Thanks for the great analysis and information. The concept of dimensionality is really good to me.

I would like to see PCA/FA/SEM with various rotation options in Mathematica. In general, PCA is a first step to understand the latent structure and then we usually apply PCA/Factor analysis (FA) with various rotations (e.g., varimax rotation) to further simplify the latent structure. Then, SEM (structural equation modeling) is applied, which is a confirmatory analysis or a hypothesis testing analysis. PCA/FA starts with data to derive latent structure (exploratory analysis) while SEM starts with a hypothesis on latent structure and validate it with data (confirmatory analysis).

I found a paper on SEM written by Reinhard Oldenburg, using MMA.

• Reinhard Oldenburg, Structural equation modeling: comparing two approaches. The Mathematica Journal Vol. 22. (https://doi.org/10.3888/tmj.22-5),

PLS (partial least square) is a widely used method in chemometrics that is recently expanded to handle the SEM, called PLS-SEM. I use the PLS frequently in automotive and would like to see the PLS in MMA also.

Maybe Anton Antonov or Andrea Lausche could work on these (I watched their video/web pages often)?

Here is PLS written in MMA.

• Patricia Van Roon, Jila Zakizadeh, Sylvain Chartier, Partial least squares tutorial for analyzing neuroimaging data. The Quantitative Methods for Psychology, Vol. 10, No.2., 2014. https://www.tqmp.org/RegularArticles/vol10-2/p200/

Here is Wikipedia sites:

1. Wikipedia on PLS (https://en.wikipedia.org/wiki/Partial_least_squares_path_modeling)
2. Wikipedia on SEM (https://en.wikipedia.org/wiki/Structural_equation_modeling)
3. Wikipedia on FA (https://en.wikipedia.org/wiki/Factor_analysis)
4. Wikipedia on PCA (https://en.wikipedia.org/wiki/Principal_component_analysis)