuous variables while controlling for a categorical variable (in this case, nominal, cohort 1, 2, or 3). How would I control for cohort when running the analysis? 

2nd question: I am trying to run a parallel growth curve model with 3 time points, and predicting high school graduation, a categorical variable with 3 possible values. Is it possible to run SEM with continuous variables to predict a categorical variable at a 4th time point?

Thank you for taking the time to answer my questions!

LauraCS

Hello!

You  have two options for your first question, the first is to do multiple-group analysis (MGA) with cohort as the grouping variable. This option is helpful if you want to examine closely potential group differences across cohorts. Here are some resources to learn more about MGA in SEM:

Blog post: 

https://community.jmp.com/t5/JMP-Blog/Multiple-Group-Analysis-in-Structural-Equation-Modeling/ba-p/604714

Example in JMP Documentation: 

https://www.jmp.com/support/help/en/18.0/index.shtml#page/jmp/example-of-multiple-group-analysis.shtml#ww676033

Video demonstration:

- MGA with regression analysis starts @ minute 13:00 and ends @ 22:20

- MGA with latent growth curves starts @ minute 29:30 and ends @ 39:20

https://community.jmp.com/t5/Discovery-Summit-Europe-2023/Exploring-Group-Differences-and-Other-New-Features-in-Structural/ta-p/572689

Alternatively, if you just want to control for cohort, you can do this by creating dummy coded variables--the same way you would do it in regression analysis (i.e., with three levels, you just need two variables). Then add those variables as predictors in your model.

For your second question, definitely look in the Model Shortcuts menu under "Longitudinal Analysis > Multivariate Latent Growth Curve" --use this prior to entering your categorical variable into the analysis. It'll allow you to understand the growth trajectories before anything else.

The same video link I posted above shows how to fit a parallel process model at minute 39:30.

We're working on handling endogenous categorical variables in a future release of the product, however, that feature isn't available yet. With that said, I'm curious what your 3 levels are for HS graduation? I'd expect 2 levels: yes, no, and perhaps missing values. If so, there are two options for this...

(1) you could add the binary variable (with missing data) into the analysis and specify it as an outcome (perhaps an outcome of intercepts and slopes in your multivariate growth curve?). You can use maximum likelihood as your estimator (the default) and the point estimate will be accurate--however, the standard error for the prediction of the categorical variable won't be. This can be addressed by going to the main red triangle menu and selecting "Inference > Robust Inference." You could also do bootstrap if you prefer.

(2) You could specify your model as described in option 1, but then go to the main red triangle menu to select: "Generate R Code" --this will produce a script that you can tweak to specify the categorical variable as and "ordered" variable and get proper standard errors that way.

Lastly, if you want to explore potential group differences in longitudinal trajectories, you could simply treat high school graduation as a grouping variable and follow the same ideas that are shown in the video link.

HTH,