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Note: This is a revision of my original question.

I have read the critique of stepwise variable selection and "all possible subsets regression" by Professor Frank Harrell here.

Are factor analysis, principal component analysis, structural equation modelling selection and loading of variables more reliable than selection of best model from a set of dependent and independent variables by stepwise methods or "all possible subsets regression"? or they have similar problems.

Let's assume we have developed the following two models. (x5 is not correlated with y1).

M1 is the result of All possible subsets To get M2 we do PCA and we choose the first 2 components and then we use those components in a two var regression.
I would like to interpret C1 and c2 and the two components that summarize the measured IVs and benefit from the reduction as the result.

  1. Will I overcome the problems of "all possible subsets regression"?
  2. Which one will have a better predictive validity?
  3. What are the comparative strength and weaknesses of the two models?

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  • $\begingroup$ Welcome to Cross Validated! It's not quite clear exactly what procedure you're describing by "FA, PCA, SEM selection and loading of variables": using principal components analysis, say, to guide selection of predictors as in Using principal component analysis (PCA) for feature selection or How to use principal components analysis to select variables for regression?; or perhaps data reduction by using the first few principal ... $\endgroup$ – Scortchi - Reinstate Monica Aug 24 '16 at 9:52
  • $\begingroup$ ... components, say, as in How can top principal components retain the predictive power on a dependent variable?. Could you edit the question to clarify? $\endgroup$ – Scortchi - Reinstate Monica Aug 24 '16 at 9:53
  • $\begingroup$ FA and PCA have very different goals than regression and they both use all the variables and don't involve variable selection. So, like @Scortchi I am confused. $\endgroup$ – Peter Flom - Reinstate Monica Aug 24 '16 at 10:41
  • $\begingroup$ Thank you for your prompt replies. Scortchi: I have been benefiting from the wonderful knowledge sharing here for a while. It is just the first time I had to ask a question instead of reading. Which led to more reading and thinking :) suggested by you. I will edit the question after carefully reading your links and thinking about Peter's point. $\endgroup$ – Amir Aug 24 '16 at 16:27
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    $\begingroup$ I'm not a SEM expert but as I understand them, it takes a lot of thinking and justification to use them in a principled way. I can't immediately think of another technique that is less compatible with automated methods of adjustment/selection than SEMs. $\endgroup$ – Wayne Aug 25 '16 at 13:27

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