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An instrument used to collect a sample from a population. Surveying often refers to sampling of human populations and is primarily done by administering questionnaires or interviewing individuals.

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Is this a valid factor analysis approach for validating a multi-domain survey?

I would not consider this a valid approach. I would recommend reading Boateng et al. (selected because it is publicly available, not because it is necessarily a seminal work) and some introductory ps …
Lyndon Walker's user avatar
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Rules for number of predictor variables in complex survey data

calculation of required sample sizes for complex surveys is a good few chapters of a book so I won't try to recreate it here other than to say that you are indeed correct that you need to include your survey … I would suggest taking a look at Holtman et al. and then finding a good survey analysis book that is used in 3rd year or postgrad statistics subjects like Complex Surveys by Lumley. …
Lyndon Walker's user avatar