SEM with data missing by design: Is MI and/or test equating appropriate? I have access to a dataset with approximately 50,000 participants and that includes a large selection of self-report scales; I planned to analyze correlations between several scales with Structural Equation Modeling. I did not realize before hand that data was missing by design, that participants responded to a subset of items from different scales, but that no participants completed a scale in its entirety. In other words, I cannot analyze the correlations as is since every scale score is missing.
I read an earlier thread (Survey analysis with missing data by design) which suggested reading Pokropek (2011) as well as looking into test equating. From Pokropek I gathered that multiple imputation could be appropriate, particularly if the data is MCAR. However, I have not been able to find anything on the use of test equating in SEM.
My questions are:
(1) is multiple imputation appropriate given this type of missing data by design?
(2) is test equating appropriate with SEM and, if so, are there any resources on this?
Any help would be extremely appreciated
Pokropek, A. (2011). Missing by design: Planned missing-data designs in social science. ASK. Research & Methods, 20, 81-105.

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*Yes. Or Full Information Maximum Likelihood.


*Yes. This is commonly used in integrative data analysis. Volume 14 of Psychological Methods was a special issue on this: https://psycnet.apa.org/PsycARTICLES/journal/met/14/2
