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I have this dataset with 50 variables for which I assume a latent structure, so I want to run a confirmatory factor analysis. My sample size is 370 but each of the participants was randomly assigned 36 out of the 50 variables. In average there are about 250 respondents for each variable, but it differs a little. Now I am not sure if I can run a factor analysis on my data or not? Should I do imputate the missing data? I would be very grateful for any recommendations what to do. Thanks!

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Provided that you are confident that the data meet the assumption of missing at random (MAR), you can either impute the data or use a full information maximum likelihood estimator (FIML). Most modern structural equation programs have a way of implementing FIML, some have ways for imputing or at least analyzing a series of imputed datasets.

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