列之间具有所有成对相互作用的模型矩阵 [英] Model matrix with all pairwise interactions between columns
问题描述
假设我有一个包含w, x, y, z列的数字数据矩阵，并且我还想添加与w*x, w*y, w*z, x*y, x*z, y*z等效的列，因为我希望我的协变量矩阵包括所有成对的交互.
Let's say that I have a numeric data matrix with columns w, x, y, z and I also want to add in the columns that are equivalent to w*x, w*y, w*z, x*y, x*z, y*z since I want my covariate matrix to include all pairwise interactions.
是否有一种干净有效的方法?
Is there a clean and effective way to do this?
推荐答案
如果在模型公式中表示 ，则^运算符会执行此操作.
If you mean in a model formula, then the ^ operator does this.
## dummy data
set.seed(1)
dat <- data.frame(Y = rnorm(10), x = rnorm(10), y = rnorm(10), z = rnorm(10))
公式是
form <- Y ~ (x + y + z)^2
给出
(使用model.matrix()-由标准模型拟合函数在内部使用)
which gives (using model.matrix() - which is used internally by the standard model fitting functions)
model.matrix(form, data = dat)
R> form <- Y ~ (x + y + z)^2
R> form
Y ~ (x + y + z)^2
R> model.matrix(form, data = dat)
(Intercept) x y z x:y x:z y:z
1 1 1.51178 0.91898 1.35868 1.389293 2.054026 1.24860
2 1 0.38984 0.78214 -0.10279 0.304911 -0.040071 -0.08039
3 1 -0.62124 0.07456 0.38767 -0.046323 -0.240837 0.02891
4 1 -2.21470 -1.98935 -0.05381 4.405817 0.119162 0.10704
5 1 1.12493 0.61983 -1.37706 0.697261 -1.549097 -0.85354
6 1 -0.04493 -0.05613 -0.41499 0.002522 0.018647 0.02329
7 1 -0.01619 -0.15580 -0.39429 0.002522 0.006384 0.06143
8 1 0.94384 -1.47075 -0.05931 -1.388149 -0.055982 0.08724
9 1 0.82122 -0.47815 1.10003 -0.392667 0.903364 -0.52598
10 1 0.59390 0.41794 0.76318 0.248216 0.453251 0.31896
attr(,"assign")
[1] 0 1 2 3 4 5 6
如果您不知道自己有多少个变量，或者将所有变量都写出来很麻烦，也可以使用.表示法
If you don't know how many variables you have, or it is tedious to write out all of them, use the . notation too
R> form <- Y ~ .^2
R> model.matrix(form, data = dat)
(Intercept) x y z x:y x:z y:z
1 1 1.51178 0.91898 1.35868 1.389293 2.054026 1.24860
2 1 0.38984 0.78214 -0.10279 0.304911 -0.040071 -0.08039
3 1 -0.62124 0.07456 0.38767 -0.046323 -0.240837 0.02891
4 1 -2.21470 -1.98935 -0.05381 4.405817 0.119162 0.10704
5 1 1.12493 0.61983 -1.37706 0.697261 -1.549097 -0.85354
6 1 -0.04493 -0.05613 -0.41499 0.002522 0.018647 0.02329
7 1 -0.01619 -0.15580 -0.39429 0.002522 0.006384 0.06143
8 1 0.94384 -1.47075 -0.05931 -1.388149 -0.055982 0.08724
9 1 0.82122 -0.47815 1.10003 -0.392667 0.903364 -0.52598
10 1 0.59390 0.41794 0.76318 0.248216 0.453251 0.31896
attr(,"assign")
[1] 0 1 2 3 4 5 6
^运算符(此处为2)中的电源"控制交互的顺序.使用^2，我们得到^运算符考虑的所有变量对的二阶相互作用.如果要进行三阶交互，请使用^3.
The "power" in the ^ operator, here 2, controls the order of interactions. With ^2 we get second order interactions of all pairs of variables considered by the ^ operator. If you want up to 3rd-order interactions, then use ^3.
R> form <- Y ~ .^3
R> head(model.matrix(form, data = dat))
(Intercept) x y z x:y x:z y:z x:y:z
1 1 1.51178 0.91898 1.35868 1.389293 2.05403 1.24860 1.887604
2 1 0.38984 0.78214 -0.10279 0.304911 -0.04007 -0.08039 -0.031341
3 1 -0.62124 0.07456 0.38767 -0.046323 -0.24084 0.02891 -0.017958
4 1 -2.21470 -1.98935 -0.05381 4.405817 0.11916 0.10704 -0.237055
5 1 1.12493 0.61983 -1.37706 0.697261 -1.54910 -0.85354 -0.960170
6 1 -0.04493 -0.05613 -0.41499 0.002522 0.01865 0.02329 -0.001047
这篇关于列之间具有所有成对相互作用的模型矩阵的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！
