I have a question: is the final model of backward elimination with AIC ​always​ the same as the final model of forward elimination with AIC? I assume that it is the same result

  • $\begingroup$ Your assumption reminds me of the proverbial frog in the gradually heated frying pan, who never leaps out because the incremental changes are never relatively so bad as to provoke a jump. The same frog, if introduced into an initially hot pan, would leap out immediately. $\endgroup$
    – whuber
    Oct 29, 2019 at 19:16

1 Answer 1



The simplest way to investigate such a question is to simulate. Here is R code with 100 observations and 20 predictors, and we compare forward and backward stepwise model building:


dataset <- as.data.frame(matrix(rnorm(2100),nrow=100,dimnames=list(NULL,c("y",LETTERS[1:20]))))


The first one stays with the intercept-only model, and the second one picks a model with two predictors labeled P and S. So the results are different.

In any case, be very careful with stepwise model selection, whether based on p values or on AIC. The result can be useful for prediction, but any NHST inference on the selected model is invalid.


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