I'm a bit lost in what you're doing, and your ultimate goal. Which that in mind, here are some things to consider.
You say have 9 inputs (Xs) and 9 outputs (Ys). You're also changing something for a treatment - is this one of these 18 variable?. I don't understand what're ultimate model will represent - the Xs vs the Ys, or 18 variables versus something else like the treatment?
You can definately use clustering techniques, like K-means, to segment your data (so which rows go together) and build a model from each subset of your data. Typically people don't use the results of the clustering in the actual model if you're segmenting, other than to divide up rows. You can do further dimension reduction on each segment independently - which means you've decided to treat each segments of your data independently.
Using Variable Clustering to identify leading variables for your model is a related, but different way to cluster compared to K-means. So you're doing two different clustering methods and it's not clear how you used them together. You most certainly don't use Variable Clustering on future Y variables. They need to stay out of the analysis until you model. Likewise, if you do K-means with all 18 variables (X's and Ys), split the data in 2 based on this, then run a model on each section, just realize you've biased your outcome because of allowing the relationships between Xs and Ys to be considered before making another model. Cluster on Xs, if you're going to use them in a model, not the Ys.
Overall, when using dimension reduction techniques on a group of variables, if you're going to use these as Xs in a further model, you don't put your future Y variable in there. The point of running a model is to have some Xs explain what is going on for a Y variable(s) of interest. If you PCA or cluster these Xs and Ys together, you're confounding why you'd do a model in the first place.
Here are a few other ideas, depending on your goals.
There is a way to do variable selection with a Y on X's - use Partition, or another tree method like Bootstrap Forest. This would give you the variables that rank highest with respect to a Y, and you can ignore other Xs of small to no effect. Then take these Xs and build a model in Fit Model.
You can also do dimension reduction on some of you variable - like all the body curvature. You'd do PCA, and use the top PCA components in the model (say 9 curvature measurements could be explained in 3 PCA components). Then use the PCA components as Xs in the model. Again don't include the future Ys in the PCA. This is nice cause the PCAs are orthogonal which is an assumption of linear modeling.
If you have JMP Pro, you can use LASSO in GenReg to do both variable reduction and fit a model at the same time. There are limits to how complex this model can be. You can use a tree method first to cut down the number of variables.
Also, because you said you have behavior data, you might consider using GenReg to fit a model because it has some resampling methods for small data sets.
If you're looking at 9Xs and 9Ys, you might want PLS.
Finally, perhaps what you are trying to do is actually a Discriminate Analysis. If you're trying to build a model that describes Treatment with all 18 variables, then Discriminate Analysis is a categorical regression with variable reduction and quite appropriate for this. You can run DA with 2 or 3 treatments and compare the fits to decide if you have 2 or 3 groups.
There are Masting JMP topics on all of the items I've mentioned above.
Have you watched this video on multivariate analysis? There is also a journal that goes with the video.
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