Logistic回归:如何尝试R中的每种预测变量组合? [英] Logistic regression: how to try every combination of predictors in R?

问题描述

这是 https://的副本stats.stackexchange.com/questions/293988/logistic-regression-how-to-try-ever-try-every-combination-of-predictors .

我想进行逻辑回归:我有1个因变量和10个预测变量.

I want to perform a logistic regression: I have 1 dependent variable and ~10 predictors.

我想尝试每种组合的详尽搜索，例如更改顺序和添加/删除预测变量等.例如:

I want to perform an exhaustive search trying every combination, such as changing order and adding/deleting predictors, etc. For example:

• y〜x1 + x2 + x3 + x4 + x5

• y ~ x1 + x2 + x3 + x4 + x5

y〜x2 + x1 + x3 + x4 + x5

y ~ x2 + x1 + x3 + x4 + x5

y〜x1 + x2 + x3

y ~ x1 + x2 + x3

y〜x5 + x1 + x2 + x3 + x4

y ~ x5 + x1 + x2 + x3 + x4

y〜x4 + x2

y ~ x4 + x2

...等等.

在这种情况下，计算时间对我而言不是一个停顿的问题:这主要是一项教育活动.

Computational time is not a stopping issue for me in this case: this is mainly an educational exercise.

您知道我该怎么执行吗?我用R.

Do you know how can I perform it? I use R.

要明确:这主要是一项教育性练习:我想测试每个模型，以便可以根据某些索引(例如AUC或伪R²)对它们进行排序向我的"学生"展示哪些预测变量看起来很有趣，但没有科学意义.我计划执行自举重采样，以进一步测试"最可疑的"模型.

To be clear: this is mainly an educational exercise: I want to test every model so I can sort them all according to some indexes (such as AUC or pseudo-R²) in order to show to my "students" which predictors seem interesting but are not scientifically meaningful. I plan to perform bootstrap resampling to test further the "fishiest" models.

推荐答案

我不确定这种教育活动"的价值，但是出于编程的目的，这是我的方法:

I am not sure about the value of this "educational exercise", but for the sake of programming, here would be my approach:

首先，让我们创建一些示例预测变量名称.我在您的示例中使用了5个预测变量，但是对于10个，您显然需要将10替换为5.

First, let's create some example predictor names. I use 5 predictors as in your example, but for 10, you would obviously need to replace 5 with 10.

X = paste0("x",1:5)
X
[1] "x1" "x2" "x3" "x4" "x5"    

现在，我们可以使用combn获得组合.

Now, we can get the combinations with combn.

例如，一次为一个变量:

For instance, for one variable at a time:

 t(combn(X,1))
     [,1]
[1,] "x1"
[2,] "x2"
[3,] "x3"
[4,] "x4"
[5,] "x5"

一次两个变量:

> t(combn(X,2))
      [,1] [,2]
 [1,] "x1" "x2"
 [2,] "x1" "x3"
 [3,] "x1" "x4"
 [4,] "x1" "x5"
 [5,] "x2" "x3"
 [6,] "x2" "x4"
 [7,] "x2" "x5"
 [8,] "x3" "x4"
 [9,] "x3" "x5"
[10,] "x4" "x5"

等

我们可以使用lapply来依次调用这些函数，其中要考虑的变量数量越来越多，并将结果捕获在列表中.例如，看看lapply(1:5, function(n) t(combn(X,n)))的输出.要将这些组合转换为公式，可以使用以下代码:

We can use lapply to call these functions successively with an increasing number of variables to consider, and to catch the results in a list. For instance, have a look at the output of lapply(1:5, function(n) t(combn(X,n))). To turn these combinations into formulas, we can use the following:

out <- unlist(lapply(1:5, function(n) {
  # get combinations
  combinations <- t(combn(X,n))
  # collapse them into usable formulas:
  formulas <- apply(combinations, 1, 
                    function(row) paste0("y ~ ", paste0(row, collapse = "+")))}))

或等效地使用combn的FUN参数(由user20650指出):

Or equivalently using the FUN argument of combn (as pointed out by user20650):

out <- unlist(lapply(1:5, function(n) combn(X, n, FUN=function(row) paste0("y ~ ", paste0(row, collapse = "+")))))

