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I am new to the topic of SEM, so my question may seem a bit naive.

I have about 60 observed variables that will be grouped in some latent variables to explain one outcome measure. One of the variables contains missing data. If I impute these data, the new data will be based on the already existing data (as I could understand some (if not all the 59 remaining) variables will go into the regression analysis to replace the missing data, right? But how come that the SEM is then not biased by the fact that it's being looking for a correlation between variables, one of which is partly a result of a correlation between the same variables?

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Your question seems to deal more with missingness than with the specific case of SEM.

Regarding imputation, it depends on the specific imputation method you want to use, for instance, Full Conditional Specification (aka Multiple Imputation with Chained Equations) will indeed use all the information available for each variable, including the iterative use of the imputed data points for each regression model.

With regards to the second question, you are right in that there is a weird feeling of self-fulfilled prophecy in testing in your analysis model what you already defined in your imputation model. Nonetheless, the alternative of imposing independence where there is not has been shown in simulations to actually bias results (see Outcome-sensitive multiple imputation: a simulation study and Using the outcome for imputation of missing predictor values was preferred, for example).

On a further note, the issue of biasedness depends on a more fundamental level in the assumptions you have regarding your missing mechanism (MCAR, MAR, MNAR), i.e. the degree to which your observed variables are supposed to have information about your missing values, but there is already enough content and resources regarding these topics elsewhere.

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  • $\begingroup$ You are welcome, in the case you consider your question answered, please accept the answer (with the green checkmark) as to mark the question as solved. $\endgroup$
    – Kuku
    Sep 2 '20 at 9:42
  • $\begingroup$ Thank you very much for your comment! The second paper you cited is exactly what I've been looking for. May I ask you a follow-up question? In your opinion, would the FIML approach deal better with the "self-fulfilled prophecy" issue? $\endgroup$
    – Aldebaran
    Sep 2 '20 at 9:46
  • $\begingroup$ I am afraid your follow-up question depends on a lot more information about your specific dataset and problem at hand, hence deserving its own thread. At the same time, I will most likely not be the best person to answer it. $\endgroup$
    – Kuku
    Sep 7 '20 at 16:44

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