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I am reading a paper (details not very relevant) which assumes that the market cost $C$ of a trade is related to $N$ predictors $X_1,\dots,X_N$ (page 25) through a linear relationship

$$C = \beta_0 + \beta^TX_{1:N}$$

where the number of predictors $N=30$. The paper makes the following claim (page 29)

We estimate the linear regression model using ordinary least squares. We apply the Akaike criterion to delete any redundant explanatory variables from the regression model.

I am familiar with AIC as a method for model selection, but here there are 30 different variables and $2^{30}$ possible models. How did the authors use the AIC to determine which explanatory variables were 'redundant'?

jII
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    Stepwise selection is a **wrong** thing to do, e.g. http://stats.stackexchange.com/questions/20836/algorithms-for-automatic-model-selection/20856#20856 or http://www.stata.com/support/faqs/statistics/stepwise-regression-problems/ or http://andrewgelman.com/2014/06/02/hate-stepwise-regression/ etc. – Tim Jan 26 '15 at 08:13

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From that methods description (I also looked briefly at the paper) I don't think it is possible to say exactly what they did, so the methods are very poorly written. I could imagine that their "final model" is an AIC- weighed model (maybe using an unknown $\Delta AIC$ cutoff) or it is simply the model that minimize AIC, but maybe you already guessed as much. Either way, it would have been just as easy to say exactly what they did, and to simply state that they deleted "redundant" variables is very unclear. It might be that the "Akaike criterion" is interpreted as something specific within the economics/trade-modelling field (I wouldn't know), but I would then have expected a citation after the statement.

Besides writing the authors of the paper and asking them exactly what they did, I don't think your question can be answered ("How did the authors use the AIC to determine which explanatory variables were 'redundant'?").

fileunderwater
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  • Thank you, I was wondering whether there is some widely used method or heuristic for such situations. – jII Jan 25 '15 at 23:25
  • @jesterII No, I don't think so. People do a number of different things, some more appropriate than others. Besides the things I mentioned, it is also possible that they did some sort of stepwise model selection using AIC as a selection criteria. – fileunderwater Jan 26 '15 at 11:49