For n predictor variables, there are 2n -1 possible combinations. The best combination of variables was selected by comparing all model subsets using AIC with the function stepAIC in R package "MASS", but i don't know how to calculate the Akaike weight for each variable based on all possible combinations of predictor variables
Here you will find R package for creating weights with Akaike information criterion (and a lot more):
http://mumin.r-forge.r-project.org,
Here you'll find a very useful article about it:
https://pdfs.semanticscholar.org/3af6/34a96dfbc2ee7fc7e44b73cf4539e503b2de.pdf
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strictly speaking, akaike weights pertain to models, not to variables
that is, a given combination of your variables leads to one akaike weight ; then model selection is done by retaining the model with the best weight
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now, it has been proposed (Burnham-Anderson) to use akaike weights to derive a "relative variable importance" as follows :
- first, have a balanced set of models (this is your case : all variables appear the same number of times across the set of models)
- second, for a given variable, just sum the akaike weights of the models where this variable is used
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this is well explained here, with more info on interactions
http://stats.stackexchange.com/questions/46289/relative-variable-importance-with-aic
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It takes at least two variables out of which one will be the dependent variable DV and the rest independent variables IV to have a model. AIC applies to models and not variables. If there are n variables there cannot be as many as 2n-1 models. The best model shall have the minimum AIC.
Here you will find R package for creating weights with Akaike information criterion (and a lot more):
http://mumin.r-forge.r-project.org,
Here you'll find a very useful article about it:
https://pdfs.semanticscholar.org/3af6/34a96dfbc2ee7fc7e44b73cf4539e503b2de.pdf
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