factor that loads on other factors

[Anonymous]

Is there a way to define a factor not by observed variables, but by other factors?

[Paras Mehta]

Yes, it is possible. The matrix to use would be a beta matrix. If a latent factor V is defined by other latent variables U_1 to U_p, a (p by 1) beta matrix with one of the paths fixed to 1.0 will do the trick.

Simplest case is the ‘hierarchical random-intercept’:
http://xxm.times.uh.edu/learn-xxm/three-level-hierarchical-model-with-observed-and-latent-variables-at-multiple-levels/

Here is an example of random-slopes for a latent DV.
http://xxm.times.uh.edu/learn-xxm/two-level-confirmatory-factor-analysis-with-a-random-slope/

In each case, a factor is defined by other latent factors.

Best,

Paras

[Anonymous]

Thank you very much for answering so quickly!

I am aware of these examples. Now I have realised that I have to fill in zeros in the columns of the factor-loading matrix for such cases.

Thank you again for your great work!

Best,
Andrea

[Author]

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