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If I have run a Confirmatory Factor Analysis and have all of the standardized loadings of each item onto its respective variable, how would I calculate the R-squared for each item? Is it simply the standardized coefficient squared, or something else?

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If each measured variable has only one loading on it, it's the square of the standardized loading.

If a measured variable has two loadings, and the latent variables are not correlated, then $R^2$ is the sum of the squared loadings.

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