这给出了:

out
 [1] "y ~ x1"             "y ~ x2"             "y ~ x3"             "y ~ x4"             "y ~ x5"            
 [6] "y ~ x1+x2"          "y ~ x1+x3"          "y ~ x1+x4"          "y ~ x1+x5"          "y ~ x2+x3"         
[11] "y ~ x2+x4"          "y ~ x2+x5"          "y ~ x3+x4"          "y ~ x3+x5"          "y ~ x4+x5"         
[16] "y ~ x1+x2+x3"       "y ~ x1+x2+x4"       "y ~ x1+x2+x5"       "y ~ x1+x3+x4"       "y ~ x1+x3+x5"      
[21] "y ~ x1+x4+x5"       "y ~ x2+x3+x4"       "y ~ x2+x3+x5"       "y ~ x2+x4+x5"       "y ~ x3+x4+x5"      
[26] "y ~ x1+x2+x3+x4"    "y ~ x1+x2+x3+x5"    "y ~ x1+x2+x4+x5"    "y ~ x1+x3+x4+x5"    "y ~ x2+x3+x4+x5"   
[31] "y ~ x1+x2+x3+x4+x5"

现在可以将其传递给您的逻辑回归函数.

This can now be passed to your logistic regression function.

示例:

让我们使用mtcars数据集，并将mpg作为因变量.

Let's use the mtcars dataset, with mpg as dependent variable.

X = names(mtcars[,-1])
X
 [1] "cyl"  "disp" "hp"   "drat" "wt"   "qsec" "vs"   "am"   "gear" "carb"

现在，让我们使用上述功能:

Now, let's use the aforementioned function:

out <- unlist(lapply(1:length(X), function(n) combn(X, n, FUN=function(row) paste0("mpg ~ ", paste0(row, collapse = "+")))))

为我们提供了所有组合的向量作为公式.

which gives us a vector of all combinations as formulas.

要运行相应的模型，我们可以做个例子

To run the corresponding models, we can do for instance

mods = lapply(out, function(frml) lm(frml, data=mtcars))

由于您要捕获特定的统计信息并相应地对模型进行排序，因此我将使用broom::glance. broom::tidy将lm输出转换为数据帧(如果您想比较系数等，则很有用)，而broom::glance将例如将r平方，sigma，F统计量，logLikelihood，AIC，BIC等转换为数据框.例如:

Since you want to capture specific statistics and order the models accordingly, I would use broom::glance. broom::tidy turns lm output into a dataframe (useful if you want to compare coefficients etc) and broom::glance turns e.g. r-squared, sigma, the F-statistic, the logLikelihood, AIC, BIC etc into a dataframe. For instance:

library(broom)
library(dplyr)
tmp = bind_rows(lapply(out, function(frml) {
  a = glance(lm(frml, data=mtcars))
  a$frml = frml
  return(a)
}))

head(tmp)
  r.squared adj.r.squared    sigma statistic      p.value df    logLik      AIC      BIC deviance df.residual       frml
1 0.7261800     0.7170527 3.205902 79.561028 6.112687e-10  2 -81.65321 169.3064 173.7036 308.3342          30  mpg ~ cyl
2 0.7183433     0.7089548 3.251454 76.512660 9.380327e-10  2 -82.10469 170.2094 174.6066 317.1587          30 mpg ~ disp
3 0.6024373     0.5891853 3.862962 45.459803 1.787835e-07  2 -87.61931 181.2386 185.6358 447.6743          30   mpg ~ hp
4 0.4639952     0.4461283 4.485409 25.969645 1.776240e-05  2 -92.39996 190.7999 195.1971 603.5667          30 mpg ~ drat
5 0.7528328     0.7445939 3.045882 91.375325 1.293959e-10  2 -80.01471 166.0294 170.4266 278.3219          30   mpg ~ wt
6 0.1752963     0.1478062 5.563738  6.376702 1.708199e-02  2 -99.29406 204.5881 208.9853 928.6553          30 mpg ~ qsec

，您可以根据需要对其进行排序.

which you can sort as you wish.

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