How can I do a permutation F test for testing if a larger model which contains a larger model is better? e.g.
Model 1 :
y ~ x1 + x2
Model 2 :
y ~ x1 + x2 + x3 + x4
H0 : $\beta_3 = \beta_4 = 0$ H1 : At least one of $\beta_3$ and $\beta_4$ is non-zero
I am guessing one way is to permute both columns
x4 independently and then compute the F statistic which gives the distribution of this statistic under the null hypothesis. But is this correct? I came across the package lmPerm in R which lets you do permutation tests for linear models. I would like to know how it does it.