R help - Jul 2024 - Difference between stats.steps() and MuMIn.dredge() to select best fit model

Hello,

I try to understand the different approaches how to select the best fit 
regression model.
This is not about AIC, BIC, etc. It is about the difference between the 
steps() function
(in stats package) and the dredge() function (in MuMIn) package.
I see several examples on the internet.

step() explore the model space with a step wise approach.
And dredge() try out all possible combinations of the variables.

But isn't that the same? I might have a mental block on this.

Which model (formula) would dredge() "test" that step() wouldn't?`

Thanks in advance,
Christian

? Wed, 31 Jul 2024 11:56:55 +0000
c.buhtz at posteo.jp ?????:
> step() explore the model space with a step wise approach.
> And dredge() try out all possible combinations of the variables.
>
> But isn't that the same? I might have a mental block on this.
> 
> Which model (formula) would dredge() "test" that step()
wouldn't?`
Suppose that the predictors a, b, c, d, e, f are arranged in the
descending order of contribution to the model.

Consider a forward stepwise algorithm that is asked to choose three
variables.

It starts by testing a, b, c, d, e, f, and chooses a.

It continues by testing a + b, a + c, a + d, a + e, a + f, and chooses
a + b.

It continues by testing a + b + c, a + b + d, a + b + e, a + b + f, and
chooses a + b + c.

By being greedy, it doesn't consider, for example, the model d + e + f,
because for that it would have to pick d before a.

A greedy algorithm for K variables out N tests N + (N-1) + ... +
(N-K+1) = N*K - K(K-1)/2 models. An exhaustive search would have to test
choose(N,K) = N!/(N-K)!/K! models.

-- 
Best regards,
Ivan