Papers on the risks of using regular subsets I'm working on my Masters thesis and am using exhaustive search (also called regular subsets) for linear models.  There was an answer on CrossValidated, I believe by whuber, which talked about the risks of using regular subsets and had a link back to a page with several papers discussing this risk.  Unfortunately, I have been searching for this post and I can't find it.
If anyone could point me toward this post, or papers on the limitations/risks/problems with using exhaustive search for linear models, I would be very grateful.
 A: Found a few papers:
Mendenhall, W. (2003). A Second Course in Statistics: Regression Analysis 6th (sixth) edition.


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*Forward-Selection (FS), Backward-Elimination (BE), and Exhaustive Search (ES) are all meant to be Variable Screening methods - i.e. only the first step in the model building process

*Using these techniques one is more likely to either include variables that are unimportant (Type I Error) or exclude variables that are important (Type II Error)

*If you don't include higher order or interaction variables in the search, the final model will be a first-order, main effects model, which excludes non-linear affects and thus may not be realistic.

*Even if you do include higher order and interaction variables in your search, the results can be nonsensical - for example including an interaction term while excluding the main effect or including a higher order term while excluding the first-order term.
Hocking, R. R. (1976). A Biometrics Invited Paper. The Analysis and Selection of Variables in Linear Regression. Biometrics, 32(1), 1. doi:10.2307/2529336


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*Using these techniques the best subsets can be missed


Gorman, J. W., & Toman, R. J. (1966). Selection of Variables for Fitting Equations to Data. Technometrics, 8(1), 27. doi:10.2307/1266260


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*There are probably several equally good subsets

*The "best" subset should provide insight to the data


Miller, A. J. (1984). Selection of Subsets of Regression Variables. Journal of the Royal Statistical Society. Series A (General), 147(3), 389. doi:10.2307/2981576


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*The simple process of starting with highly correlated variables, examining scatterplots, adding higher order terms, transforming, and removing outliers as necessary is an extension of FS but it can "provide some protection against the selection of what might be considered stupid models".

