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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.

enter image description here I think that number...

  • 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?

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1 Answer 1

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  1. Doesn't really matter. A correlation is a covariance. It's more interpretable if you use the correlation. If you want to report the confidence intervan, you should use the covariance though.
  2. It's single headed, it's regression. I don't recall seeign a paper that says that. Your model is drawn strangely - WM is a mediator of the relationship between age and Gf, but that's not clear from the way it's drawn. Typically if it's later in the causal flow it should mov one level.
  3. Yes, but a factor loading is a regression coefficient.
  4. Same answer.

Also, why is age latent?

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  • $\begingroup$ Also, why is age both latent and observed!? $\endgroup$
    – Galen
    Commented Mar 3, 2022 at 17:47
  • $\begingroup$ Thank you so much! Regarding your answer for 2: You don't recall a paper saying it's regression? Or you don't recall a paper using beta coefficients? Here's an example for the latter: doi.org/10.1016/j.intell.2014.05.007 Regarding the latent age variable - yeah, that's wrong and I just changed it. Thanks! I did it because semPaths gave me really messy plots when age was observed, so it's merely a cosmetic thing. Same reason for the not-so-visible mediation. $\endgroup$
    – louise
    Commented Mar 3, 2022 at 18:38
  • $\begingroup$ ...more specifically: Could you clarify if I should report the regression in (2) with r or with betas or if those two measures are the same thing as long as they are standardized and thus I can choose freely? $\endgroup$
    – louise
    Commented Mar 4, 2022 at 8:49
  • $\begingroup$ Sorry, don't recall a paper saying a single headed arrow is a correlation. Generally software that draws a plot for you doesn't do a good job. $\endgroup$ Commented Mar 6, 2022 at 0:19

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