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I wanted to reduce a large number of items down to a smaller number (e.g. 140 items to 40), and then show that these 40 items can accurately predict two related variables.

I have attempted CFA however this has revealed a very large number of factors (20+). I was wondering what statistical technique would be the best to achieve this? Is it possible to complete regressions but setting the number of items in the final model (rather than basing it upon a given significance level)?

user29898
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    What is CFA? De-abbreviate please. – ttnphns Feb 05 '14 at 04:51
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    @ttnphns: I assume it is confirmatory factor analysis. But I may be wrong. – nico Feb 05 '14 at 06:54
  • Could you expand a little bit? What are your items? A series of observations of multiple predictors? How do you use them for prediction? Reading your question I think *bootsrap*... but the problem is not completely clear to me. Maybe a little example even with some mock data would help clarifying the issue. – nico Feb 05 '14 at 06:57
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    I ment confirmatory factor analysis. The items are supposed to all be focusing upon the one latent construct, there are only single observations (each item is a likert scale) and I have been using the mean of the items in regression analysis (to predict related constructs). – user29898 Feb 05 '14 at 09:15
  • I don't understand how CFA could reveal the number of factors; generally, the analyst specifies the factors of the model to be confirmed, as well as their indicators. I'm also unclear on what significance levels you'd be using to set the number of items in the final model. Anyway, you may want to check out these related questions: (1) [Factor analysis of questionnaires composed of Likert items](http://stats.stackexchange.com/q/2374/32036) and (2) [Regression testing after dimension reduction](http://stats.stackexchange.com/q/83512/32036). – Nick Stauner Feb 06 '14 at 02:00

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