The Indeterminacy of the Latent Factor Score

In a common factor model, you are not hypothesising the existence of this latent variable that gives rise to patterns of correlations in your data. You do get a closed form expression of the score on the component. It is calculated as a direct function of your weights and your items. They get lumped together so often, and i don't think it's that agreed s for the following reason. When you have a really strong underlying latent variable that induces a very high degree of correlation among a set of items,  it's very easy to build one very strong component out of them. So what's going on at the underlying latent level and what you can do at a composite level often map