I would like to report results from SEM I did in R using the lavaan package. I have gotten increasingly confused about how papers use different terms and units to describe latent factor relationships seemingly interchangeably.
Here is a picture of one of the models with a number for each relationship I would like to describe. I know they are not all latent, but I want to make sure I understand all concepts properly. The depicted coefficients are all standardized. I know I will need to report their significance levels in the final report.
- 1 with the double-headed arrow is a latent covariance. However, I have read that correlation is standardized covariance, which makes me think that this would have to be reported as correlation with the unit r (e.g., r = .30) because it is standardized. But I have also read that standardized values are reported without unit. Which of the options is correct?
- 2 with the single-headed arrow is a latent correlation and should be reported as r = .86. However, I have seen many papers reporting this as regression instead and call it a beta coefficient (e.g., beta = .86). Is this the same thing?
- 3 and all other coefficients on this level are factor loadings and should be reported as that without a unit (e.g., "the standardized factor loading of mz was .82").
- 4 with the double-headed arrow is a covariance, but on a manifest level. I have the same question about this one as for 1, as this is also a standardized value and I might have to report it as correlation instead.
Can someone help me untangle this theoretical mess?