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I have some questions on the information theoretic approach to linear modelling:

  1. Why not just use residuals instead of likelihood?

  2. Can same variables with different subsets of data be used to build a 'best model'?

  3. Can same variables with different error distributions (for example poisson, negative binomial) be used to build a 'best model'?

  4. Can same variables with different transformations (for example square root, log) be used to build a 'best model'?

  5. Can interactions be included in candidate models that aren't included in global model?

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    $\begingroup$ For 1. -- in what way? The residuals are effectively already in the sample likelihood. $\endgroup$ – Glen_b May 2 '14 at 8:04
  • $\begingroup$ As in why bring the check concept of likelihood. Why not used sum of squared residuals or r-squared? $\endgroup$ – luciano May 2 '14 at 8:11
  • $\begingroup$ If you've so many questions I'd suggest reading a book explaining the principles, perhaps Burnham & Anderson (2002), Model Selection and Multimodel Inference, & seeing how many remain: a list of things you can & can't do could go on forever. In any case I think you'll already find answers here by searching for questions with the AIC tag. $\endgroup$ – Scortchi May 2 '14 at 12:14

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