# connection between standardized values in SEM output

I'm sorry if this seems a basic question. Can someone please tell me (once and for all) how standardized estimates in a SEM model are mathematically related? I don't understand how these values are logically linked together.
Edit: Considering the model below (from Khosravi, 2014): 1. are errors calculated based on loadings? how? what about error correlations?
2. does changing the path SCFs-IFs to IFs-SCFs change path coefficient (0.71)? does it change other estimates (like SCFs-WCFs coefficient)?
3. what did we standardize here, variances/residual variances or sth else?
4. why often direct path coefficient isn't the product of indirect coefficients (like original structural model of the article)?
Thanks very much in advance.

• does the distribution of indicators (Mean/SD for example) matter? – sar.ali May 12 '16 at 15:03
• Even if F2 and F3 have indicators, I don't think that the model is identified. I don't see how F1 is identified with two correlated indicators. – Jeremy Miles May 12 '16 at 16:08
• If a = b * c, that's a coincidence, there is no need for that to be the case. – Jeremy Miles May 12 '16 at 16:08
• @JeremyMiles I edited my question :) – sar.ali May 12 '16 at 21:43

## 1 Answer

1. This appears to be a standardized solution. Given no other constraints, for each variable the error = 1 - loading^2. So look at SCF1. 0.84^2 + 0.27 = 1 (within rounding error).
2. Yes. Removing one parameter in the model and replacing it with another like that can change every other parameter estimate in the model. It might not, but it can.
3. Not sure I understand that one. We standardize everything based on the variance.

4. There is no reason that the direct and indirect effects should be equal, similar or even in the same direction (one can be positive, one can be negative).