I'm looking for a simple concrete example of Confirmatory Factor Analysis. What are the precise steps?

What I (think) understand so far:

  1. Get data (random sample).

  2. Bring in a theory along the line of

    This unobserved variable $\eta_1$ is correlated to the observed variables $x,y,z$ and not to $v, w$, $\eta_1$ is correlated to $v, w, z$ (and not $x,y$).

The unobserved variables are chosen because theory predicts they cause the others and are called latent or underlying factors.

  1. Compute the covariance matrix of $x,y,z,v,w$.

  2. Fit a linear models... (but the $\eta$'s are the dependent variable (but still unbserved) so how can we know the coefficients on the observed variables (which are called loadings $\lambda$)?)

  3. Compute (how?) the implied covariance matrix and compare to the actual covariance matrix use some kind of a statistic to estimate how likely the observed difference between that matrices is due to random chance.



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