I am trying to understand the way ICA is used as factor rotation in the traditional orthogonal factor model. The idea of using ICA as a specific factor rotation is often mentioned in the literature (ex. Independent component analysis by Hyvärinen, Karjunen, Oja), but it is not really explained.

I found this one paper "The independent factor analysis approach to latent variable modeling" by Montanari and Viroli, and based on it my understanding is as follows:

Assume an orthogonal factor model $X = L F + \epsilon$, with the usual assumptions.

First, we estimate the loadings $L_r$ and factors (scores) $F_r$ up to a rotation, for example by using PCA and least squares.

After this, we consider the ICA model according to which $F_r = AF$, where the factor $F$ represents the independent sources. Now by estimating the above ICA model we get the "independent factors" as $F = A^{-1}F_r$.

Now my question has two parts: (1) How do I obtain from this the actual loadings $L$ of the factor model? (2) Is my overall understanding of the process correct? And generally, if there is something that I have misunderstood, or if you know there is a better approach to this problem please let me know.

Thanks for the help, really appreciate it :)


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